A Novel Nonlinear Dictionary Learning Algorithm Based on Nonlinear-KSVD and Nonlinear-MOD

Abstract

AbstractAt present, scholars have proposed numerous linear dictionary learning methods. In the field of dictionary learning, linear dictionary learning is the most commonly applied method, and it is typically utilized to address various signal processing problems. However, linear dictionary learning cannot meet the requirements of nonlinear signal processing, and the nonlinear signals cannot be accurately simulated and processed. In this study, we first construct a nonlinear dictionary learning model. Then we propose two algorithms to solve the optimization problem. In the dictionary update stage, based on the K-SVD and the method of optimal directions (MOD), we design nonlinear-KSVD (NL-KSVD) and nonlinear-MOD (NL-MOD) algorithms to update the dictionary. In the sparse coding stage, the nonlinear orthogonal matching pursuit (NL-OMP) algorithm is designed to update the coefficient. Numerical experiments are used to verify the effectiveness of the proposed nonlinear dictionary learning algorithms.KeywordsSparse representationDictionary learningNonlinearNonlinear-KSVDNonlinear-MOD