Recovery of piecewise finite-dimensional continuous signals by exploiting sparsity
Recovery of piecewise finite-dimensional continuous signals by exploiting sparsity
复制标题
DOI：
10.1109/sampta.2017.8024431
复制
发表时间：
2017-07
期刊：
影响因子：
--
通讯作者：
Hiroki Kuroda;M. Yamagishi;I. Yamada
中科院分区：
文献类型：
--
作者：
Hiroki Kuroda;M. Yamagishi;I. Yamada
科学和工程中的许多反问题都可以归结为对分段有限维连续（PFC）信号的恢复。虽然高阶全变分（HTV）是已知的，是特别有效的分段多项式的稀疏意识恢复，它仍然不清楚到目前为止，是否HTV可以扩展到其他信号模型。在本文中，我们提出了一个凸正则化成为推广的PFC信号的HTV。我们首先设计了一个线性变换，该变换使得PFC信号的样本具有一定的组稀疏性。这种线性变换是基于大多数局部样本可以用已知基的固定线性组合插值的事实而设计的。此外，我们还从理论上证明了线性变换后的样本具有群稀疏性。然后，提出的正则化设计，以提高组稀疏性，通过使用的1，2范数。分段正弦信号恢复的数值实验表明了所提出的正则化方法的有效性。
Many inverse problems in science and engineering are formulated as recovery of piecewise finite-dimensional continuous (PFC) signals. Although the higher-order total variation (HTV) is known to be particularly effective for the sparsity-aware recovery of piecewise polynomials, it remains unclear so far whether the HTV can be extended to other signal models. In this paper, we present a convex regularizer which becomes a generalization of the HTV for the PFC signals. We first design a linear transformation which induces a certain group sparsity of samples of the PFC signals. This linear transformation is designed based on the fact that most of local samples can be interpolated by a fixed linear combination of known basis. Moreover, we provide theoretical evidence that the linear transformed samples have the group sparsity. Then, the proposed regularizer is designed to promote the group sparsity by using the ℓ1,2 norm. A numerical experiment on recovery of piecewise sinusoidal signals shows the effectiveness of the proposed regularization.