CREW: Compression with Reversible Embedded Wavelets

Abstract

Compression with Reversible Embedded Wavelets (CREW) is a unified lossless and lossy continuous-tone still image compression system. It is wavelet-based using a "reversible" approximation of one of the best wavelet filters. Reversible wavelets are linear filters with non-linear rounding which implement exact-reconstruction systems with minimal precision integer arithmetic. Wavelet coefficients are encoded in a bit-significance embedded order, allowing lossy compression by simply truncating the compressed data. For coding of coefficients, CREW uses a method similar to Shapiro's zerotree, and a completely novel method called Horizon. Horizon coding is a context based coding that takes advant.age of the spatial and spectral information available in the wavelet domain. CREW provides state of the art lossless compression of medical images (greater than 8 bits deep), and lossy and lossless compression of 8-bit deep images with a single system. CREW has reasonable software and hardware implement at ions.

Matrix factorizations for parallel integer transforms

“…The inverse transform is computed in a recursive way, like the forward elimination (2) where is any given rounding arithmetic, which can be rounding off at bits before or after the decimal point. The computation is similar to that for an upper TERM, except that the computational ordering of the inverse is upward.…”

“…This area has been explored for some time. The early work has concentrated on some simple integer-reversible transforms, such as S transform [1], TS transform [2], and S+P transform [3]. This has suggested a promising future for reversible integer mapping in image compression, region-of-interest coding, and unified lossy/lossless compression systems.…”

Optimal filter banks for multiple description coding: analysis and synthesis

“…Equations (33)- (35) show that minimization in (15) reduces to (36) where the minimum, now, is over all the distortions , , such that , . Now, combining (24), (25), and (36), we can see that the MD rate region of reduces, indeed, to the sum of the MD rate region of each component and that the original minimization problem reduces to (37) (38) (39) Thus, the problem now is to understand how each component should contribute to the total distortion to minimize the quantities in (37)- (39) or, stated in a different way, the problem is to understand how the rates , should be allocated to the various components to minimize (37)- (39). Using Lagrange multipliers we can construct the following three functionals:…”

Block TERM factorization of block matrices

“…Reversible integer transform (or integer mapping) is such a type of transform that maps integers to integers and realizes perfect reconstruction (PR). People started to work in this area long ago, and their early work, such as S transform [1] , TS transform [2] , S+P transform [3] , and color space transforms [4] , suggested a promising future of reversible integer mapping in image compression, region-of-interest (ROI) coding, progressive transmission, and unified lossy/lossless compression systems. However, to construct such integer transforms, they used to resort to some special skills.…”