Many regions of the sky are currently being observed with a high number of spectral bands with various instruments and this trend shall develop considerably in the coming years. Even with few wavelength-bands, it is not easy to match the objects identified in each individual image, or to get consistent measurements and classify them spectrally. A detection based on fusion images is proposed. Different algorithms are tested for building such an image. The best results in terms of object detection are obtained from those involving a deconvolution with a wavelet approach. Another way to sort the pixels of astronomical images into a coherent set of physical sources is to classify them following some basic assumptions. The main difficulty comes from the fact that astronomical sources fill a multidimensional continuum of spectral classes leading to a significant color classes increase with the number of bands. The pixels spectral behaviour is assumed here to be a superimposition of several pure elements. The resulting mixing categories define a set of intermediate classes, and the application of the matching pursuit algorithm allows then to get class percentages, providing very promising results for the analysis of multi-wavelength astronomical images.
Large surveys at high angular resolution have a lot of interest for astrophysical studies. Their achievements with space missions imply a significant data transmission if a resolution close to 0.1 arcsec is wished. A satisfying telemetry rate is conceivable thanks to a selection of the significant information on board. An image composed of detected stars is first subtracted. A thresholding is then applied in order to keep significant wavelet coefficients. Coding these bright stars as a catalogue with a position and a magnitude estimated on board is less expensive for the telemetry than the coding of their images on the focal plane. Tests were carried out with the technical features of the European astrometric Gaia mission. The consequence of such a lossly compression on the restored images are illustrated. At the end of the space mission, thanks to a combination of fields with different orientations, an improvement of 2 to 3 magnitudes for the detection and a higher resolution are obtained. Even though this approach showed us some difficulties and limits for the Gaia mission, it allowed us to conceive a specific mission dedicated to a full-sky imaging at high angular resolution.
Multiscale analyses can be provided by application wavelet transforms. For image processing purposes, we applied algorithms which imply a quasi isotropic vision. For a uniform noisy image, a wavelet coefficient W has a probability density function (PDF) p(W) which depends on the noise statistic. The PDF was determined for many statistical noises: Gauss, Poission, Rayleigh, exponential. For CCD observations, the Anscombe transform was generalized to a mixed Gasus+Poisson noise. From the discrete wavelet transform a set of significant wavelet coefficients (SSWC)is obtained. Many applications have been derived like denoising and deconvolution. Our main application is the decomposition of the image into objects, i.e the vision. At each scale an image labelling is performed in the SSWC. An interscale graph linking the fields of significant pixels is then obtained. The objects are identified using this graph. The wavelet coefficients of the tree related to a given object allow one to reconstruct its image by a classical inverse method. This vision model has been applied to astronomical images, improving the analysis of complex structures.
The problem we are interested in is the restoration of nuclear medicine images acquired by a gamma camera. In a previous paper the authors have developed a wavelet based filtering method enabling to remove one of the major sources of error in nuclear medicine, namely Poisson noise. The purpose of this paper is to show how the restoration algorithm has been improved by introducing the point spread function as additional constraint in the restoration of the wavelet coefficients and choosing the regularization constraint in the object space. We describe a new restoration algorithm where filtering and deconvolution are coupled in a multiresolution frame. The performances are illustrated with simulated data and phantom images.
Nuclear medicine imaging is a widely used commercial imaging modality which relies on photon detection as the basis of image formation. As a diagnosis tool, it is unique in that it documents organ function and structure. It is a way to gather information that may be otherwise unavailable or require surgery. Practical limitations on imaging time and the amount of activity that can be administered safely to patients are serious impediments to substantial further improvements in nuclear medicine imaging. Hence, improvements of image quality via optimized image processing represent a significant opportunity to advance the state-of-the-art int his field. We present in this paper a new multiscale image restoration method that is concerned with eliminating one of the major sources of error in nuclear medicine imaging, namely Poisson noise, which degrades images in both quantitative and qualitative senses and hinders image analysis and interpretation. The paper then quantitatively evaluates the performances of the proposed method.
