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The matching pursuit algorithm has been successfully applied in many areas such as data compression and pattern recognition. The performance of matching pursuit is closely related to the selection of the dictionary. In this paper, we propose an algorithm to estimate the optimal dictionary distribution ratio and discuss the decay of the norm of residual signal in matching pursuit when the coefficients are quantized by a uniform scalar quantizer. It is proposed that if the approximation error E and the dimension of the space N are given, the optimal size of the dictionary and the optimal quantizer step should be obtained by minimizing the number of bits required to store the matching pursuit representation of any signal in the space to satisfy the error bound.