l(1)-K-SVD: A robust dictionary learning algorithm with simultaneous update

Mukherjee, Subhadip and Basu, Rupam and Seelamantula, Chandra Sekhar (2016) l(1)-K-SVD: A robust dictionary learning algorithm with simultaneous update. In: SIGNAL PROCESSING, 123 . pp. 42-52.

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Abstract

We develop a new dictionary learning algorithm called the l(1)-K-svp, by minimizing the l(1) distortion on the data term. The proposed formulation corresponds to maximum a posteriori estimation assuming a Laplacian prior on the coefficient matrix and additive noise, and is, in general, robust to non-Gaussian noise. The l(1) distortion is minimized by employing the iteratively reweighted least-squares algorithm. The dictionary atoms and the corresponding sparse coefficients are simultaneously estimated in the dictionary update step. Experimental results show that l(1)-K-SVD results in noise-robustness, faster convergence, and higher atom recovery rate than the method of optimal directions, K-SVD, and the robust dictionary learning algorithm (RDL), in Gaussian as well as non-Gaussian noise. For a fixed value of sparsity, number of dictionary atoms, and data dimension, l(1)-K-SVD outperforms K-SVD and RDL on small training sets. We also consider the generalized l(p), 0 < p < 1, data metric to tackle heavy-tailed/impulsive noise. In an image denoising application, l(1)-K-SVD was found to result in higher peak signal-to-noise ratio (PSNR) over K-SVD for Laplacian noise. The structural similarity index increases by 0.1 for low input PSNR, which is significant and demonstrates the efficacy of the proposed method. (C) 2015 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Publication:	SIGNAL PROCESSING
Publisher:	ELSEVIER SCIENCE BV
Additional Information:	Copy right for this article belongs to the ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Keywords:	Dictionary learning; Sparsity; Noise robustness; l(1)-minimization; Iteratively reweighted least-squares (IRLS) algorithm; l(1)-K-SVD
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	07 Apr 2016 05:07
Last Modified:	07 Apr 2016 05:07
URI:	http://eprints.iisc.ac.in/id/eprint/53601

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