Optimum design of vector-quantized multiresolution codecs

The wavelet transform has recently emerged as a powerful tool for non-stationary analysis. Its discrete version is closely related to a dyadic filter bank which has been used in image processing. In order to obtain a higher data compression we use vector quantizers. We compute the mean squared reconstruction error (MSE) which depends on N, the number of the entries in each codebook, and k, the length of each codeword (that is, the average bit rate) and on the dyadic filter bank coefficients. We form this MSE measure in terms of the equivalent scalar quantization model and find the optimum FIR filter coefficients for each equivalent channel in the dyadic tree subband structure for a given bit rate, given filter length, and given input signal correlation model. Specific design examples are worked out for 4-tap filter in a 3-stage dyadic paraunitary filter bank structure. Theoretical results are confirmed by extensive Monte Carlo simulation