Efficiency in Computing Correlation Matrix of Wavelet Coefficients by Exploiting Index Structure
نویسنده
چکیده
Abstract—Correlation matrices are ubiquitous throughout signal processing, networking and in many areas of science [1][2][3]. However, our study of the literature found that there is limited research on the structure of the indices in correlation matrix of wavelet coefficients, and in the exploitation of that structure to improve its computational efficiency. This article seeks to make a contribution in this area. Specifically, it will be shown that four matrices of the indices of the correlation matrix of wavelet coefficients may be visualized. The matrices are of a simple structure. Two of them consists of the scaling indices of the wavelet coefficients. They are related by the transpose operation. The other two matrices consists of shift indices and are also related by the transpose operation. By exploiting these facts, an efficient method for implementing the correlation matrix of wavelet coefficients may be realized.
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