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 performances of the regularized and non-regularized compression algorithms for Haar and spline filters. We show that the point spread function can be used;Is 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.