cient orthogonal realization of image transformsGerben

| One can nd 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(N 2)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 rst 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 of 2 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 eeciently implemented as illustrated in this paper. Compression of X-ray image series with the transforms implemented as proposed in the paper has shown that high accuracy at low bit rates can be achieved at a small implementation cost. Real time compression and coding of image sequences giving rise to Gbit/sec datarates is achievable using a single chip and transforms of any size between 8 8 and 32 64.