2017/11/26 by Khanh Quoc Dinh, Dinh, Khanh Quoc, Thuong Nguyen Canh +3
Computer Science · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #Image and Signal Denoising Methods #Image and Video Processing (eess.IV) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1711.09375
openalex publication_date 2017/11/26 · openalex created_date 2017/12/04 · openalex updated_date 2026/07/28
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.