Matrix Form of Wavelet Transformation and a Boundary Revision Algorithm

摘要

This paper mainly examine the matrix property of WT in numerical image processing. First by comparing WT matrix with DFT matrix, we have a better understanding over WT in its digital signal application, Next we give a vivid description of wavelet's orthogonality through the corresponding matrix relationship, We also point out that the famous pyramid algorithm in numerical image processing is in essence a special similar-transform, and then give a divided-matrix version of it, In this way, the algorithm's whole procedure and employing techniques become even more clearly and easy to understand, At last, with the aid of WT matrix, a boundary revision algorithm is proposed, Not only in theory, but also in the practice of numerical image processing, the newly-proposed approach performs better than that periodic-extended one in resolving WT's border problem.