This paper explores the application of wavelets to a variety of real-life problems and more specifically to image processing problems. A general review of the construction and analysis of wavelet analysis will be presented. The issues like multiresolution analysis in the context of sensor integration and pattern recognition and other salient features of the images using wavelets will be discussed in detail.

Recently, a new image compression algorithm was developed which employs wavelet transform and a simple binary linear quantization scheme with an embedded coding technique to perform data compaction. This new family of coder, Embedded Zerotree Wavelet (EZW), provides a better compression performance than the current JPEG coding standard for low bit rates. Since EZW coding algorithm emerged, all of the published coding results related to this coding technique are on monochrome images. In this paper the author has enhanced the original coding algorithm to yield a better compression ratio, and has extended the wavelet-based zerotree coding to color images. Color imagery is often represented by several components, such as RGB, in which each component is generally processed separately. With color coding, each component could be compressed individually in the same manner as a monochrome image, therefore requiring a threefold increase in processing time. Most image coding standards employ de-correlated components, such as YIQ or Y, C_B, C_R and subsampling of the 'chroma' components, such coding technique is employed here. Results of the coding, including reconstructed images and coding performance, will be presented.

Registration is the process of mapping one image onto another image. This is done quite often in the area of Medical Imaging for clinical as well as diagnostic reasons. Registration of images is useful from a medical perspective to detect growth of tumors, locate tumors with respect to bone structure, determine how well a bone graft is taking. Registration is also the first step in object recognition algorithms and has applications in the areas of aerial surveillance, automatic target recognition, etc.

An image model based on Hermite spline multiresolution analysis ins considered. To compute image representations, the algorithm of fast biorthogonal multiwavelet transform is used. The transform depends on the choice of multi-scaling functions biorthogonal to Hermite splines. An algorithm for the construction of such functions is given and examples for cubic Hermite splines are shown.

Modern image and signal processing methods strive to maximize signal to nose ratios, even in the presence of severe noise. Frequently, real world data is degraded by under sampling of intrinsic periodicities, or by sampling with unevenly spaced intervals. This results in dropout or missing data, and such data sets are particularly difficult to process using conventional image processing methods. In many cases, one must still extract as much information as possible from a given data set, although available data may be sparse or noisy. In such cases, we suggest algorithms based on wavelet transform and fractal theory will offer a viable alternative as some early work in the area has indicated. An architecture of a software system is suggested to implement an improved scheme for the analysis, representation, and processing of images. The scheme is based on considering the segments of images as wavelets and fractals so that small details in the images can be exploited and the data can be compressed. The objective is to improve this scheme automatically and rapidly decompose a 2D image into a combination of elemental images so that an array of processing methods can be applied. Thus, the scheme offers potential utility for analysis of image could be the patterns that the system is required to recognize, so that the scheme offers potential utility for industrial and military applications involving robot vision and/or automatic recognition of targets.

We used a higher-order correlation-based method for signal denoising. In our approach, we applied a third-order correlation technique for identification of wavelet coefficients uncorrupted by noise by considering triple correlation coefficients of wavelet-signal correlations for thresholding. Because the higher second-order moments of the Gaussian probability function are zero, the third-order correlation coefficient will not have statistical contribution from Gaussian noise under certain conditions. Therefore, in our approach, we examined correlation coefficients in an environment where the noise had been reduced. Our results compared favorably and was less sensitive to threshold selection when compared to a more common denoising method.

An important class of nonparametric signal processing methods is to form a set of predictors from an overcomplete set of basis functions associated with a fast transform. In these methods, the number of basis functions can far exceed the number of samples values in the signal, leading to an ill-posed prediction problem. The 'basis pursuit' denoising method of Chen, Donoho, and Saunders regularizes the prediction problem by adding an L₁ penalty term on the coefficients for the basis functions. Use of an L₁ penalty instead of L₂ has significant benefits, including higher resolution of signals close in time/frequency and a more parsimonious representation. The L₁ penalty, however, poses a challenging optimization problem that was solved by Chen, Donoho and Saunders using a novel application of interior point methods. In this paper, we investigate an alternative optimization approach based on 'block coordinate relaxation' (BCR) techniques. We show that BCR is globally convergent, and empirically, BCR is faster than interior point methods for a variety of signal de- noising problems.

The effects of noise modulation on the power spectral density functions of a sinusoidal wave are calculated in closed form. Frequency, phase, and amplitude modulation are considered. Noise processes are modeled using Butterworth filters of various integer orders. Both stationary and nonstationary noise processes are included with Daubechies wavelet filters used for the nonsteady case.

This paper presents new vector filter banks, in particular biorthogonal Hermite cubic multiwavelets with short, smooth duals. We study different preprocessing techniques and the covariance structure of corresponding transforms. Results of numerical experiments in signal denoising and image compression using multi-filters are discussed.We compare the performance of several multi-filters with the performance of standard scalar wavelets such as Daubechies orthogonal external phase and least asymmetric ones and biorthogonal 9- 7 pair. Often multiwavelet scheme turn out to be better. We analyze these results.

The scaling function for the Super Haar wavelet is a linear combination of shifts in the Haar scaling function; the coefficients of this linear combination are assumed to be integers. If the scaling function satisfies the dilation equation the coefficients are said to be Super Haar Admissible. It has been shown that the z transform of Super Haar Admissible coefficients results in a polynomial that satisfies certain conditions. We define a related condition, which we call the Super Haar Condition and show that cyclotomic polynomials of odd order satisfy it. Further, dilation coefficients associated with such polynomials can immediately be found from relations among the cyclotomic polynomials. Using these results, a large class of Super Haar Admissible coefficients is identified and we conjecture that this class includes all admissible coefficients. We discuss applications to denoising and present an example.

