The use of overcomplete dictionaries, or frames, has receivedincreased attention in low-bit-rate compression. Several vectorselection algorithms, such as Matching Pursuit, Orthogonal MatchingPursuit and FOCUSS have been developed to get sparse representations ofsignals. In these algorithms, continuous valued coefficients are foundand subsequently quantized. The latter part can cause unwanted effectson the quality of the reconstructed signal. We propose an algorithm thatmerges the selection and quantization procedures by using 0-1 integerprogramming. The object is to minimize the distortion measured by the l1-norm, subject to a bound on the number of“ones” in a binary representation of the frame coefficients.This bound is an indirect measure of the bit rate. Our new algorithmfinds the globally optimal solution based on the abovementioned criteria
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