Estimation of the location of sound sources is usually done using microphone arrays. Such settings provide an environment where we know the difference between the received signals among different microphones in the terms of phase or attenuation, which enables localization of the sound sources. In our solution we exploit the properties of the room transfer function in order to localize a sound source inside a room with only one microphone. The shape of the room and the position of the microphone are assumed to be known. The design guidelines and limitations of the sensing matrix are given. Implementation is based on the sparsity in the terms of voxels in a room that are occupied by a source. What is especially interesting about our solution is that we provide localization of the sound sources not only in the horizontal plane, but in the terms of the 3D coordinates inside the room.
A number of new localized, multiscale transforms have recently been introduced to analyze data residing on weighted graphs. In signal processing tasks such as regularization and compression, much of the power of classical wavelets on the real line is derived from their theoretically and empirically proven ability to sparsely represent piecewise-smooth signals, which appear to be locally polynomial at sufficiently small scales. As of yet in the graph setting, there is little mathematical theory relating the sparsity of localized, multiscale transform coefficients to the structures of graph signals and their underlying graphs. In this paper, we begin to explore notions of global and local regularity of graph signals, and analyze the decay of spectral graph wavelet coefficients for regular graph signals.
We present a method for joint reconstruction of a set of images representing a given scene from few multi-view measurements obtained by compressed sensing. We model the correlation between measurements using global geometric transformations represented by few parameters. Then, we propose an algorithm able to jointly estimate these transformation parameters and the observed images from the available measurements. This method is also robust to occlusions appearing in the scene. The reconstruction algorithm minimizes a non-convex functional and generates a sequence of estimates converging to a critical point of this functional. Finally, we demonstrate the efficiency of the proposed method using numerical simulations.
We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented structure in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal from its wavelet coefficients. We present exact and efficient algorithms to compute the scale-discretized wavelet transform of band-limited signals on the sphere. These algorithms are implemented in the publicly available S2DW code. We release a new version of S2DW that is parallelized and contains additional code optimizations. Note that scale-discretized wavelets can be viewed as a directional generalization of needlets. Finally, we outline future improvements to the algorithms presented, which can be achieved by exploiting a new sampling theorem on the sphere developed recently by some of the authors.
The real-time development of multi-camera systems is a great challenge. Synchronization and large data rates of
the cameras adds to the complexity of these systems as well. The complexity of such system also increases as the
number of their incorporating cameras increases. The customary approach to implementation of such system is a
central type, where all the raw stream from the camera are first stored then processed for their target application.
An alternative approach is to embed smart cameras to these systems instead of ordinary cameras with limited or
no processing capability. Smart cameras with intra and inter camera processing capability and programmability
at the software and hardware level will offer the right platform for distributed and parallel processing for multi-
camera systems real-time application development. Inter camera processing requires the interconnection of smart
cameras in a network arrangement. A novel hardware emulating platform is introduced for demonstrating the
concept of the interconnected network of cameras. A methodology is demonstrated for the interconnection
network of camera construction and analysis. A sample application is developed and demonstrated.
We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association
between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem
requires less than half the number of samples of other equiangular sampling theorems on the sphere, such as
the canonical Driscoll & Healy sampling theorem. A reduction in the number of samples required to represent
a band-limited signal on the sphere has important implications for compressive sensing, both in terms of the
dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on
the sphere, where we show superior reconstruction performance when adopting the new sampling theorem.
Distributed compressed sensing is the extension of compressed sampling (CS) to sensor networks. The idea is to
design a CS joint decoding scheme at a central decoder (base station) that exploits the inter-sensor correlations, in
order to recover the whole observations from very few number of random measurements per node. In this paper,
we focus on modeling the correlations and on the design and analysis of efficient joint recovery algorithms.
We show, by extending earlier results of Baron et al.,<sup>1</sup> that a simple thresholding algorithm can exploit the
full diversity offered by all channels to identify a common sparse support using a near optimal number of
We consider the problem of reconstruction of astrophysical signals probed by radio interferometers with baselines
bearing a non-negligible component in the pointing direction. The visibilities measured essentially identify with
a noisy and incomplete Fourier coverage of the product of the planar signals with a linear chirp modulation. We
analyze the related spread spectrum phenomenon and suggest its universality relative to the sparsity dictionary,
in terms of the achievable quality of reconstruction through the Basis Pursuit problem. The present manuscript
represents a summary of recent work.
This paper introduces p-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel
signals over redundant dictionaries. We work out both worst case and average case recovery analyses of this algorithm and show that the latter results in much weaker conditions on the dictionary. Numerical simulations confirm our theoretical findings and show that
<i>p</i>-thresholding is an interesting low complexity alternative to simultaneous greedy or convex relaxation algorithms for processing sparse multichannel signals with balanced coefficients.
This paper investigates video coding with wavelet transforms applied in the temporal direction of a video sequence. The wavelets are implemented with the lifting scheme in order to permit motion compensation between successive pictures. We improve motion compensation in the lifting steps and utilize complementary motion-compensated signals. Similar to superimposed predictive coding with complementary signals, this approach improves compression efficiency. We investigate experimentally and theoretically complementary motion-compensated signals for lifted wavelet transforms. Experimental results with the complementary motion-compensated Haar wavelet and frame-adaptive motion compensation show improvements in coding efficiency of up to 3 dB. The theoretical results demonstrate that the lifted Haar wavelet scheme with complementary motion-compensated signals is able to approach the bound for bit-rate savings of 2 bits per sample and motion-accuracy step when compared to optimum intra-frame coding of the input pictures.
