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A α-Divergence-Based Approach for Robust Dictionary Learning
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DOI：10.1109/TIP.2019.2922074.png)
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Abstract
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In this paper, a robust sequential dictionary learning (DL) algorithm is presented. The proposed algorithm is motivated from the maximum likelihood perspective on dictionary learning and its link to the minimization of the Kuliback-Leibler divergence. It is obtained by using a robust loss function in the data fidelity term of the DL objective instead of the usual quadratic loss. The proposed robust loss function is derived from the a-divergence as an alternative to the Kuliback-Leibler divergence, which leads to a quadratic loss. Compared to other robust approaches, the proposed loss has the advantage of belonging to class of redescending M-estimators, guaranteeing inference stability from large deviations from the Gaussian nominal noise model. The algorithm is obtained by solving a sequence of penalized rank-I matrix approximation problems, where the l(1)-norm is introduced as a penalty promoting sparsity and then using a block coordinate descent approach to estimate the unknowns. Performance comparison with similar robust DL algorithms on digit recognition, background removal, and gray-scale image denoising is performed highlighting efficacy of the proposed algorithm.
Keywords:
alpha-Divergence
dictionary learning
robust estimation
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