SAR produce coherent, and speckled, high resolution images of the ground. Because modern systems can generate large amounts of imagery, there is substantial interest in applying image compression techniques to these products. In this paper, we examine the properties of speckled imagery relevant to the task of data compression. In particular, we demonstrate the advisability of compressing the speckle mean function rather than the literal image. The theory, methodology, and an example are presented.

Ferrari, Berenguer, and Alengrin recently proposed an algorithm for velocity ambiguity resolution in coherent pulsed Doppler radar using multiple pulse repetition frequencies (PRF). In this algorithm, two step estimations for the Doppler frequency is used by choosing particular PRF values. The folded frequency is the fractional part of the Doppler frequency and is estimated by averaging the folded frequency estimates for each PRF. The ambiguity order is the integer part of the Doppler frequency and is estimated by using the quasi maximum likelihood criterion. The PRF are grouped into pairs and each pair PRF values are symmetry about 1. The folded frequency estimate for each pari is the circular mean of the two folded frequency estimates of the pair due to the symmetry property. In this paper, we propose a new algorithm based on the optimal choice of the PRF values, where the PRF values are also grouped into pairs. In each pair PRF values, one is given and the other is optimally chosen. The optimality is built upon the minimal sidelobes of the maximum likelihood criterion. Numerical simulations are presented to illustrate the improved performance.

In active sonar the acoustic backscatter may contain multiple specular components, resonant components, Gaussian, reverberation and other noises as well as multipath effects. One purpose of sonar signal processing is to extract information from the backscatter for underwater target classification. Matching pursuit together with a variation of annealing can be used to separate the specular components and to estimate the corresponding delays and intensities. The effectiveness of this algorithm for linear frequency modulated transmit signals is demonstrated by numerical simulation.

In this paper we apply the continuous wavelet transform, along with multilayer feedforward neural networks, to the estimation of time-dependent radar doppler frequency. The wavelet transform employs the real-valued Morlet wavelet, which is well matched to the doppler signals of interest. The neural networks are trained with the Levenberg-Marquardt rule, which is much faster than purely gradient-descent learning algorithms such as back propagation. We also apply Donoho's wavelet denoising with the novel super-Haar wavelet to improve performance for noisy signals. The techniques are applied to the problem of radar proximity fuzing.

The paper investigates an algorithm for dynamic multi- resolutional distributed prediction and filtering for target tracking. The algorithm incorporates a wavelet transform for integrating sensor signals at different resolution levels. Simulating the performance of an aircraft pilot; comparisons for real-time and semi-real-time performances are conducted for tracking situations in which a pilot makes decisions incremental or after waiting for a history of information respectively. By predicting from learned experiences and filtering current multi-resolutional data achieves optimal filtering control under dynamic uncertainty.

Recently, there has been a great deal of interest in the application of wavelet transforms to signal processing applications. Fundamentally, the wavelet transform of a signal is the correlation of the signal with a basis function derived from a mother wavelet and its called versions called daughter wavelets. Thus any real-time correlator can be sued for the implementation of the wavelet transform. Since a 1D input signal produces a 2D wavelet transform, optical correlators provide a natural advantage over conventional electronic implementations. Examples of optical correlation architecture include the VanderLugt correlator, the joint transform correlator and its derivative, the quasi-Fourier transform joint transform correlator. Any optical correlator architecture can be used to implement the wavelet transform provided a suitable spatial light modulator is used to convert the electrical input signal into an appropriate optical signal. The concept of the smart pixel is to integrate both electronic circuitry and individual optical devices on a common integrated circuit to take advantage of the complexity and programmability of electronic processing circuits and the switching speed of optical devices. Arrays of these smart pixels would then bring with them the advantage of parallelism that optics provides. Smart pixel arrays can function as spatial light modulators providing additional electronic processing features at each individual pixel and therefore are naturally well-suited to realize the wavelet transform.

There are two kinds of RRP: (1) invertible ones, such as global Fourier transform (FT), local wavelet transform (WT), and adaptive wavelet transform (AWT); and (2) non-invertible ones, e.g. ICA including the global principle component analysis (PCA). The invertible FT and WT can be related to the non-invertible ICA when the continuous transforms are approximate din discrete matrix-vector operations. The landmark accomplishment of ICA is to obtain, by unsupervised learning algorithm, the edge-map as image feature ayields, shown by Helsinki researchers using fourth order statistics of nyields -- Kurosis K(uyields), and derived from information- theoretical first principle is augmented by the orthogonality property of the DWT subband used necessarily for usual image compression. If we take the advantage of the subband decorrelation, we have potentially an efficient utilization of a pari of communication channels if we could send several more mixed subband images through the pair of channels.

There have been numerous approaches for the optimal selection of wavelet basis. Two well known approaches are the 'matching pursuit' and 'entropy based' algorithms. While these approaches have been shown to have good results, they suffer by having large, highly redundant dictionaries in order to represent complex waveforms. In this paper, we present a novel approach for selecting independent wavelet feature basis. In this approach we will leverage the neural net 'super mother' principal along with neural net blind demixing/deconvolution techniques based on the statistical mechanics canonical ensemble for constrained Max-Ent approach with selection of basis may be ideal for independent feature extraction in reducing processing requirement for invariant pattern recognition.

