Learning dictionary for efficient signal compression

Abstract

We consider the problem of learning dictionaries for data compression. Different from ordinary learning methods, the objective is to design a dictionary such that the signal has a low entropy representation in the basis of the dictionary, rather than giving a sparse or low-energy representation. To achieve this goal, we need to consider the effect of quantization on the rate-distortion curve as well as an estimation of the distributions of the coefficients. Based on this probability estimation, the coefficients are computed, quantized and then entropy-coded. As such, we have developed algorithms for different classes of dictionaries; orthonormal, union of orthonormals and general dictionaries with unit-norm atoms, to iteratively learn the dictionary and the distribution models of the coefficients. A mixture of Gaussians is adopted to estimate the probability and is updated using the expectation maximization algorithm together with the dictionary learning. Simulation results on the real seismic data show the effectiveness of the proposed algorithm compared to ordinary dictionary learning methods.