Yves Bobichon

A Regularized Image Restoration Algorithm for Lossy Compression in Astronomy

Astronomical images currently provide large amounts of data. Lossy compression algorithms have recently been developed for high compression ratios. These compression technique introduce distortion in the compressed images and for high compression ratios, a blocking effect appears. We propose a modified compression algorithm based on the hcompress scheme, and we introduce a new decompression method based on the regularization theory The image is restored scale by scale in a multiresolution scheme and the information lost during the compression is recovered by applying a Tikhonov regularization constraint. The experimental results show that the blocking effect is reduced and some measurements made on a simulated image show that the astrometric and the photometric properties of the restored images are improved.

Regularized multiresolution methods for astronomical image enhancement

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.

Digital image compression in astronomy morphology or wavelets

A wide-fleld astronomical image is often considered as a set of quasi point-like sources spread on a slow-varying backgound. With this model, the image is described as a set of connected flelds. We have to code the fleld positions, the fleld boundaries and their pixel values. It exists difierent methods for coding this information, they are mainly connected to the Mathematical Morphology. The flelds may be coded from their contours, their binary skeletons or the grey-tone ones. On difierent examples, we show that the morphological skeleton transformation in general gives us the best results. The H-transform is a two-dimensional generalization of the Haar transform, a typical wavelet transform. It is to-day often used for compressing astronomical images. Blocking efiects appear in the restored image. The quality of the restoration is improved by introducing in the inverse H-transform scheme an a priori knowledge on the solution which consists to choose the smoothest image at each scale. These two difierent approaches lead to high compression rates on classical astronomical images. In fact, the images are very difierently described. With the morphological methods, the highest compression rates are obtained if the images is composed only of small point-like sources, while the wavelet transform is well adapted to the compression of images with information at difierent scales. So the best compression technique is directly connected to the image modelling. The use of compression methods depends also of the further application. A perfect solution does not exist for image compression, we must take into account the image texture and the futur use.

The analysis of SAR images by multiscale methods

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.

Multiscale methods applied to the analysis of SAR images

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.

Restoration of lossy compressed astronomical images

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 astrometric and the photometric properties of the restored images are improved.

Regularization constraints in lossy compressed astronomical image restoration

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.