The purpose of this investigation is to apply 3D wavelet denoising to resolve spatial, as well as spectral, data in Landsat images. The use of multiple thresholds will be extended to achieve image classification. Wavelet denoising has been shown to be effective for noise reduction in 1D signals and 2D images. 3D wavelet transforms have the potential for multi-resolution surface reconstruction from volume data. 3D wavelet denoising will be applied to spatial potential for multi-resolution surface reconstruction form volume data. 3D wavelet denoising will be applied to spatial and spectral data. Landsat images were produced from a multispectral scanner on Landsat satellites. Wavelet have been used to achieve some level of image classification. Finer classification can be achieved in agricultural areas because of temporal difference between crops and because of spectral difference sin transmission spectra. Varying threshold should achieve image classification based on spectral difference between crops. 3D wavelet data processing is expected to offer greater potential for improving resolution of volume data. Use of multi threshold for spectral resolution might be usefully applied to images generated by nonvisible wavelengths: radar, IR and laser radar.

The challenge of narrow-band video transmission is to produce smooth motion and acceptable image quality. Advances in commercial video teleconferencing have produced products capable of transmitting audio, video, and control information over wired communication channels at increasingly lower bit rates. Wireless narrow-band communication channels require a portion of their bandwidth to be reserved for error resilient coding further reducing the amount of available bandwidth for video. This paper presents the results of wavelet based pre- and post- processing algorithms wrapped around an industry standard video coder/decoder. This WaveNet Wrapper provides an increase in frame rate and codec efficiency for a given bit rate.

Tactical battlefield surveillance systems will require the transmission of compressed video images to utilize these systems limited communication bandwidth and data capacity. The compression techniques used will result in some loss of information.It is important to assess the quality of the video output to determine its performance in Aided Target Recognition applications. The traditional rate of distortion formula is shown by Mallet to be inappropriate for wavelet compression in high compression ratios. The reason is that the histogram change form all gray scale to a concentration singularity near the origin of very low bit rate such that the discrete approximation of the density function of the histogram is no longer valid. Thus we can not theoretically predict the distortion due to wavelet compression. Therefore we conduct an empirical investigation to evaluate the spatial and temporal effects of lossy wavelet compression and reconstruction on tactical IR video. We quantify a resultant temporal ensemble of all local variation curves within a transmitted video frame when compared to the original video frame, using local peak signal-to-noise ratio and feature persistence measure developed by Szu et al. and objective assessment techniques developed by the Institute for Telecommunication Sciences, US Department of Commerce to asses video impairment. We therefore measure video degradation rather than absolute video quality which is difficult to quantify. We also evaluate the comparison results in a movie using split screen presentation of the original and reconstructed video frames and their corresponding metric performance to enhance visual inspection of motion cues enhancement of edge texture maps.

This paper presents a method to evaluate image quality using the continuous wavelet transform. The method utilizes a bank of filters tuned to different scales and orientations to extract the image details. The filters are designed according to the criterion suggested by Antoine and Murenzi. The wavelet transform of a given image and the reconstructed images at various quality levels are represented in the form of energy density plots. These density plots highlight image features such as edges, object boundaries and texture. Thus, they represent the details contained in the image. A quality metric is proposed based on the absolute difference between the energy densities corresponding to the original and reconstructed images. The proposed metric is used to measure the relative quality of the image. In addition, the metric is also used to study the performance of a specific ATR algorithm as a function of image quality.

Current transceiver designs for wavelet-based communication systems are typically reliant on analog waveform synthesis, however, digital processing is an important part of the eventual success of these techniques. In this paper, a transceiver implementation is introduced for the recently introduced wavelet packet modulation scheme which moves the analog processing as far as possible toward the antenna. The transceiver is based on the discrete wavelet packet transform which incorporates level and node parameters for generalized computation of wavelet packets. In this transform no particular structure is imposed on the filter bank save dyadic branching, and a maximum level which is specified a priori and dependent mainly on speed and/or cost considerations. The transmitter/receiver structure takes a binary sequence as input and, based on the desired time- frequency partitioning, processes the signal through demultiplexing, synthesis, analysis, multiplexing and data determination completely in the digital domain - with exception of conversion in and out of the analog domain for transmission.

Our objective is the design and simulation of an efficient system for detection of signals in communications in terms of speed and computational complexity. The proposed scheme takes advantage of two powerful frameworks in signal processing: wavelets and neural networks. The decision system will take a decision based on the computation of the a prior probabilities of the input signal. For the estimation of such probability density functions, a wavelet neural network has been chosen. The election has risen under the following considerations: (a) neural networks have been established as a general approximation tool for fitting nonlinear models from input/output data and (b) the increasing popularity of the wavelet decomposition as a powerful tool for approximation. The integration of the above factors leads to the wavelet neural network concept. This network preserves the universal approximation property of wavelet series, with the advantage of the speed and efficient computation of a neural network architecture. The topology and learning algorithm of the network will provide an efficient approximation to the required probability density functions.

In this paper, we introduce a new time-dependent power spectrum, the Gabor spectrogram. Compared to other methods, the Gabor spectrogram is not only easier for balancing crossterm interference, time-frequency resolution, and other useful properties, but it is also amenable to software as well as hardware implementation. Over the last five years, the Gabor spectrogram has been successfully applied in many areas, such as radar and medical images, noise and vibration, and non-destructive testing.

The application of joint time-frequency techniques for the analysis of electromagnetic backscattered data is reviewed. In the joint time-frequency features space, discrete time events such as scattering centers, discrete frequency events such as target resonances, and dispersive mechanisms due to surface waves and guided modes can be simultaneously displayed. We discuss the various joints time-frequency representations including the short-time Fourier transform, wavelet transform, Wigner-Ville distribution, windowed super-resolution algorithms and the adaptive spectrogram. Emphasis is placed on how these algorithms can be used to represent with good resolution the scattering phenomenology in electromagnetic data. We highlight and application of joint time-frequency processing for radar image enhancement and feature extraction. It is shown that by applying joint time-frequency processing to the conventional inverse synthetic aperture radar imagery, it is possible to remove non-point scattering features in the image, leading to a cleaned image containing only physically meaningful point scatterers. The extracted frequency-dependent mechanisms can be displaced in an alternative feature space to facilitate target identification.

