Abstract
In this paper, we consider the dictionary learning problem for the sparse analysis model. A novel algorithm is proposed by adapting the simultaneous codeword optimization (SimCO) algorithm, based on the sparse synthesis model, to the sparse analysis model. This algorithm assumes that the analysis dictionary contains unit l2-norm atoms and learns the dictionary by optimization on manifolds. This framework allows multiple dictionary atoms to be updated simultaneously in each iteration. However, similar to several existing analysis dictionary learning algorithms, dictionaries learned by the proposed algorithm may contain similar atoms, leading to a degenerate (coherent) dictionary. To address this problem, we also consider restricting the coherence of the learned dictionary and propose Incoherent Analysis SimCO by introducing an atom decorrelation step following the update of the dictionary. We demonstrate the competitive performance of the proposed algorithms using experiments with synthetic data and image denoising as compared with existing algorithms.
Highlights
M ANY problems in signal processing can be regarded as inverse problems, for example, denoising [1], inpainting [2] and super-resolution [3]
Compared with the methods used in existing analysis dictionary learning (ADL) algorithms to avoid similar atoms, the decorrelation step applied in the Incoherent Analysis simultaneous codeword optimization (SimCO) algorithm has some advantages
The coherence limit of Incoherent Analysis SimCO and the correlation threshold of ASimCO-IKDVD were both set as 0.2, which was lower than the value used in the experiments with synthetic data, since we found that, in general, the image dictionaries learned have a relatively lower coherence, as compared with that in the synthetic case
Summary
M ANY problems in signal processing can be regarded as inverse problems, for example, denoising [1], inpainting [2] and super-resolution [3]. These problems aim to reconstruct original signals from their observed measurements. Two signal models to capture the sparse property of the signals have been proposed, namely, the sparse synthesis model [4] and sparse analysis model [5], [6]. The sparse analysis model has been extended to a more generalized model, referred to as the sparsifying transform model [7].
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