Analysis of running discrete orthogonal transforms

Karen O. Egiazarian; Jaakko T. Astola

doi:10.1117/12.301384

1 February 1998 Analysis of running discrete orthogonal transforms

Proceedings Volume 3346, Sixth International Workshop on Digital Image Processing and Computer Graphics: Applications in Humanities and Natural Sciences; (1998) https://doi.org/10.1117/12.301384
Event: Sixth International Workshop on Digital Image Processing and Computer Graphics, 1997, Vienna, Austria

Abstract

In this paper, we investigate a problem in computation of running discrete orthogonal transforms (RDOT). Due to overlapping blocks of signals, the RDOT for the signal block j can be computed recurrently by representing it as sum of tow terms. The first one is obtained by a multiplication of the circular advance matrix (CAM) by the RDOT of signal block j-1, and the second term is the transform of the sparse vector, formed from the weighted differences of the samples discarded from the block j-1 and the incoming samples of the block j. The second term of this RDOT decomposition could be efficiently implemented using fast prunned algorithms. The computational complexity of the RDOT depend mainly on the implementation of the first term. General conditions on the transform matrix for which CAM is completely sparse is established.

Citation Download Citation

Karen O. Egiazarian and Jaakko T. Astola "Analysis of running discrete orthogonal transforms", Proc. SPIE 3346, Sixth International Workshop on Digital Image Processing and Computer Graphics: Applications in Humanities and Natural Sciences, (1 February 1998); https://doi.org/10.1117/12.301384

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