Enhancement of Compressed Images by Optimal Shift-Invariant Wavelet Packet Basis

form-based (DCT-based) coding algorithms (e.g., the A novel postprocessing method based on the optimal shiftJPEG standard for still image compression [1]). The invariant wavelet packet (SIWP) representation and wavelet enhancement of compressed images has been regarded as shrinkage is proposed to enhance compressed images. At the a filtering problem. Various linear/nonlinear spaceencoder, the optimal (in the mean square error sense) SIWP invariant/space-variant filtering methods have been probasis is searched using a fast optimization algorithm and the posed [2–7]. These filtering methods often suffer from a location of the best basis in the entire SIWP library is transmittrade-off between reduction of coding artifacts and preserted as overhead information to the decoder. The selected basis vation of image features. On the other hand, enhancement is jointly optimal in terms of both the time-frequency tiling and of compressed images has also been viewed as a restoration the relative time-domain offset (or shift) between a signal and problem. Various restoration methods such as projection its wavelet packet representation. After the decoder reconstructs the compressed image, the postprocessor performs onto convex sets, constrained least-squares, and maximum wavelet shrinkage using the optimal basis. Due to its powerful a posteriori estimation, have been proposed [8–14]. Since adaptability, the method is shown to achieve a better trade-off these restoration methods are typically recursive, their between enhancement performance and decoder complexity computational complexity is high. than both the orthonormal wavelet transform and the undeciIn this paper, we study the enhancement problem from mated wavelet transform-based methods.  1998 Academic Press a new point of view; i.e., we formulate it as a noise reduction or de-noising problem. Wavelet shrinkage due to Donoho and Johnstone [15, 16] has been demonstrated to