Exploiting Sparsity in Tight-Dimensional Spaces for Piecewise Continuous Signal Recovery
Exploiting Sparsity in Tight-Dimensional Spaces for Piecewise Continuous Signal Recovery
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DOI：
10.1109/tsp.2018.2876328
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发表时间：
2018-12
影响因子：
5.4
通讯作者：
Hiroki Kuroda;M. Yamagishi;I. Yamada
中科院分区：
文献类型：
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作者：
Hiroki Kuroda;M. Yamagishi;I. Yamada
从噪声观测中恢复某些分段连续信号一直是科学和工程领域的一个重大挑战。在紧维表示空间中，我们利用了一类可能不连续的信号的稀疏性，即有限维分段连续信号。更准确地说，我们提出了一种紧维线性变换，它揭示了FPC信号的离散样本具有一定的稀疏性。这个变换是通过利用大多数连续样本都包含在特殊子空间中的事实来设计的。对分段多项式信号和分段正弦信号的恢复进行了数值实验，结果表明了该方法的有效性。
Recovery of certain piecewise continuous signals from noisy observations has been a major challenge in sciences and engineering. In this paper, in a tight-dimensional representation space, we exploit sparsity hidden in a class of possibly discontinuous signals named finite-dimensional piecewise continuous (FPC) signals. More precisely, we propose a tight-dimensional linear transformation which reveals a certain sparsity in discrete samples of the FPC signals. This transformation is designed by exploiting the fact that most of the consecutive samples are contained in special subspaces. Numerical experiments on recovery of piecewise polynomial signals and piecewise sinusoidal signals show the effectiveness of the revealed sparsity.