A relaxation approach to computation of second-order wedgelet transform with application to image compression

• We will use non-linear least squares to approximate image by relaxed second-order wedgelets.
• Rate-distortion analysis for tree-based coding of second-order platelets will be presented.
• Performance will be evaluated in compression of both natural images and disparity images.
• Our method is fast and provides better quality comparing to moments-based approach.

Wedgelet approximation of an image block is classically obtained by an exhaustive search in a predefined dictionary where representation error of all basis elements is examined. Although this strategy leads to the selection of the best atom, due to intolerable computational complexity, the practical applications of classical wedgelet transform is severely limited. In this paper, by employing non-linear least squares and discontinuity relaxation, we suggest an iterative estimation procedure to speed up computation of the second-order wedgelet transform. Accuracy and speed of this wedgelet computation approach is studied by an image compression framework which utilizes both wedgelets and platelets to approximate image blocks. The M-term approximation of second-order wedgelets and second-order platelets is studied in this framework and is concluded to be O(M−3)O(M−3). Our proposed wedgelet computation surpasses the state of the art Moments-based Second-order Wedgelet Transform in accuracy while achieving roughly the same speed. It also achieved noticeable quality improvement over JPEG2000 in compression of disparity images (5 dB at 0.15 bpp).

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