Iteratively re-weighted least squares for sparse signal reconstruction from noisy measurements

机译：迭代地重新加权最小二乘，从噪声测量中重建稀疏信号

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Finding sparse solutions of under-determined systems of linear equations is a problem of significance importance in signal processing and statistics. In this paper we study an iterative reweighted least squares (IRLS) approach to find sparse solutions of underdetermined system of equations based on smooth approximation of the L₀ norm and the method is extended to find sparse solutions from noisy measurements. Analysis of the proposed methods show that weaker conditions on the sensing matrices are required. Simulation results demonstrate that the proposed method requires fewer samples than existing methods, while maintaining a reconstruction error of the same order and demanding less computational complexity.

机译：寻找欠定线性方程组的稀疏解是在信号处理和统计中非常重要的问题。本文研究了一种基于L _{0 范式的平滑逼近的迭代加权最小二乘（IRLS）方法来找到欠定方程组的稀疏解，并将该方法扩展到从噪声中找到稀疏解测量。对提出的方法的分析表明，需要在感测矩阵上使用较弱的条件。仿真结果表明，与现有方法相比，该方法所需样本更少，同时保持了相同阶数的重构误差，并且所需的计算复杂度更低。}

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《Information Sciences and Systems, 2009. CISS 2009》|2009年|448-453|共6页
会议地点 Baltimore MD(US);Baltimore MD(US);Baltimore MD(US)
作者
Carrillo R.E.; Barner K.E.;
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Dept. of Electr. Comput. Eng., Univ. of Delaware, Newark, DE;

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iterative methods; least squares approximations; signal reconstruction; statistical analysis; iteratively re-weighted least squares approximation; linear equations; reconstruction error; signal processing; sparse signal reconstruction; Compressed sensing; re-weighted least squares; sampling methods; underdetermined systems of linear equations;

机译：迭代方法;最小二乘近似;信号重构;统计分析;迭代地重新加权最小二乘近似;线性方程;重构误差;信号处理;稀疏信号重构;压缩感测;重新加权最小二乘;采样方法;欠定线性系统方程式;

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专利

1. Sparse Signal Reconstruction from Quantized Noisy Measurements via GEM Hard Thresholding [J] . Kun Qiu Signal Processing, IEEE Transactions on . 2012,第5期

机译：通过GEM硬阈值从量化噪声测量中重建稀疏信号
2. Sparse Signal Reconstruction from Quantized Noisy Measurements via GEM Hard Thresholding [J] . Kun Qiu Signal Processing, IEEE Transactions on . 2012,第5期

机译：通过GEM硬阈值从量化噪声测量的稀疏信号重建
3. Sparse Approximation Property and Stable Recovery of Sparse Signals From Noisy Measurements [J] . Sun Q. Signal Processing, IEEE Transactions on . 2011,第10期

机译：稀疏近似特性和从噪声测量中稳定恢复稀疏信号
4. Iteratively Re-weighted Least Squares for Sparse Signal Reconstruction from Noisy Measurements [C] . Rafael E. Carrillo, Kenneth E. Barner Annual Conference on Information Sciences and Systems . 2009

机译：从嘈杂测量中迭代地重复重新加权最小二乘性，稀疏信号重建
5. Joint Recovery of High-Dimensional Signals From Noisy and Under-Sampled Measurements Using Fusion Penalties [D] . Poddar, Sunrita 2018

机译：使用融合惩罚从噪声和采样不足的测量中联合恢复高维信号
6. Convergence and Stability of a Class of Iteratively Re-weighted Least Squares Algorithms for Sparse Signal Recovery in the Presence of Noise [O] . Behtash Babadi, Demba Ba, Patrick L. Purdon, -1

机译：噪声存在下一类用于稀疏信号恢复的迭代加权最小二乘算法的收敛性和稳定性
7. Iteratively re-weighted least squares minimization: Proof of faster than linear rate for sparse recovery [O] . Ingrid Daubechies, Ronald Devore, Massimo Fornasier, 2011

机译：迭代重新加权最小二乘最小化：稀疏恢复的速度快于线性速率的证明

Iteratively re-weighted least squares for sparse signal reconstruction from noisy measurements

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