Reversible integer-to-integer (I2I) mapping of orthonormal transforms are vital for developing lossless coding with scalable decoding functionalities. A general framework for reversible I2I mapping of N-point, where N...
详细信息
Reversible integer-to-integer (I2I) mapping of orthonormal transforms are vital for developing lossless coding with scalable decoding functionalities. A general framework for reversible I2I mapping of N-point, where N is a positive integer power of 2, orthonormal block transforms using recursive factorization of such transform matrices and the lifting scheme is presented. Designs include the discrete cosine transform (dct) that maps integers to integers (I2I-dct), the discrete sine transform that maps integers to integers (I2I-DST) and the Walsh-Hadamard transform that maps integer to integers (I2I-WHT). The main significant feature of these designs is that the transform coefficients are normalized according to the conventional scaling factors, which is vital for embedded coding, while preserving the integer-to-integer mapping and perfect reconstruction. This makes these transforms usable in both lossless and lossy image coding, especially in scalable lossless coding. These generic N-point design of the above transforms enables evaluating the effect of block sizes of such transforms in lossless coding. The performance is evaluated in terms of lossless image and video coding, quality scalable decoding, complexity and lifting step rounding effects. (c) 2006 Elsevier B.V. All rights reserved.
integerdcts have a wide range of applications in lossless coding, especially in image compression. An integer-to-integer dct of radix-2-length n is a nonlinear, left-invertible mapping, which acts on Z(n) and approxi...
详细信息
integerdcts have a wide range of applications in lossless coding, especially in image compression. An integer-to-integer dct of radix-2-length n is a nonlinear, left-invertible mapping, which acts on Z(n) and approximates the classical discrete cosine transform (dct) of length n. All known integer-to-integer dct-algorithms of length 8 are based on factorizations of the cosine matrix C-8(II) into a product of sparse matrices and work with lifting steps and rounding off. For fast implementation one replaces floating point numbers by appropriate dyadic rationals. Both rounding and approximation leads to truncation errors. In this paper, we consider an integer-to-integer transform for (2 x 2) rotation matrices and give estimates of the truncation errors for arbitrary approximating dyadic rationals. Further, using two known integer-to-integer dct-algorithms, we show examplarily how to estimate the worst-case truncation error of lifting based integer-to-integer algorithms in fixed-point arithmetic, whose factorizations are based on (2 x 2) rotation matrices.
暂无评论