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

Subhadip Mukherjee, Rupam Basu, Chandra Sekhar Seelamantula

Abstract: Highlights•We propose an algorithm, which we refer to as ℓ1-K-SVD, to learn data-adaptive dictionaries in the presence of non-Gaussian noise. The fundamental idea behind the algorithm is to replace the usual ℓ2-norm-based data-fidelity metric with ℓ2-norm, and minimize it using iteratively reweighted least-squares (IRLS).•In the dictionary update stage of ℓ1-K-SVD, we adopt a simultaneous updating strategy similar to K-SVD, that is found to result in faster convergence.•We elucidate how the proposed idea can be extended to minimize the ℓp data error, where 0<p<1<math><mn is="true">0</mn><mo is="true">&lt;</mo><mi is="true">p</mi><mo is="true">&lt;</mo><mn is="true">1</mn></math>, in scenarios where one has to deal with sparse/impulsive noise contamination.•We demonstrate experimentally that the ℓ1-K-SVD algorithm results in faster convergence and more accurate atom detection performance compared with the state-of-the-art algorithms. It is also shown that ℓ1-K-SVD is more suitable than the competing algorithms, when the training dataset contains fewer examples.•As an application, we deploy the algorithm for image denoising. It is found that ℓ1-K-SVD results in peak signal-to-noise ratio (PSNR) values that are on par with the K-SVD algorithm, but the improvement in structural similarity index (SSIM) over K-SVD is approximately 0:08–0:10, indicating its efficacy in preserving the structural content of images.