The analysis of SAR images requires to reduce the speckle noise due to the coherent character of the radar signal. This noise is multiplicative, which often leads to logarithmically transform the modulus. A bias, which depends on the local homogeneity is introduced, and the noise is amplified. The minimum variance estimator leads to process the energy image instead of the modulus one for reducing this multiplicative noise. The proposed methods are based on a multiscale vision model for which the image is only described by its significant structural features on a set of scales. The multiscale analysis is performed by a redundant discrete wavelet transform, the a trous algorithm. We have determined the distribution law of the wavelet coefficient of the energy in the case of a statistically uniform image. This allows us to extract the significant wavelet coefficients, according to the noise. A filtering algorithm is derived by taking into account only these coefficients. This method is extended to a co-addition of SAR images. Taking into account the multiresolution support obtained from the thresholding in the wavelet transform space (WTS), the image is decomposed into a set of objects, by a 3D segmentation in WTS.

The large-scale distribution of galaxies in the Universe exhibits structures at various scales, these so-called groups, clusters, and superclusters of galaxies being more or less hierarchically organized. A specific vision model is needed in order to detect, describe, and classify each component of this hierarchy. To do so, we have developed a multiscale vision model based on an unfolding into a scale space allowing us to detect structures of different sizes. A discrete wavelet transform is done by the a trous algorithm. The algorithm is implemented for astronomical images and also for lists of object positions, currently called catalogues in astronomical literature. Some applications on astrophysical data of cosmological interest are briefly described: (1) inventory procedures for galaxy counts on wide-field images, (2) processing of X-ray cluster images lending to the analyses of the total matter distribution, and (3) detection of large-scale structures from galaxy counts, From the analyses of N-body simulations we show that the vision model from the wavelet transform provides a new statistical indicator on cosmological scenarios.