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首页> 外文期刊>Circuits, systems, and signal processing >A Tutorial on Sparse Signal Reconstruction and Its Applications in Signal Processing
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A Tutorial on Sparse Signal Reconstruction and Its Applications in Signal Processing

机译：稀疏信号重构教程及其在信号处理中的应用

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摘要

Sparse signals are characterized by a few nonzero coefficients in one of their transformation domains. This was the main premise in designing signal compression algorithms. Compressive sensing as a new approach employs the sparsity property as a precondition for signal recovery. Sparse signals can be fully reconstructed from a reduced set of available measurements. The description and basic definitions of sparse signals, along with the conditions for their reconstruction, are discussed in the first part of this paper. The numerous algorithms developed for the sparse signals reconstruction are divided into three classes. The first one is based on the principle of matching components. Analysis of noise and nonsparsity influence on reconstruction performance is provided. The second class of reconstruction algorithms is based on the constrained convex form of problem formulation where linear programming and regression methods can be used to find a solution. The third class of recovery algorithms is based on the Bayesian approach. Applications of the considered approaches are demonstrated through various illustrative and signal processing examples, using common transformation and observation matrices. With pseudocodes of the presented algorithms and compressive sensing principles illustrated on simple signal processing examples, this tutorial provides an inductive way through this complex field to researchers and practitioners starting from the basics of sparse signal processing up to the most recent and up-to-date methods and signal processing applications.
机译：稀疏信号的特征在于其变换域之一中的一些非零系数。这是设计信号压缩算法的主要前提。压缩感测作为一种新方法，利用稀疏性作为信号恢复的前提。稀疏信号可以从一组减少的可用测量中完全重建。本文的第一部分讨论了稀疏信号的描述和基本定义，以及重构它们的条件。为稀疏信号重建开发的众多算法分为三类。第一个基于匹配组件的原理。分析了噪声和非稀疏性对重建性能的影响。第二类重建算法基于问题表达的约束凸形式，其中线性规划和回归方法可用于找到解决方案。第三类恢复算法基于贝叶斯方法。所考虑的方法的应用通过使用通用变换和观察矩阵的各种说明性和信号处理示例进行了演示。通过在简单的信号处理示例中说明了所提出算法的伪代码和压缩感测原理，本教程为研究人员和从业人员提供了从稀疏信号处理的基础到最新的最新知识的归纳方法。方法和信号处理应用。

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