Synthetic aperture radar (SAR) is used for imaging of terrain and stationary objects. For stationary targets, Doppler drifts are determined only by their geometric locations. However, for moving targets, the Doppler drifts are determined not only by their locations but also by their velocities. Therefore, the SAR images of moving targets become smeared due to interactions between their geometric locations and velocities; the cross-range of moving targets does not reflect their true geometric locations. In this paper, we analyze the effects of target motion on SAR images, review methods for SAR imaging of moving targets, and apply time-frequency analysis to SAR images of moving targets.

Pyramidal structures are defined which are locally a combination of low and highpass filtering. The structures are analogous to but different from wavelet packet structures. In particular, new frequency decompositions are obtained; and these decompositions can be parameterized to establish a correspondence with a large class of Cantor sets. Further correspondences are then established to relate such frequency decompositions with more general self- similarities. The role of the filters in defining these pyramidal structures gives rise to signal reconstruction algorithms, and these, in turn, are used in the analysis of speech data.

This paper describes methods for using wavelets to perform image registration at high speed. The basic idea of Le Moigne is to do fast registration on low-resolution images, and then improve the registration by progressively sharpening the resolution. Reduction in resolution by a factor of N reduces the number of operations by a factor of N², while requiring only a small number of subsequent operations to refine the registration to full-resolution accuracy. The operation count can be reduced further by performing the wavelet correlations in the Fourier-wavelet domain with no additional reduction in accuracy. For examples in the paper, this yielded another order of magnitude reduction in complexity. The Fourier techniques are most appropriate for image mappings that are rigid translations, but they also can be applied to more general image mappings. We show how to discover small rotations by selecting several distinct subimages and registering them individually as pure translations. The translation data re then used to recover both an angular and a translation displacement of the full image. For a test involving an image with a half-million pixels these techniques yielded a speed-up of about 34,000 to 1 when compared to a full- resolution search in the pixel domain. Example registrations for two different image sets required 13 operations per full-resolution pixel at 1/64th resolution and 46 resolution and 46 operations per pixel at 1/16th resolution.

Two different problems are investigated. The first is the construction of orthogonal, bandlimited, triadic decompositions. It is shown that the solution involves a scaling function that is a generalization of the Meyer scaling function to the triadic case. The squared sum of the Fourier transform magnitudes of the corresponding wavelet pair displays properties that are a generalization of properties of the Fourier transform of the Meyer wavelet. The paper formulates equations for splitting the sum into two orthogonal wavelets. The second problem is the formulation of a simple, iterative, pseudo-inverse algorithm to provide solution to a triadic extension of the Cohen- Daubechies-Feasuveau method of designing regular, compact biorthogonal wavelets and filter banks.

A new algorithm fusion approach using wavelet filters is used to detect edges with low contrast in the presence of noise. Gabor wavelet edge filters are used that two scales and these are combined using algorithm fusion to locate edges of various sizes under varying contrast and noise conditions. This novel algorithm fusion approach is tested on different microscopy images of several materials and shown to be robust to these changing imaging conditions. A real-time skeletonization approach is also discussed that applies a new and efficient hit and miss transform to produce lines of one pixel width.

The classical problem of recognition of patterns irrespective of their actual size, displacement and orientation is approached in a context of estimation theory. To simplify mathematical derivations, the image and the reference pattern are represented on a complex support, which converts the four positional parameters into tow complex numbers: complex displacement and complex scale factor. The latter one represents isotropic dilations with its magnitude, and rotations with its phase. In this context, evaluation of the likelihood function under additive Gaussian noise assumption allows to relate basic template matching strategy to wavelet theory. In particular, it is shown that using circular harmonic wavelets drastically simplifies the problem from a computational viewpoint. A general purpose pattern detection/estimation scheme is further introduced by decomposition of the images on a orthogonal basis formed by complex Laguerre-Gauss Harmonic Wavelets. Based on this decomposition a solution of ambiguity problems with a progressive coarse to fine parameter estimation is finally presented.

Many shape features are based on a 1D function known as the radial distance measure (RDM). These include its mean, standard deviation, zero crossings, entropy, and roughness index. Recently, wavelet-based features, computed via the RDM, have been sued for object shape recognition. In particular the RDM scalar-energy feature is used in this study. We analyze the effects of centroid errors on the RDM- based feature measures listed above by measuring their mean- square-errors. The error analysis is conducted on a set of 60 images consisting of simplistic shapes: ellipses, triangles, rectangles, and pentagons. The error analysis is also conducted on a set of mammograms where mammographic lesions are to be discriminated into the shape classes: circumscribed, irregular, and stellate. These shape classes are typically used to aid in the classification of lesions as either benign or malignant. Sixty pre-segmented mammographic lesions are used in this analysis. A minimum distance classifier is used to classify the lesion shapes. The effects on the traditional feature vectors are compared with the wavelet-based feature vectors. Lastly, the effects of centroid errors are analyzed with respect to classification rates.

We introduce an object recognition system using Gabor filters to model the biological visual field and a saccadic behavioral model to emulate biological active vision. A high resolution image containing an object of interest is first processed by an ensemble of multi-resolution, multi- orientation Gabor filters. The object can then be described by an alternating sequence of fixation coordinates and the Gabor responses at pixel locations surrounding that fixation point. Once this sequence is memorized, a complex image can be searched for the same location/feature sequence, indicating the presence of the memorized object. The model is suitable for memorization of arbitrary objects, and a simple example is presented using a human face as the object of interest.

