发帖
雷达卡
摘要翻译：
现在已经很好地理解（1）可以从看起来高度不完全的线性测量集精确地重建稀疏信号，(2)这可以通过约束L1最小化来实现。在本文中，我们研究了一种稀疏信号恢复的新方法，它在许多情况下优于L1最小化，因为精确恢复所需的测量量大大减少。该算法包括求解一系列加权L1-极小化问题，其中下一次迭代所用的权值由当前解的值计算。实验结果表明，该算法在稀疏信号恢复、统计估计、误差校正和图像处理等方面具有良好的性能和广泛的适用性。有趣的是，当我们的方法用于恢复过完备表示中假设的近稀疏性信号时，也获得了优越的增益--不是像常见的那样通过重新加权系数序列的L1范数，而是通过重新加权变换对象的L1范数。一个直接的结果是通过改进一种称为压缩传感的技术来实现高效的数据采集协议的可能性。
---
英文标题：
《Enhancing Sparsity by Reweighted L1 Minimization》
---
作者：
Emmanuel J. Candes, Michael B. Wakin, and Stephen P. Boyd
---
最新提交年份：
2007
---
分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
--
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
--
一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--
---
英文摘要：
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we study a novel method for sparse signal recovery that in many situations outperforms L1 minimization in the sense that substantially fewer measurements are needed for exact recovery. The algorithm consists of solving a sequence of weighted L1-minimization problems where the weights used for the next iteration are computed from the value of the current solution. We present a series of experiments demonstrating the remarkable performance and broad applicability of this algorithm in the areas of sparse signal recovery, statistical estimation, error correction and image processing. Interestingly, superior gains are also achieved when our method is applied to recover signals with assumed near-sparsity in overcomplete representations--not by reweighting the L1 norm of the coefficient sequence as is common, but by reweighting the L1 norm of the transformed object. An immediate consequence is the possibility of highly efficient data acquisition protocols by improving on a technique known as compressed sensing.
---
PDF链接：
https://arxiv.org/pdf/711.1612
京公网安备 11010802022788号