We present a regularized method for wavelet thresholding in a multiresolution framework. For astronomical applications, classical methods perform a standard thresholding by setting to zero non-significant coefficients. The regularized thresholding uses a Tikhonov regularization constraint to give a value for the non-significant coefficients. This regularized multiresolution thresholding is used for various astronomical applications. In image filtering, the significant coefficients are kept, and we compute the new value for each non-significant coefficients according to the regularization constraint. In image compression, only the most significant wavelet coefficients are coded. With lossy compression algorithms such as hcompress, the compressed image has a block-like appearance because of coefficients that are set to zero over large areas. We apply the Tikhonov constraint to restore the coefficients lost during the compression. By this way the distortion is decreasing and the blocking effect is removed. This regularization applies with any kind of wavelet functions. We compare the performance of the regularized and non-regularized compression algorithms for Haar and spline filters. We show that the point spread function can be used as an additional constraint in the restoration of astronomical objects with complex shape. We present a regularized decompression scheme that includes filtering, compression and image deconvolution in a multiresolution framework.
Astronomical images currently provide large amounts of data. Lossy compression algorithms have recently been developed for high compression ratios. These compression techniques introduce distortion in the compressed images and for high compression ratios, a blocking effect appears. A new algorithm based on the regularization theory is proposed for the restoration of such lossy compressed astronomical images. The image is restored scale by scale in a multiresolution scheme and the information lost during the compression is recovered by applying a regularization constraint. The experimental results show that the blocking effect is reduced and some measurements made on a simulated image show that the astrometic and photometric properties of the restored images are improved.
A multiscale vision model based on a pyramidal wavelet transform is described in the present paper. The pyramidal wavelet algorithm is modified in order to satisfy a correct sampling at each scale. Objects are defined by trees of statistically significant coefficients in the wavelet transform space. The object images are then restored using the conjugate gradient method. By comparing with the model based on the a trous algorithm, tests on simulated and real images show that this model presents a good compromise between analysis quality and the memory space and computation time needed.
The analysis of SAR images requires in a first step to reduce the speckle noise which is due to the coherent character of the RADAR signal. The application of the minimum variance bound estimator leads to process the energy image instead of the amplitude one for the reduction of this multiplicative noise. The proposed analyzing methods are based on a multiscale vision model for which the image is only described by its significant structural features at a set of dyadic scales. The multiscale analysis is performed by a redundant discrete wavelet transform, the a trous algorithm. The filtering algorithm is interactive. At each step we compute the ratio between the observed energy image and the restored one. We detect at each scale the significant structures, by taking into account the exponential probability distribution function of the energy for the determination of the significant wavelet coefficients. The ratio is restored from its significant coefficients, and the restored image is updated. The iterations are stopped when any significant structure is detected in the ratio. Then, we are interested to extract and to analyze the contained objects. The multiscale analysis allows us an approach well adapted to diffused objects, without contrasted edges. An object is defined as a local maximum in the wavelet transform space (WTS). All the structures form a 3D connected set which is hierarchically organized. This set gives the description of an object in the WTS. The image of each object is restored y an inverse algorithm. The comparison between images taken at different epochs is done using the multiscale vision model. THat allows us to enhance the features at a given scale which have significantly varied. The correlation coefficients between the structures detected at each scale are far form the ones obtained between the pixel energy. For example, this method is very suitable to detect and to describe faint large scale variations.
We describe a new method for the computation of a disparity map between two stereoscopic satellite images. The disparities are computed along the x and y axis respectively at each point of the image, without the use of the epipolarity condition. In order to compute the disparity field, first a set of ground control points is detected in both images. Next, a mapping of the disparities over the entire image is done using the kriging method. Finally, the two stereoscopic images are geometrically registered using the disparity maps.
We describe a new method for the computation of a disparity map between two stereoscopic satellite images. The disparities are computed along the x and y axis respectively at each point of the image, without the use of the epipolarity condition. In order to compute the disparity field, first a set of ground control points is detected in both images. Next, a mapping of the disparities over the entire image is done using the Kriging method. Finally, the two stereoscopic images are geometrically registered using the disparity maps.
The notion of a multiresolution support is introduced. This is a sequence of boolean images, related to significant pixels at each of a number of resolution levels. The multiresolution support is then used for noise suppression, in the context of iterative image restoration. Algorithmic details and examples illustrate this approach.
Geometrical registration of two images is nowadays a current and an important step in remote sensing before any further processing and interpretation of the data. Geometrical registration of images with a different ground resolution is useful for a better comprehension of dynamical processes (i.e. deforestation, desertification), as well as for extrapolating models of interpretation obtained on small regions to large areas. We present in this paper a procedure for a fully automatic registration of remotely sensed data based on the multiresolution decomposition of the images with the use of the wavelet transform. We have successfully applied this technique to register images having the same ground resolution, (SPOT HRV and LANDSAT MSS), and different ground resolutions (SPOT HRV with LANDSAT MSS, LANDSAT TM with SPOT HRV).
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