Analysis dictionary learning based on max transvection function

Abstract

Analysis dictionary learning (ADL) aims to design dictionaries from training data based on an analysis sparse representation model. Sparse analysis model is an alternative model to the sparse synthesis model used in a variety of signal processing areas. This paper introduces a new ADL method called MAX-ADL algorithm used to estimate the dictionary directly from the noisy measurements. The algorithm employs MAX transvection function instead of 11-norm to construct the objective function, and then the analysis dictionary can be obtained by using a gradient method to iteratively optimize the objective function. Experimental results show that the algorithm performs well in natural image denoising.