We study the texture classification problem, i.e., allocating an observed texture sample to one of known texture classes. We propose a multiresolution approach based on wavelet maxima representation for texture classification. First, a multiscale wavelet maxima representation of the image is generated by a wavelet transform. Energy and entropy are calculated and weighted at each scale. These features form a feature vector of the image. A minimum- distance classifier is used in texture classification. Classification experiments with 18 Bordatz texture indicates that this method is both translation and rotation invariant and achieves 99 percent classification accuracy. Noise sensitivity analysis shows that this method has excellent performance in noisy situation. Finally a detailed comparison of various wavelet transform based texture classification methods is provided.

Previously, methods to estimate the number of jumps in a piecewise constant signal were presented in the framework of projection libraries. In this paper, these concepts are extended to general piecewise projection libraries appropriate for modeling, for example, piecewise polynomial and piecewise stationary signals. A general piecewise best basis algorithm is also presented that offers an efficient alternative to standard methods. Particularly, an algorithm for best piecewise wavelet basis is shown to reduce the entropy over wavelet packets. While a dynamic programming algorithm can still be employed to efficiently calculate optical estimates for these new piecewise projection libraries, additional modifications are often needed to reduce the computational requirements for practical implementation. An alternative approach, termed subspace pursuit, is presented that is applicable to all projection libraries and is especially suited for signal dimension estimation. The method is an order-recursive least square implementation of matched pursuit that requires roughly twice the computation but has the advantage that at each iteration the coefficients are optimal, that is, are obtained by a projection onto the subspace spanned by signals in the dictionary. Additionally, for the signal dimension estimation problem, an interesting paradox is presented where estimates are shown to be worse with increased signal-to-noise ratio (SNR) past a certain threshold and to converge to a level less than this optimum performance for infinite SNR.

One of the problems of 5 percent error rate encountered in continuous speech recognition is partly due to the difficulty in the identification of a mixed up to two phonemes in a close concatenation. For instance, one speaks of 'Let's go' instead of 'Let us go'. There are two kinds of speech segmentations: the linguistic segmentation and the acoustic segmentation. The linguistic segmentation relies on a combination of acoustic, lexical, semantic, and statistical knowledge sources, which has been studied. Daily spoken conversations are usually abbreviated for speakers' convenience. The acoustic segmentation is to separate the mixed sounds such as /ts/ into /t/ and /s/ for automatically finding linguistic units. Adaptive wavelet transform (AWT) developed by Szu is a linear superposition of banks of constant-Q zero-mean mother wavelets implemented by an ANN called a 'wavenet'. Each neuron is represented by a daughter wavelet, which can be an affine scale change of identical or different method wavelet for a continuous AWT. AWT was designed for the cocktail party effect and to solve the acoustic segmentation of phonemes using a supervised learning ANN architecture. In this paper, we reviewed AWT from Independent Component Analysis viewpoint, and then applied blind source separation to the acoustic de-mixing and segmentation.

Nuclear Quadrupole Resonance (NQR) is effective for the detecting and identification of certain types of explosives such as RDX, PETN and TNT. In explosive detection, the NQR response of certain 14N nuclei present in the crystalline material is proved. The 14N nuclei possess a nuclear quadrupole moment which in the presence of an electric field gradient produces an energy level splitting which may be excited by radio-frequency magnetic fields. Pulsing on the sample with a radio signal of the appropriate frequency produces a transient NQR response which may then be detected. Since the resonant frequency is dependent upon both the quadrupole moment of the 14N nucleus and the nature of the local electric field gradients, it is very compound specific. Under DARPA sponsorship, the authors are using multiresolution methods to investigate the enhancement of operation of NQR explosives detectors used for mine detection. For this application, NQR processing time must be reduced to less than one second. False alarm response due to acoustic and piezoelectric ringing must be suppressed. Also, as TNT is the most prevalent explosive found in land mines NWR detection of TNT must be made practical despite unfavorable relaxation times. All three issues require improvement in signal-to-noise ratio, and all would benefit from improved feature extraction. This paper reports some of the insights provided by multiresolution methods that can be used to obtain these improvements. It includes results of multiresolution analysis of experimentally observed NQR signatures for RDX response and various false alarm signatures in the absence of explosive compounds.

Awareness of the viewer's gaze position in a virtual environment can lead to significant savings in scene processing in fine detail information is presented 'just in time' only at locations corresponding to the participant's gaze, i.e., in a gaze-continent manner. In the development of a gaze-continent manner. In the development of a gaze- contingent system, a model of eye movements is necessary for the exploration of vision and its underlying visual stimuli. The need here is to confidently classify eye movements within natural human viewing patterns. Assuming eye movements composed of dynamic fixations denote overt locations of visual attention, localization of these features is crucial to a gaze-contingent analysis and synthesis of visual information. Due to its simplicity and ease of implementation, a particularly attractive strategy for eye movement modeling involves linear time-invariant (LTI) filtering. In this paper, a conceptual piecewise auto- regressive integrated moving average (PARIMA) model of conjugate eye movements is proposed. The PARIMA model is a piecewise-LTI representation of stochastic signals. The analytical framework of the PARIMA model features a wavelet- based strategy for eye movement segmentation. An off-line video frame-based 3D wavelet analysis technique is proposed for classification of eye movements into smooth pursuits, fixations, and saccades.

The wavelet transform dilates and translates a selected fundamental wavelet. Selective sampling of the continuous wavelet transform identifies discrete components used as a basis for signal projections. Similarly, some properties of early vision may be descried in terms of dilations and translations of fundamental waveforms. Examples include the optical point spread function, spectral absorption curves of photoreceptors, receptive fields of photoreceptors. Receptive fields of post-receptor cells, and eye movements. These vision features are described with respect to the dilation and translation of candidate waveforms. Spatial, temporal, and chromatic filtering in the vision pathways are also describe with respect to similarities with wavelet subband analysis.

