基于组稀疏表示和加权全变分的图像压缩感知重构

传统的基于组稀疏表示(group sparse representation, GSR)的压缩感知(compressd sensing, CS)重构算法利用信号的稀疏性和非局部相似性来重构图像信号,但没有充分考虑图像的局部平滑特性,影响了算法的重构性能。考虑信号的稀疏性、非局部相似性、平滑性3种先验信息,提出一种基于GSR和加权全变分(weighted total variation, WTV)的图像CS重构算法,并针对传统的WTV采用全局加权会引入错误的纹理以及边缘状伪影的问题,利用一种新的WTV策略,只对图像的高频分量设置权重来保证图像重构质量。此外，针对硬阈值迭代法忽略低频的主分量系数,采用硬阈值-模平方方法来更好地保护非主分量系数。实验表明,相同采样率下,所提算法的峰值信噪比比非局部正则化全变分和基于GSR的CS算法平均分别提高5.4 dB和0.62 dB,验证了所提算法有效保护图像的细节信息。

Image compressive sensing reconstruction via group sparse representation and weighted total variation

The traditional compression sensing (CS) reconstruction algorithm based on group sparse representation (GSR) uses the sparsity and nonlocal similarity of the signal to reconstruct the image signal. However, the local smoothness of the image is not sufficiently consiclered, which affects the reconstruction performance of the algorithm. Considering the three prior informations of signal sparsity, nonlocal similarity and smoothness, an image CS reconstruction algorithm based on GSR and weighted total variation (WTV) is proposed. Aiming at the problem that global weighting will introduce wrong texture and edge artifacts for the traditional WTV, a new WTV strategy only sets the weight of high frequency cmponet of image is used to protect the image reconstruction quality. In addition, aiming at the problem that the hard threshold iteration ignores the low frequency principal component coefficient, the hard threshold modulus square method is used to better protect the non-principal component coefficient. Experimental results show that the peak signal to noise ratio of the proposed algorithm is improved 5.4 dB and 0.62 dB compared with the total variation nonlocal regularization and CS algorithm based on GSR at the same sampling rate respectively, which proves that the proposed algorithm effectively protects the details of the image.