Optimum design of vector-quantized subband codecs

The subband coding method holds a preeminent position for image compression. The discrete version of the wavelet transform is closely related to dyadic subband filter banks which have been used in image processing. Subband coding and vector quantization have been shown to be effective methods for coding images at low bit rates. 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 subband filter bank coefficients. We form this MSE measure in terms of the equivalent quantization model and find the optimum FIR filter coefficients for each equivalent channel in the subband structure for a given bit rate, given filter length, and given input signal correlation model. Specific design examples are shown for 4-tap filter paraunitary filter bank structure. Theoretical results are confirmed by extensive Monte Carlo simulation