Neural networks and wavelet transform have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. So, mathematical model is a very important tool to guarantee the development of the neural network area. In this article we will introduce one series of mathematical demonstrations that guarantee the wavelets properties for the PPS functions. As application, we will show the use of PPS- wavelets in pattern recognition problems of handwritten digit through function approximation techniques.

We present a new empirical consistent method for estimation of the order of an ARMA process. All the inconvenience of the usual criterions are solved. In particular in our method, it is not necessary to know an a prior lower bound for the zeros of the spectra and we do not need an a priori known upper bound for the order. Moreover our criterion is very easy to compute.

In this paper we describe techniques relating to intelligent data processing, on line identification and neural networks predictors for complex nonlinear systems with multiple switching models the initial model identification is provided based on the realization theory non-iterative algorithm.

The analysis of gas turbine vibration is enhanced by the use of wavelet characterization and Wigner-Ville distribution processing to represent vibration features. The output of vibration sensors is digitized and the signal is processed by these means to identify signals associated with damage and progressive turbine wear. Wavelet processing provides fast transient detection useful in minimizing subsequent damage to turbine components through quick reaction. During turbine operation, short duration features appear, such as rotating stall conditions, that are well suited for detection with wavelet techniques. The Wigner-Ville distribution provides very accurate determination of vibration amplitudes in the nonstationary environment encountered in the use of gas turbines for vehicular propulsion. The Wigner-Ville distribution is described, and techniques for obtaining highly accurate amplitude information in the presence of noise and nonstationarity are presented. The wavelet transform is capable of making trade- offs between time and frequency resolutions, a property that makes it appropriate for the analysis for the analysis of nonstationary signals. Its ability to 'zoom in' on short lived high frequency phenomena is particularly attractive for the analysis of transients. Features of interest can be characterized form the evolution of the transform coefficients across distinct scales. Different types of wavelet transforms for an efficient time-frequency processing of the vibration signals are investigated. The resulting wavelet and Wigner features are used as inputs to a neural net which combine them with system health parameters. The result is a viable turbine monitor system, which can respond to long and short term events in a reliable and responsive manner.

Continuous wavelet transform and linear time-frequency transforms are coefficients of continuous unitary group representations of the affine and Heisenberg groups. Many properties of these transforms that are important for wideband radar and sonar signal processing follow directly from group representation theory. These properties include volume invariance and variance of narrowband and wideband ambiguity functions and wavelet transform domain implementations of detects and signal estimators. For several radar, sonar, and array processing applications, the basic definition of wavelet and time-frequency representations must be generalized by using unitary representations of other groups and using reproducing kernel Hilbert space (RKHS) inner products in the definition of the linear transforms. The general definition then leads to weighted continuous wavelet transforms where the RKHS is determined by a nonstationary covariance function; generalized wideband ambiguity functions also follow from this general definition along with other important generalizations that arise in wideband array processing and model based signal processing in complex scattering and propagation media. This paper presents the generalized wavelet transform along with the weighted wavelet transforms. The classical narrowband and wideband ambiguity functions are then special cases. The application of generalized transform to multidimensional transforms for space-time processing are also presented, along with the application to conformal groups for detections and estimation of accelerating scatterers.

Gabor and Morlet wavelet filterbanks are popular in signal and image processing because they provide good time- frequency resolutions. This paper shows how to realize efficient Gabor and Morlet wavelet filterbanks based on approximations through frequency sampling filters in the Residue Number System which provides an exact pole-zero annihilating for poles on the unit circle in the complex z- plane. The aim of the paper is that the computational 'gap' between dyadic DWT and transforms with Gabor and Morlet wavelet filterbanks becomes less dramatic.

An orthogonal m-band discrete wavelet transform has an O(m²) complexity. In this paper, we present a fast implementation of such a discrete wavelet transform. In an orthonormal m-band wavelet system, the vanishing moments and orthogonality conditions are imposed on the scaling filter only. Given a scaling filter, one can design the other m-1 wavelet filters. It is well-known that there are infinitely many solutions in such designing procedure. Here we choose one specific type of solutions and implement the corresponding wavelet transform in a scheme which has complexity O(m). Thus for any scaling filter, one can always construct a full orthogonal m-band wavelet matrix with an O(m) discrete wavelet transform.

The principle of perception redundancy states that by optimally balancing between the information reduction of the input data and sufficient redundancy, classification performance should improve due to smaller search space from the reduced dimensions and noise-invariant from retained redundancy. For dimensionality reduction using global information, principal component analysis (PCA) is a well suited method especially for signal processing task. However, for pattern classification purpose and for image classification in particular, operating on raw input data sometimes limits the benefit of the PCA. Following the expansion-reduction model of data-processing, we propose the use of multiple resolution analysis through continuous wavelet transform (WT) to rearrange input data into different combinations according to wavelet kernel criteria. Quantization further provides intrinsic de-noising result plus sparseness in the transform space which preconditions the orthogonality. PCA is then performed on each level of the data resolution, generating mutually supportive classification discriminants. All together, this multiple resolution principal wavelet component method provides two significant advantages over traditional PCA: i) providing integrated de-noising and redistribution of information content, thereby establishes controlled and mathematically sound downsampling scheme, which alleviates the curse of dimensionality and, at the same time, attenuates noises. ii) Establishing a multiple resolution decision process, whereas each resolution level provides supplemental principal wavelet components, being at least quasi-orthogonal by nature, to support classification with maximum tolerance.

