IEEE Trans Image Process. 2016 Jul;25(7):3126-3140. doi: 10.1109/TIP.2016.2562563. Epub 2016 May 3.
Compressive sensing (CS) is a recently emerging technique and an extensively studied problem in signal and image processing, which suggests a new framework for the simultaneous sampling and compression of sparse or compressible signals at a rate significantly below the Nyquist rate. Maybe, designing an effective regularization term reflecting the image sparse prior information plays a critical role in CS image restoration. Recently, both local smoothness and nonlocal self-similarity have led to superior sparsity prior for CS image restoration. In this paper, first, an adaptive curvelet thresholding criterion is developed, trying to adaptively remove the perturbations appeared in recovered images during CS recovery process, imposing sparsity. Furthermore, a new sparsity measure called joint adaptive sparsity regularization (JASR) is established, which enforces both local sparsity and nonlocal 3-D sparsity in transform domain, simultaneously. Then, a novel technique for high-fidelity CS image recovery via JASR is proposed-CS-JASR. To efficiently solve the proposed corresponding optimization problem, we employ the split Bregman iterations. Extensive experimental results are reported to attest the adequacy and effectiveness of the proposed method comparing with the current state-of-the-art methods in CS image restoration.
压缩感知（CS）是信号和图像处理中新兴的技术和广泛研究的问题，它为稀疏或可压缩信号的同时采样和压缩提供了一个新的框架，其速率远低于奈奎斯特率。也许，设计一个有效的正则化项来反映图像的稀疏先验信息，在 CS 图像恢复中起着至关重要的作用。最近，局部平滑和非局部自相似性都为 CS 图像恢复提供了优越的稀疏先验。在本文中，首先，提出了一种自适应曲波阈值准则，试图自适应地去除 CS 恢复过程中恢复图像中出现的扰动，施加稀疏性。此外，建立了一种新的稀疏度量方法，称为联合自适应稀疏正则化（JASR），它在变换域中同时强制局部稀疏和非局部 3-D 稀疏。然后，提出了一种基于 JASR 的高保真 CS 图像恢复的新方法——CS-JASR。为了有效地解决所提出的相应优化问题，我们采用了分裂布格曼迭代法。报告了广泛的实验结果，以证明与 CS 图像恢复中的现有最先进方法相比，该方法的充分性和有效性。
