Subband Decomposition Filter Bank Design from the Inverse Block Wavelet Transform Using Lms Optimization

Block Wavelet Transforms (BWTs) are orthogonal matrix transforms that can be obtained from orthogonal subband filter banks. They were initially generated to produce matrix transforms which may carry nice properties inheriting from wavelets, as alternatives to DCT and similar matrix transforms. Although the construction methodology of BWT is clear, the reverse operation was not researched. In certain cases, a desirable matrix transform can be generated from available data using the Karhunen–Loeve transform (KLT). It is, therefore, of interest to develop a subband decomposition filter bank that leads to this particular KLT as its BWT. In this work, this dual problem is considered as a design attempt for the filter bank, hence the wavelets. The filters of the decomposition are obtained using a constrained least mean square (LMS) search on the parameterized filter coefficient domain.