Parametric dictionary learning using steepest descent

In this paper, we suggest to use a steepest descent algorithm for learning a parametric dictionary in which the structure or atom functions are known in advance. The structure of the atoms allows us to find a steepest descent direction of parameters instead of the steepest descent direction of the dictionary itself. We also use a thresholded version of Smoothed-ℓ⁰ (SL0) algorithm for sparse representation step in our proposed method. Our simulation results show that using atom structure similar to the Gabor functions and learning the parameters of these Gabor-like atoms yield better representations of our noisy speech signal than non parametric dictionary learning methods like K-SVD, in terms of mean square error of sparse representations.