Compressed Sensing Image Restoration Based on Non-local Low Rank and Weighted Total Variation
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摘要: 为准确有效地实现自然图像的压缩感知(CS)重构，该文提出一种基于图像非局部低秩(NLR)和加权全变分(WTV)的CS重构算法。该算法考虑图像的非局部自相似性(NSS)和局部光滑特性，对传统的全变分(TV)模型进行改进，只对图像的高频分量设置权重，并用一种差分曲率的边缘检测算子来构造权重系数。此外，算法以改进的TV模型与NLR模型为约束构建优化模型，并分别采用光滑非凸函数和软阈值函数来求解低秩和全变分优化问题，很好地利用了图像的自身性质，保护了图像的细节信息，并提高了算法的抗噪性和适应性。仿真结果表明，与基于NLR的CS算法相比，相同采样率下，该文所提算法的峰值信噪比最高可提高2.49 dB，且抗噪性更强，验证了算法的有效性。Abstract: In order to reconstruct natural image from Compressed Sensing(CS) measurements accurately and effectively, a CS image reconstruction algorithm based on Non-local Low Rank(NLR) and Weighted Total Variation(WTV) is proposed. The proposed algorithm considers the Non-local Self-Similarity(NSS) and local smoothness in the image and improves the traditional TV model, in which only the weights of image’s high-frequency components are set and constructed with a differential curvature edge detection operator. Besides, the optimization model of the proposed algorithm is built with constraints of the improved TV and the non-local low rank model, and a non-convex smooth function and a soft thresholding function are utilized to solve low rank and TV optimization problems respectively. By taking advantage of them, the proposed method makes full use of the property of image, and therefore conserves the details of image and is more robust and adaptable. Experimental results show that, compared with the CS reconstruction algorithm via non-local low rank, at the same sampling rate, the Peak Signal to Noise Ratio(PSNR) of the proposed method increases by 2.49 dB at most and the proposed method is more robust, which proves the effectiveness of the proposed algorithm.
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表 1 基于非局部低秩和加权全变分的图像压缩感知重构算法(NLR-WTV)
输入： 从原始图像${{u}}$采样得到的压缩感知测量值${{y}}$ 初始化：${{{u}}_0} = {{{Φ}} ^{\rm{T}}}{{y}}$, ${{a}}$, ${{b}}$, ${{c}}$, ${\lambda _1}$, ${\lambda _2}$, ${\mu _1}$, ${\mu _2}$； Outer loop for $k{\rm{ }} = 1, {\rm{ }}2, ·\!·\!·, K$ (1) 根据块匹配法找到图像各相似像素点的位置； (2) 根据式(6)、式(7)和式(8)计算图像的低频分量${{{u}}_{\rm{L}}}$和高频分
量${{{u}}_{\rm{R}}}$；(3) if $k \le {K_{{0}}}$, ${{{w}}_i} = 1$ else 根据式(9)计算${{{w}}_i}$；end if Inner loop for $t{\rm{ }} = 1, {\rm{ }}2, ·\!·\!·, T\;$ (a) 根据式(17)计算${{{L}}_i}^{(k + 1)}$； (b) 根据式(19)计算${{{x}}^{(k + 1)}}$； (c) 分别根据式(21)和式(22)计算图像在低频和高频的梯度
${{{z}}_1}^{(k + 1)}$和${{{z}}_2}^{(k + 1)}$；(d) 根据式(25)计算${{{u}}^{(k + 1)}}$； end for 根据式(14)更新${{a}}$, ${{b}}$和${{c}}$； end for 输出：重构图像${ {{ u} } \!\,\!\! { { {\widehat} }= { {{u} }^{(k + 1)} }$ 
下载: 导出CSV
表 2 不同算法重构图像的PSNR(dB)和SSIM比较
采样率 算法 性能指标 Monarch Barbara Lena Boats Parrots Cameraman 5% TVAL3 PSNR 20.06 19.79 23.08 22.38 22.87 22.89 SSIM 0.508 0.412 0.560 0.543 0.593 0.605 BM3D-CS PSNR 22.73 21.34 24.12 23.31 24.13 23.76 SSIM 0.642 0.523 0.693 0.610 0.692 0.658 TVNLR PSNR 23.02 22.65 25.41 24.79 25.89 24.39 SSIM 0.751 0.568 0.745 0.696 0.800 0.737 NLR-CS PSNR 26.38 27.94 30.64 29.81 31.71 25.38 SSIM 0.848 0.830 0.875 0.830 0.885 0.770 NLR-WTV PSNR 28.21 29.10 30.83 30.14 32.31 27.87 SSIM 0.883 0.862 0.879 0.857 0.891 0.817
下载: 导出CSV
表 3 算法测量值含噪的SSIM值比较
图像 算法 15 20 25 30 35 Monarch NLR-CS 0.374 0.550 0.748 0.874 0.939 NLR-WTV 0.387 0.569 0.761 0.890 0.948 Boats NLR-CS 0.276 0.452 0.672 0.824 0.904 NLR-WTV 0.281 0.466 0.681 0.844 0.927
下载: 导出CSV
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