arXiv subjects

Subhadip Mukherjee

Publications and source records attributed to Subhadip Mukherjee.

38 records · Page 3Linked to original sources

arXiv2015

$\ell_1$-K-SVD: A Robust Dictionary Learning Algorithm With Simultaneous Update

We develop a dictionary learning algorithm by minimizing the $\ell_1$ distortion metric on the data term, which is known to be robust for non-Gaussian noise contamination. The proposed algorithm exploits the idea of iterative minimization of weighted $\ell_2$ error. We refer to this algorithm as $\ell_1$-K-SVD, where the dictionary atoms and the corresponding sparse coefficients are simultaneously updated to minimize the $\ell_1$ objective, resulting in noise-robustness. We demonstrate through experiments that the $\ell_1$-K-SVD algorithm results in higher atom recovery rate compared with the K-SVD and the robust dictionary learning (RDL) algorithm proposed by Lu et al., both in Gaussian and non-Gaussian noise conditions. We also show that, for fixed values of sparsity, number of dictionary atoms, and data-dimension, the $\ell_1$-K-SVD algorithm outperforms the K-SVD and RDL algorithms when the training set available is small. We apply the proposed algorithm for denoising natural images corrupted by additive Gaussian and Laplacian noise. The images denoised using $\ell_1$-K-SVD are observed to have slightly higher peak signal-to-noise ratio (PSNR) over K-SVD for Laplacian noise, but the improvement in structural similarity index (SSIM) is significant (approximately $0.1$) for lower values of input PSNR, indicating the efficacy of the $\ell_1$ metric.

cs.CV↗

arXiv2014

A Split-and-Merge Dictionary Learning Algorithm for Sparse Representation

In big data image/video analytics, we encounter the problem of learning an overcomplete dictionary for sparse representation from a large training dataset, which can not be processed at once because of storage and computational constraints. To tackle the problem of dictionary learning in such scenarios, we propose an algorithm for parallel dictionary learning. The fundamental idea behind the algorithm is to learn a sparse representation in two phases. In the first phase, the whole training dataset is partitioned into small non-overlapping subsets, and a dictionary is trained independently on each small database. In the second phase, the dictionaries are merged to form a global dictionary. We show that the proposed algorithm is efficient in its usage of memory and computational complexity, and performs on par with the standard learning strategy operating on the entire data at a time. As an application, we consider the problem of image denoising. We present a comparative analysis of our algorithm with the standard learning techniques, that use the entire database at a time, in terms of training and denoising performance. We observe that the split-and-merge algorithm results in a remarkable reduction of training time, without significantly affecting the denoising performance.

cs.LG↗