Total Variation Regularized Reconstruction Algorithms for Block Compressive Sensing
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摘要: 针对分块压缩感知(BCS)重建图像质量较差问题，该文提出一种最小化l0范数的分块压缩感知全变差(TV)正则化迭代阈值图像重构算法(BCS-TVIT)。BCS-TVIT算法考虑图像的局部平滑、有界变差等性质，将最小化l0范数与图像的全变差TV正则项结合，构建目标函数。针对目标函数中l0范数项和分块测量约束项无法直接优化问题，采用迭代阈值法使重构图像l0范数最小化，并通过凸集投影保证满足约束条件，完成了目标函数的优化求解。实验表明，与基于l0范数最小化的分块压缩感知平滑投影算法(BCS-SPL)相比，BCS-TVIT算法重构图像峰值信噪比提高2 dB，能消除BCS-SPL的“亮斑”效应，且在视觉效果上明显优于BCS-SPL算法；与最小全变差算法相比，BCS-TVIT算法重构图像峰值信噪比提升1 dB，且能降低重构时间约2个数量级。Abstract: In order to improve the quality of reconstruction image by Block Compressed Sensing (BCS), a Total Variation Iterative Threshold regularization image reconstruction algorithm (BCS-TVIT) is proposed. Combining the properties of local smoothing and bounded variation of the image, BCS-TVIT uses the minimization l0 norm and total variation to construct the objective function. To solve the problem that l0 norm term and the block measurement constraint can not be optimized directly, the iterative threshold method is used to minimize the l0 norm of the reconstructed image, and the convex set projection is employed to guarantee the block measurement constraint condition. Experiments show that BCS-TVIT has better performance than BCS-SPL in PSNR by 2 dB. Meanwhile, BCS-TVIT can eliminate the " bright spot” effect of BCS-SPL, having better visual effect. Comparing with the minimum total variation, the proposed algorithm increases PSNR by 1 dB, and the reconstruction time is reduced by two orders of magnitude.
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表 1 各算法的重构PSNR (dB)
算法 采样率 0.1 0.2 0.3 0.4 0.5 BCS-SPL[6] 22.50 24.02 25.64 27.28 28.91 Barbara BCS-TV[15] 22.38 23.52 24.48 25.56 26.73 BCS-TVIT 22.67 24.41 26.46 28.73 31.58 BCS-SPL[6] 23.73 25.30 26.57 27.72 29.01 Lax BCS-TV[15] 23.75 26.05 28.06 29.93 31.77 BCS-TVIT 24.16 26.88 28.69 30.50 32.28 BCS-SPL[6] 25.54 27.10 28.27 29.39 30.59 Building BCS-TV[15] 25.45 27.99 29.88 31.69 33.50 BCS-TVIT 26.28 28.99 30.63 32.19 33.74 BCS-SPL[6] 23.37 25.32 26.80 28.31 29.56 Aerial BCS-TV[15] 23.22 25.63 27.67 29.42 31.41 BCS-TVIT 24.02 27.28 29.57 31.56 33.26 
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表 2 各算法的重构时间(s)
算法 采样率 0.1 0.2 0.3 0.4 0.5 BCS-SPL[6] 52 16 12 12 9 Barbara BCS-TV[15] 1210 1514 1759 2136 2690 BCS-TVIT 70 57 32 21 21 BCS-SPL[6] 35 28 27 25 24 Lax BCS-TV[15] 1179 1499 1737 2097 2638 BCS-TVIT 39 30 28 29 25 BCS-SPL[6] 51 35 25 24 21 Building BCS-TV[15] 1222 1539 1781 2153 2684 BCS-TVIT 53 38 26 26 22 BCS-SPL[6] 50 30 26 24 18 Aerial BCS-TV[15] 1170 1492 1750 2125 2666 BCS-TVIT 51 30 28 23 19
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