In this paper we address the problem of target tacking when flare decoys and severe noise are present in the acquired sensor data. The input imagery is assumed to be obtained from an optical sensor mounted on the interceptor missile, where the goal of the interceptor is to neutralize the target. For this purpose algorithms running on on-board processors must extract information from the input imagery in order to steer the interceptor's course toward the target. Two challenging cases are considered here. First, the input imagery is assumed to be corrupted by additive Gaussian nose. Here we see, to determine the usefulness of our approach when low cost poor quality sensors are employed for acquisition. Second, scenarios where standard flare decoys are released by the target aircraft are considered, which represent a challenge due to the disparity in intensity of the target aircraft versus the decoys. Results using synthetically generated test sequences are presented.

Based on the adaptive joint time-frequency processing techniques, a new methodology is proposed in this paper to separate the interference due to fast rotating parts from the original ISAR image of the target. The technique entails adaptively searching for the linear chirp bases which best represent the time-frequency behavior of the signal and fully parameterizing the signal with these basis functional. The signal components due to the fast rotating part are considered to be associated with those chirp bases having large displacement and slope parameters, while the signal components due to the target body motion are represented by those chirp bases which have relatively small displacement and slope parameters. By sorting these chirp bases according to their slopes and displacements, the scattering due to the fast rotating part can be separated form that due to the target body. Consequently, the image artifacts overlapping with the original image of the target can be well removed and a clean ISAR image can be produced. Successful applications of the algorithm to numerically simulated and measurement data show the robustness of the algorithm.

This paper investigates the use of various wavelet transform as a method of performing data reduction on static signature images presented to be backpropagation neural network. It is shown that a particular subset of 64 Daubechies D₄ wavelet transform coefficients act as an efficient representation of a static signature image when sued to train a backpropagation network to perform static signature verification. Results indicate a signature verification performance of at least 95 percent.

Content-based indexing and retrieval of image database has become quite a popular research focus during the pats few years. Although several retrieval approaches based on low- level features have been proposed up to now, an efficient combination of these features which would remarkably improve the performance still needs to be developed. In the paper oriented towards the retrieval of images in a textured color image database, we propose a novel approach which effectively combines both the texture and the color information in a non-separate way. In the approach, we apply adaptive wavelet frame packet analysis which we proposed earlier to both the transformed texture channel and the color channel, we obtain textured features, colored features and correlated features of both texture and color form all the decomposed subbands and we measure similarity of images using a simple and symmetric distance. Images are returned in order of similarity to the query sample. Experiments show that the proposed approach retrieves images in a progressive way. It can produce appealing performance in terms of both retrieval efficiency and retrieval effectiveness.

In this paper, the importance of edge extracting in image processing and the analysis of the superiorities in edge extracting by using wavelet transform are given, these superiorities are described as: time and frequency domains, multiresolution, pure mathematical method. Based on much reference, some wavelet functions for edge extracting are made, the effect and methods for edge extracting by using these wavelet functions are also made, and the computer simulation results for Linna image by using these wavelet functions and methods are given, from these simulation results we can get that the derivative of Gauss function is often used as wavelet function and has good effect in image edge extracting, at last, we give the computer simulation results for edge extracting by using the derivative of Gauss function, we process a building under different clarities.

Efficient feature extraction metrics are crucial in many computer vision applications. One such application is texture classification which involves classifying samples as members of one of a preset number of classes. These classes are chosen to correspond with our human intuition of which textures are different from others. In this work we use the wavelet-based fractal signature, a new multichannel texture model introduced previously which characterizes patterns as 2D functions in a Besov space. The wavelet-based fractal signature generates an n-dimensional surface, which is then used for classification by a fuzzy self-organizing feature map as well as two other supervised classification techniques. The feature space has a low dimensionality and as a result is classified in few training epochs. Experimental results are presented for a test set of textures of different types.

This paper discusses a possible improvement for a common control system for unmanned aerial vehicles (UAVs). The common control system will provide command, control and data dissemination for tactical UAVs. Adding wavelet image technology and adaptive resonance theory to the common control system will provide an advanced foundation for interoperability and commonality to the tactical UAV family and the common core software elements.

In this paper, a new approach is introduced to generate and compose CHinese typefaces employing B-spline wavelet transform. Firstly, we model each area-based curved outline of the Chinese characters using a B-spline curve, which is determined by a set of control points. Secondly, the B- spline wavelet transform is used to represent the control points with several sequences of wavelet coefficients on several different scales. We then modify the details on different scales by editing them or by combining the coefficients obtained from different standard typefaces. Finally, the modified wavelet coefficients are reconstructed, resulting in a new curved outline for the character being processed. Experiments show that the proposed approach is capable of generating many special kinds of typefaces by applying different editing strategies on the wavelet coefficients.

In this paper, we describe a wavelet-based vision system created to detect unexploded ordnances (UXOs). This system was created to test whether or not a vision system could be a useful component on a mobile robot platform whose purpose is the exploration of possibly unknown environments for the detection of UXOs. As a first phase, we describe here, the extraction of relatively simple features in the wavelet domain. We capitalize upon the fact that the wavelet domain is multiresolutional in nature, and compactly represents local frequency information in the feature extraction phase. These features are used in a neural network system for the purpose of recognition. Results show that these features perform well for localization, but, suggest additional features are needed for identification. This work compliments other ongoing research in UXO detection at the Naval PostGraduate School. In the past, magnetometer readings have been used for underground UXO detection. A possible avenue of future research is to create a multi- sensor system using visual, magnetometer and possibly other data to arrive at better decisions.

