Dictionary learning for signals in additive noise with generalized Gaussian distribution

Abstract

We propose a dictionary learning (DL) algorithm for signals in additive noise with generalized Gaussian distribution (GGD) by redesigning three key components used in DL for Gaussian signals: (i) the orthogonal matching pursuit algorithm, (ii) the approximate K-SVD algorithm and (iii) the information theoretic criteria. In experiments with simulated data, we show that the performance of the new algorithm is higher or equal to the performance of the DL algorithms for signals in Laplacian noise. We also discuss how the shape parameter of the GGD noise can be estimated. For image data, we examine the relationship between the complexity of the DL model and the errors obtained on the test set. This provides guidance on the values of the shape parameter that should be employed in image modeling.