Sparse Signal Approximation via Nonseparable Regularization
Sparse Signal Approximation via Nonseparable Regularization
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DOI：
10.1109/tsp.2017.2669904
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发表时间：
2017-05-15
影响因子：
5.4
通讯作者：
Farshchian, Masoud
中科院分区：
文献类型：
--
作者：
Selesnick, Ivan;Farshchian, Masoud
线性方程组的稀疏近似解的计算通常使用L1-范数正则化和凸优化或非凸正则化和非凸优化来执行。结合这些原则，本文描述了一种类型的非凸正则化，保持目标函数的凸性，从而允许通过凸优化的稀疏近似解的计算。在所提出的方法中，凸性的保持是可行的，因为它使用了不可分离的正则化器。所提出的方法的动机和证明稀疏信号近似使用紧框架的计算。去噪的例子证明了相对于L1范数正则化的改进。
The calculation of a sparse approximate solution to a linear system of equations is often performed using either L1-norm regularization and convex optimization or nonconvex regularization and nonconvex optimization. Combining these principles, this paper describes a type of nonconvex regularization that maintains the convexity of the objective function, thereby allowing the calculation of a sparse approximate solution via convex optimization. The preservation of convexity is viable in the proposed approach because it uses a regularizer that is nonseparable. The proposed method is motivated and demonstrated by the calculation of sparse signal approximation using tight frames. Examples of denoising demonstrate improvement relative to L1 norm regularization.