Compressive Sensing of Color Images Using Nonlocal Higher Order Dictionary

TL;DR

This paper introduces a novel compressive sensing method for color images that leverages nonlocal similarities and higher order dictionaries to improve reconstruction quality, outperforming existing techniques.

Contribution

It proposes a nonlocal higher order dictionary learning approach using tensor decompositions for better color image recovery from compressive measurements.

Findings

Achieves superior reconstruction quality compared to state-of-the-art methods.

Effectively utilizes nonlocal similarities in color images.

Demonstrates robustness in experimental results.

Abstract

This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal similarities inherently existing in images by treating each patch of a color image as a 3D tensor consisting of not only horizontal and vertical but also spectral dimensions. A group of nonlocal similar patches form a 4D tensor for which a nonlocal higher order dictionary is learned via higher order singular value decomposition. The multiple sub-dictionaries contained in the higher order dictionary decorrelate the group in each corresponding dimension, thus help the detail of color images to be reconstructed better. Furthermore, we promote sparsity of the final solution using a sparsity regularization based on a weight tensor. It can distinguish those coefficients of the sparse representation generated by the higher order dictionary which are expected to have large magnitude from the others in the optimization. Accordingly, in the iterative solution, it acts like a weighting process which is designed by approximating the minimum mean squared error filter for more faithful recovery. Experimental results confirm improvement by the proposed method over the state-of-the-art ones.