Robust Tensor Approximation With Laplacian Scale Mixture Modeling for Multiframe Image and Video Denoising

Sparse and low-rank models have been widely studied in the literature of signal processing and computer vision. However, as the dimensionality of dataset increases (e.g., multispectral images, dynamic MRI images, and video sequences), the optimality of vector and matrix-based data representations and modeling tools becomes questionable. Inspired by recent advances in sparse and low-rank tensor analysis, we propose a novel robust tensor approximation (RTA) framework with the Laplacian Scale Mixture (LSM) modeling for three-dimensional (3-D) data and beyond. Our technical contributions are summarized as follows: first, conceptually similar to robust PCA, we consider its tensor extension here—i.e., low-rank tensor approximation in the presence of outliers modeled by sparse noise; second, built upon previous work on tensor sparsity, we propose to model tensor coefficients with an LSM prior and formulate a maximum a posterior estimation problem for noisy observations. Both unknown sparse coefficients and hidden LSM parameters can be efficiently estimated by the method of alternating optimization; and third, we have derived closed-form solutions for both subproblems and developed computationally efficient denoising techniques for multiframe images and video. Experimental results on three datasets have shown that the proposed algorithm can better preserve the sharpness of important image structures and outperform several existing state-of-the-art image/video denoising methods (e.g., BM4D/VBM4D and tensor dictionary learning).