We propose the construction of directional - or Gabor - continuous wavelets on the sphere. We provide a criterion to measure their angular selectivity. We finally discuss implementation issues and potential applications. The code for the spherical wavelet transform is available in the YAWTB Matlab Toolbox, http://www.yawtb.be.tf.
Very low bit rate image coding is an important problem regarding applications such as storage on low memory devices or streaming data on the internet. The state of the art in image compression is to use 2-D wavelets. The advantages of wavelet bases lie in their multiscale nature and in their ability to sparsely represent functions that are piecewise smooth. Their main problem on the other hand, is that in 2-D wavelets are not able to deal with the natural geometry of images, i.e they cannot sparsely represent objects that are smooth away from regular submanifolds. In this paper we propose an approach based on building a sparse representation of images in a redundant geometrically inspired library of functions, followed by suitable coding techniques. Best N-term non- linear approximations in general dictionaries is, in most cases, a NP-hard problem and sub-optimal approaches have to be followed. In this work we use a greedy strategy, also known as Matching Pursuit to compute the expansion. Finally the last step in our algorithm is an enhancement layer that encodes the residual image: in our simulation we have used a genuine embedded wavelet codec.
This paper presents a new, highly flexible, scalable image coder
based on a Matching Pursuit expansion. The dictionary of atoms is
built by translation, rotation and anisotropic refinement of
gaussian functions, in order to efficiently capture edges in
natural images. In the same time, the dictionary is invariant
under isotropic scaling, which interestingly leads to very simple
spatial resizing operations. It is shown that the proposed scheme
compares to state-of-the-art coders when the compressed image is
transcoded to a lower (octave-based) spatial resolution. In
contrary to common compression formats, our bit-stream can
moreover easily and efficiently be decoded at any spatial
resolution, even with irrational re-scaling factors. In the same
time, the Matching Pursuit algorithm provides an intrinsically
progressive stream. This worthy feature allows for easy rate
filtering operations, where the least important atoms are simply
discarded to fit restrictive bandwidth constraints. Our scheme is
finally shown to favorably compare to state-of-the-art
progressive coders for moderate to quite important rate
We introduce an isotopic measure of local contrast for natural images that is based on analytic filters and present the design of directional wavelet frames suitable for its computation. We show how this contrast measure can be used within a masking model to facilitate the insertion of a watermark in an image while minimizing visual distortion.
The analysis of oriented features in images requires 2D directional wavelets, for instance in standard tasks such as edge detection or directional filtering. In addition we present here a new application, namely a technique for determining all the (statistical) symmetries of a given pattern with respect to rotations and dilations. Examples are Penrose tilings, mathematical quasicrystals or various quasiperiodic planar point sets or patterns.
In this paper, we present two filters that simulate the behavior of biological end-stopped cells. Both are zero-mean filters, and are well located in the spatial as well as frequency domains, that is, these filters are admissible wavelets. We refer to the two filters as ES1 and ES2. The ES1 filter responds to ends of linear structures which have a specific orientation, and the ES2 filter responds to line- segments which have a specific orientation, and which have a length within a specific range. We show sample results to demonstrate the behavior of the proposed wavelets, and we also discuss the scale-space behavior of these wavelets briefly.
Automatic target detection and recognition (ATR) requires the ability to optimally extract the essential features of an object from (usually) cluttered environments. In this regard, efficient data representation domains are required in which the important target features are both compactly and clearly represented, enhancing ATR. Since both detection and identification are important, multidimensional data representations and analysis techniques, such as the continuous wavelet transform (CWT), are highly desirable. First we review some relevant properties of two 2D CWT. Then we propose a two-step algorithm based on the 2D CWT and discuss its adequacy for solving the ATR problem. Finally we apply the algorithm to various images.
Both in 1D (signal analysis) and 2D (image processing), the wavelet transform (WT) has become by now a standard tool. Although the discrete version, based on multiresolution analysis, is probably better known, the continous WT (CWT) plays a crucial role for the detection and analysis of particular features in a signal, and we will focus here on the latter. In 2D however, one faces a practical problem. Indeed, the full parameter space of the wavelet transform of an image is 4D. It yields a representation of the image in position parameters (range and perception angle), as well as scale and anisotropy angle. The real challenge is to compute and visualize the full continuous wavelet transform in all four variables--obviously a demanding task. Thus, in order to obtain a manageable tool, some of the variables must be frozen. In other words, one must limit oneself to sections of the parameter space, usually 2D or 3D. For 2D sections, two variables are fixed and the transform is viewed as a function of the two remaing ones, and similarly for 3D sections. Among the six possible 2D sections, two play a privileged role. They yield respectively the position representation, which is the standard one, and the scale-angle representation, which has been proposed and studied systematically by two of us in a number of works. In this paper we will review these results and investigate the four remaining 2D representations. We will also make some comments on possible applications of 3D sections. The most spectacular property of the CWT is its ability at detecting discontinuities in a signal. In an image, this means in particular the sharp boundary between two regions of different luminosity, that is, a contour or an edge. Even more prominent in the transform are the corners of a given contour, for instance the contour of a letter. In a second part, we will exploit this property of the CWT and describe how one may design an algorithm for automatic character recognition (here we obviously work in the position--range-perception angle--representation). Several examples will be exhibited, illustrating in particluar the robustness of the method in the presence of noise.