Statistical wavelet and filter bank optimization

We deal with three problems of optimal multiresolution representation and approximation of random processes. The first problem is that of finding a scaling function which will give the best approximation of a random process at a given scale. Approximation of inner products of ensemble members of a random process and a scaling function is the second problem. The approach to the above problems is similar. We first find the autocorrelation functions of errors, then their power spectra and finally, the variances. The third problem is the coding gain optimization of a subband coding system, more specifically, the choice of filters in a filter bank which maximizes the coding gain. An optimization algorithm is derived and an efficient implementation scheme proposed