Efficient orthogonal realization of image transforms

Gerben J. Hekstra; Ed F. A. Deprettere; Richard R. Heusdens; Zhiqiang Zeng

doi:10.1117/12.255448

22 October 1996 Efficient orthogonal realization of image transforms

Gerben J. Hekstra, Ed F. A. Deprettere, Richard R. Heusdens, Zhiqiang Zeng

Proceedings Volume 2846, Advanced Signal Processing Algorithms, Architectures, and Implementations VI; (1996) https://doi.org/10.1117/12.255448
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

One can find ample examples in the literature of implementations of image transforms such as the discrete cosine transform and the lapped orthogonal transform. The objective is invariantly the minimization of the number of multiplies and adds. Of course, a reduction of operations from O(N²) to O(NlogN) is a great achievement, yet the cost resulting from non-local communication and operation accuracy is seldom taken into account. Especially accuracy needed to preserve the dominant property of the transforms may turn out to be expensive. These properties are that the transforms are a collection of highly structured orthonormal basis functions and the first concern should be to preserve these properties by enforcing them through a decomposition of the transforms in terms of inexpensive elementary operations which can be inaccurate without violating the global properties. This paper presents a decomposition of image transforms into a network 2 X 2 so-called fast rotations which are inexpensive and orthonormal within the accuracy required by the application. The network results from a recursive decomposition which turns out to be applicable for most of the popular transforms. But even transforms that do not allow such a decomposition can be efficiently implemented as illustrated in this paper. Compression of X-ray image series with the transforms implemented as proposed in this paper has shown that high accuracy of low bit rates can be achieved at a small implementation cost. Real time compression and coding of image sequence giving rise to Gbit/sec datarates is achievable using a single chip and transforms of any size between 8 X 8 and 32 X 64.

Citation Download Citation

Gerben J. Hekstra, Ed F. A. Deprettere, Richard R. Heusdens, and Zhiqiang Zeng "Efficient orthogonal realization of image transforms", Proc. SPIE 2846, Advanced Signal Processing Algorithms, Architectures, and Implementations VI, (22 October 1996); https://doi.org/10.1117/12.255448

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