Compressed sensing of time-varying signals

Daniele Angelosante, G. Giannakis, E. Grossi
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引用次数: 115

Abstract

Compressed sensing (CS) lowers the number of measurements required for reconstruction and estimation of signals that are sparse when expanded over a proper basis. Traditional CS approaches deal with time-invariant sparse signals, meaning that, during the measurement process, the signal of interest does not exhibit variations. However, many signals encountered in practice are varying with time as the observation window increases (e.g., video imaging, where the signal is sparse and varies between different frames). The present paper develops CS algorithms for time-varying signals, based on the least-absolute shrinkage and selection operator (Lasso) that has been popular for sparse regression problems. The Lasso here is tailored for smoothing time-varying signals, which are modeled as vector valued discrete time series. Two algorithms are proposed: the Group-Fused Lasso, when the unknown signal support is time-invariant but signal samples are allowed to vary with time; and the Dynamic Lasso, for the general class of signals with time-varying amplitudes and support. Performance of these algorithms is compared with a sparsity-unaware Kalman smoother, a support-aware Kalman smoother, and the standard Lasso which does not account for time variations. The numerical results amply demonstrate the practical merits of the novel CS algorithms.
时变信号的压缩感知
压缩感知(CS)降低了重建和估计稀疏信号所需的测量次数,当在适当的基础上扩展时。传统的CS方法处理时不变的稀疏信号,这意味着,在测量过程中,感兴趣的信号不表现出变化。然而,在实践中遇到的许多信号随着观测窗口的增加而随时间变化(例如,视频成像,其中信号是稀疏的,并且在不同帧之间变化)。本文基于稀疏回归问题中常用的最小绝对收缩和选择算子(Lasso),开发了时变信号的CS算法。Lasso专门用于平滑时变信号,这些信号被建模为矢量值离散时间序列。提出了两种算法:当未知信号支持是时不变的,但允许信号样本随时间变化时,组融合Lasso算法;动态套索,用于具有时变幅度和支持的一般类型的信号。将这些算法的性能与稀疏不敏感卡尔曼平滑、支持感知卡尔曼平滑和不考虑时间变化的标准Lasso进行了比较。数值结果充分证明了该算法的实用价值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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