Posterior Information-Based Image Measurement Matrix Optimization
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Posterior Information-Based Image Measurement Matrix Optimization Hui Zhao1
· Cheng Huang1 · Chao Sun1 · Yanzhou Liu1 · Tianqi Zhang1
Received: 3 September 2019 / Revised: 7 October 2020 / Accepted: 15 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In order to enhance the robustness of image compression sensing system and reduce the mutual coherence between measurement matrix and sparse basis, this paper proposes an image measurement matrix optimization algorithm based on posterior information. Based on the traditional measurement matrix optimization model, the proposed algorithm considers the image reconstruction error from the OMP algorithm and uses it as a regular term. Matrix F-norm expansion and singular value decomposition are used to reduce the computational complexity and ensure the convergence of algorithm. Besides, the gradient matrix method is used to iteratively solve the measurement matrix. The proposed measurement matrix optimization model makes full use of the reconstruction error information of the image itself, not only improves the robustness of image compression sensing system, but also reduces the mutual coherence between the measurement matrix and the sparse basis. Experiments results show that compared with the state-of-the-art measurement matrix optimization algorithms, the proposed algorithm can reduce the average correlation coefficient more effectively, and the peak signal-to-noise ratio of the image can be increased by up to 1.2 dB. Keywords Image measurement matrix · Mutual coherence · Posterior information · Robustness
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Hui Zhao [email protected] Cheng Huang [email protected] Chao Sun [email protected] Yanzhou Liu [email protected] Tianqi Zhang [email protected]
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School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Circuits, Systems, and Signal Processing
1 Introduction Compressed sensing (CS) theory [3, 4, 7] breaks through the limitation of the traditional Nyquist sampling theorem and achieves the simultaneous acquisition and compression of image data. In CS, the sparsity is an essential requirement for the signals; however, it is not sufficient for a signal to be reconstructed successfully. Choosing a suitable measurement matrix is especially important in CS which ensures an exact recovery of the signal from the linear measurements with high probability. Research shows that the performance of measurement matrix is mainly based on the following three properties: the null space property (NSP), the restricted isometry property (RIP), and the coherence property. Cohen A et al. [4] proposed the NSP and proved that the measurement matrix in CS should be satisfied with NSP in order to ensure the accurate reconstruction. However, the proposed NSP do not take into account the effects of noise. Hence, Candès et al. [5] proposed the RIP for noisy environments and showed that the measurement matrix satisfying the RIP is robust to noise. Actually, to veri
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