A family of the subgradient algorithm with several cosparsity inducing functions to the cosparse recovery problem
A family of the subgradient algorithm with several cosparsity inducing functions to the cosparse recovery problem
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DOI：
10.1016/j.patrec.2016.05.012
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
Guinan Wang;Hongjuan Zhang;Shiwei Yu;Shuxue Ding
中科院分区：
文献类型：
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作者：
Guinan Wang;Hongjuan Zhang;Shiwei Yu;Shuxue Ding
在过去的十年中，信号的稀疏综合模型引起了人们极大的兴趣。研究者们在稀疏表示方面取得了一系列的成果。余分析模型作为稀疏合成模型的相应版本，近年来受到了广泛的关注。已经提出了许多方法来解决这个模型。在一些常规的方法中，这些方法通常将l0范数松弛为l1范数或l2范数来表示信号的共轴性，并由此发展出一些合理的算法。此外，本文还提出了一种新的替代方法，即基于余度诱导函数来代替l0-范数，它比l1-范数和l2-范数更接近于l0-范数。在此基础上，我们首先构造了目标函数，并给出了余分解恢复问题的约束优化模型。然后提出了一种次梯度算法--余度诱导函数（CIF）算法，它属于一种两层优化算法。具体地说，通过将约束优化问题转化为无约束优化问题，首先得到一个临时最优变量，在该变量中，为了避免余度诱导函数的非凸性，用其局部线性逼近来逼近余度诱导函数.其次，通过将临时最优变量投影到余分析子空间中并保持最小元素，给出了一种新的余支撑。此外，利用共轭梯度算法在新的协支撑下估计期望信号。此外，本文还对CIF算法的相关理论进行了研究。最后通过对余分析模型中未知信号的恢复进行仿真，验证了余分析模型的良好性能。
In the past decade, there has been a great interest in the sparse synthesis model for signal. The researchers have obtained a series of achievements about the sparse representation. The cosparse analysis model as the corresponding version of the sparse synthesis model has drawn much attention in recent years. Many approaches have been proposed to solve this model. In some conventional general, these methods usually relaxedl0-norm tol1-norm orl2-norm to represent the cospasity of signal, from which some reasonable algorithms have been developed. Furthermore, this work will present a new alternative way to replace thel0-norm based on the cosparsity inducing function, which is closer tol0-norm thanl1-norm andl2-norm. Based on this function, we firstly construct the objective function and give a constrained optimal model of the cosparse recovery problem. Then we propose a subgradient algorithm – cosparsity inducing function (CIF) algorithm, which belongs to a two-layer optimization algorithm. Specifically, through converting the constrained optimal problem into the unconstrained case, we firstly obtain a temporary optimal variable, in which the cosparsity inducing function is approximated using its local linear approximation in order to avoid its nonconvex property. Secondly, a new cosupport is given by projecting the temporary optimal variable into the cosparse subspace and then keeping thelsmallest elements. Besides, the desired signal is estimated using a conjugate gradient algorithm on the new cosupport. Moreover, we study the relative theoretical analysis about CIF algorithm. Simulations on the recovering of the unknown signal in the cosparse analysis model indicate its better performance at last.