Block Compressive Sensing Algorithm Based on Interleaving Extraction in Contourlet Domain
Open Cybernetics and Systemics Journal
We propose a block image compressive sensing algorithm based on interleaving extraction in Contourlet domain to improve the performance of image sparse representation and quality of reconstructed images. First, we propose the interleaving extraction scheme and partition an image into several sub-images using interleaving extraction. Second, we represent the sub-images in Contourlet domain and measure Contourlet sub-band coefficient matrices using different dimensional Gaussian random matrices.
... inally, we rebuild the sub-band coefficients with the orthogonal matching pursuit algorithm and conduct Contourlet inverse transform to reconstruct the original images. Experimental results show that the subjective visual effect and peak signal to noise ratio of the proposed algorithm are superior to those of the original compressive sensing algorithms under the same sampling rate. According to CS theory, the sparse representation, measurement matrix, and reconstruction algorithm are the three key elements in reconstructing the original signal from the sparse signal with high probability  . Currently, the commonly used sparse representation methods include discrete cosine transform (DCT), discrete wavelet transform (DWT), multi-scale geometric analysis, and redundant dictionaries  . DCT demonstrates poor time-frequency analytical performance; DWT experiences difficulty in reflecting image edge information accurately, and thus unable to meet the requirement of image sparse representation. In 2002, Do and Vetterli proposed Contourlet transform. Contourlet transform can represent the anisotropic characteristics and approximate singular curve of an image with minimal coefficients, effectively solving the sparse representation problem of high-dimensional space data. The image representation performance of Contourlet transform is better than most widely used wavelet transform methods, compensating for the lack of multi-directional wavelets [5, 6] . The CS reconstruction algorithm can be divided into three categories: convex relaxation method, greedy algorithm, and combinational algorithm. Convex relaxation algorithms include basis pursuit, interior-point method, gradient projection, and iterative threshold algorithm [7, 8] . Greedy algorithms include matching pursuit (MP), orthogonal MP This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/legalcode), which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.