The underwater acoustic signals detected by a hydrophone can be separated into two categories, i.e., transient signals and stationary signals. Transient signals are hard to be detected but they could include important features for target identification. Recently the wavelet transform is considered as a good method to detect transient signals. However, the occurring time and the effective time-frequency product are asked to be determined before the wavelet transform can be successfully applied. In this paper, a multi-scaling wavelet is developed to cover signals with distinct time and frequency resolutions and hence makes the detection performance better. Furthermore, a multi- translation wavelet is designed to explore the characteristics of the transient signal. To illustrate the effectiveness of the new design method, some experiments are taken to perform by using simulation and recorded real underwater acoustic signals. Experimental result showed that the fusion of the two wavelets with (omega) ₀ equals 5.3 and 50 can have better detection performance than traditional techniques. The resultant translation-spectrum graph showed that both the frequency and the repetition interval for the transient signal can be successfully detected.

We introduce a continuous scale wavelet detector for identifying masses in mammograms. Continuous-scale wavelet algorithms have been discussed in the past, however this is the first reported algorithm that uses a scaled version of the same mother wavelet at each scale of analysis. This single mother wavelet property leads to a simpler implementation and a more direct application of detection theory to recognition problems than traditional multiscale analysis. In addition, we show that a continuous-scale search is necessary for computer aided diagnosis of mammography since traditional solutions using dyadic scales either fail to detect some masses or signal too many false alarms. Our novel wavelet detector combines a wavelet formulation with the classical theory of constant false alarm rates detectors. Finally, we show that our algorithm is able to detect masses in actual mammograms that could not be seen using conventional windowing and leveling or other traditional methods of contrast enhancement.

In this paper, we propose to incorporate both spatial and frequency models of HVS into wavelet transform image coding. The process of wavelet transform decomposition, which splits the spatial frequency domain to several octave bands by dilation and translation of a single basic wavelet, is similar to that of frequency model HVS. Moreover, according to spatial model of HVS, some compact physical features like contours and regions are with high visual perceptive significance to human vision system. Based on the spatial model we develop a visual perception sensitive map and use the map to develop a wavelet thresholding scheme in order to achieve a high image compression ratio while retaining a high visual quality of the reconstructed image.After removing the less visually significant coefficients, we developed an adaptive quantization scheme for transformed coefficients at each of the subbands. This quantization scheme is developed based on the HVS frequency model to minimize the visual error due to quantization. In our image compression system, both frequency and spatial aspects of HVS to the image have been taken into consideration. We preserve the highly visual perceptive wavelet coefficients and minimize the visual distortion of coefficients in each of the decomposed band. As a result, a high compression ratio and low visual distortion coder is obtained.

In general case, the interpolant in the Walter's wavelet sampling theorem is not necessarily compactly supported. Requiring that it is compactly supported is equivalent to requiring that the corresponding scaling function has the sampling property. Our focus in this paper is on considering the case where the scaling function is not only compactly supported, but also orthogonal and of the sampling property. This paper makes a parameterization of two regular unitary M-band sampling scaling filters of the length 3M, constructs a 3-band sampling scaling function and show that it is not only compactly supported, but also orthogonal and continuous. However, in 2-band case, there is no such scaling function except Haar scaling function. G. Walter's sampling theorem for wavelet subspaces corresponding to this scaling function has the interpolant with compact support. Therefore, the signals in multiresolution subspaces can be reconstructed exactly and fast without truncated errors.

We present three recent developments in wavelets and subdivision: wavelet-type transforms that map integers to integers, with an application to lossless coding for images; rate-distortion bounds that realize the compression given by nonlinear approximation theorems for a model where wavelet compression outperforms the Karhunen-Loeve approach; and smoothness results for irregularly spaced subdivision schemes, related to wavelet compression for irregularly spaced data.

The introduction of wavelets in signal and image processing has provided a new tool to create innovative and novel methods for solving problems in the areas of data compression, signal analysis, and nose removal, to name a few. Although wavelets are popular and used extensively in research and in engineering applications, their use in signature detection and classification is still an area open to extensive investigation. This paper discusses wavelet image processing working in synergy with other processing techniques to detect and recognize abnormal and cueing signature that are important to diagnostic medicine - detection and recognition of microcalcification clusters in mammograms. In this application, an innovative detection algorithm that takes advantage of wavelet multiresolution analysis and synthesis is developed to assist radiologists looking for clusters of microcalcification in digitized mammograms. Microcalcification regions may not be detectable by visual inspection or other detection techniques because of their inherent complexity. The algorithm presented in this paper successfully unmasks the complexity and limits the false positives. A thorough analysis, algorithm description and examples are shown in this paper.

We present a method for constructing efficient hierarchical organization of image databases for fast recognition and classification. The method combines a wavelet preprocessor with a tree-structured-vector-quantization for clustering. We show results of application of the method to ISAR data from ships and to face recognition based on photograph databases. In the ISAR case we show how the method constructs a multi-resolution aspect graph for each target.

In this paper, an efficient computational framework for the extraction of mesoscale features, i.e. internal waves, present in SAR images is discussed. The first problem in a mesoscale detection system is to distinguish sea from land in the SAR imagery. A method for coastline detection based on a sequence of basic processing procedures followed by a contour tracing algorithm is introduced in order to obtain sea-land separation to enhance the internal wave detection problem the utility of wavelet analysis as a tool for automatic oceanic internal wave detection and location from SAR images is then examined using the 2D wavelet transform based on the multiscale gradient detection method. We show that the evolution of local maxima of the wavelet transform across scale characterize the local shape of these quasi- linear periodic structures. The results from this study show that wavelet analysis is an excellent tool to detect and locate internal wave features from satellite images against internal wave look-a-likes.