ADMM-IDNN：基于ADMM的基于分组先验的非凸压缩感知迭代双重加权核范数算法
ADMM-IDNN: Iteratively Double-reweighted Nuclear Norm Algorithm for Group-prior based Nonconvex Compressed Sensing via ADMM
摘要：
基于组先验的正则化方法在各种图像处理任务中取得了巨大的成功，这些任务通常可以被认为是低秩矩阵最小化问题。作为一种广泛使用的低秩代理函数，基于核范数的凸代理函数由于核范数同时收缩了秩分量（奇异值），因此经常会出现过收缩现象.在本文中，我们提出了一种新的基于组先验的非凸图像压缩感知（CS）重建框架，通过一个家庭的非凸核范数函数，其中包含共同的凹和单调性质。为了解决由此产生的非凸核范数最小化（NNM）问题，我们开发了一个基于组的迭代双加权核范数算法（IDNN）通过交替方向方法的乘数（ADMM）框架。我们提出的算法可以将非凸核范数优化问题转化为双重加权奇异值阈值（DSVT）问题。大量的实验表明，我们提出的框架取得了良好的重建性能相比，目前国家的最先进的凸方法。
英文摘要：
Group-prior based regularization method has led to great successes in various image processing tasks, which can usually be considered as a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear norm based convex surrogate usually lead to over-shrinking phenomena, since the nuclear norm shrinks the rank components (singular value) simultaneously. In this paper, we propose a novel Group-prior based nonconvex image compressive sensing (CS) reconstruction framework via a family of nonconvex nuclear norms functions which contain common concave and monotonically properties. To solve the resulting nonconvex nuclear norm minimization (NNM) problem, we develop a Group based iteratively double-reweighted nuclear norm algorithm (IDNN) via an alternating direction method of multipliers (ADMM) framework. Our proposed algorithm can convert the nonconvex nuclear norms optimization problem into a double-reweighted singular value thresholding (DSVT) problem. Extensive experiments demonstrate our proposed framework achieved favorable reconstruction performance compared with current state-of-the-art convex methods.
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