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Ways to Sparse Representation: A Comparative Study

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Tsinghua Science and Technology 2009年第4期14卷 434-443页

作者：杨敬钰彭义刚徐文立戴琼海 Tsinghua National Laboratory for Information Science and Technology Department of Automation Tsinghua University

Many algorithms have been proposed to achieve sparse representation over redundant dictionaries or transforms. A comprehensive understanding of these algorithms is needed when choosing and designing algorithms for particular applications. This research studies a representative algorithm for each category, matching pursuit （MP）, basis pursuit （BP）, and noise shaping （NS）, in terms of their sparsifying capability and computational complexity. Experiments show that NS has the best performance in terms of sparsifying ca- pability with the least computational complexity. BP has good sparsifying capability, but is computationally expensive. MP has relatively poor sparsifying capability and the computations are heavily dependent on the problem scale and signal complexity. Their performance differences are also evaluated for three typical ap- plications of time-frequency analyses, signal denoising, and image coding. NS has good performance for time-frequency analyses and image coding with far fewer computations. However, NS does not perform well for signal denoising. This study provides guidelines for choosing an algorithm for a given problem and for designing or improving algorithms for sparse representation.

关键词： sparse representation redundant dictionary/transform nonlinear approximation matching pursuit basis pursuit noise shaping

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Ways to sparse representation:An overview

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Science in China(Series F) 2009年第4期52卷 695-703页

作者： YANG JingYu PENG YiGang XU WenLi DAI QiongHai Department of Automation Tsinghua University Beijing 100084 China

Many algorithms have been proposed to find sparse representations over redundant dictionaries or transforms. This paper gives an overview of these algorithms by classifying them into three categories： greedy pursuit algorithms, lp norm regularization based algorithms, and iterative shrinkage algorithms. We summarize their pros and cons as well as their connections. Based on recent evidence, we conclude that the algorithms of the three categories share the same root： lp norm regularized inverse problem. Finally, several topics that deserve further investigation are also discussed.

关键词： sparse representation redundant dictionary redundant transform nonlinear approximation matching pursuit basis pursuit iterativeshrinkage

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A New Optimization Neural Network for High Resolution Time-Frequency Analysis

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电路与系统学报 1997年第1期 1-7页

作者： Z.S. Wang,Y.S.Xia,J.D.Z. Chen,W.H.Li,Z.Y.He,(Dept. of Radio Engineering, Southeast University, Nanjing, 210096)(Dept. of Mathematics,Nanjing University of Posts & Telecommunications)(Institute for Healthcare Researc, Baptist Medical Center, Oklahoma City,

The authors present a new optimization neural network, which can be called as constrained smallest l1-norm neural network (CSl1NN), to implement the basis pursuit(BP)[1][2][3]for high resolution time-frequency analysis. As the new and generalized one of the communities of overcomplete signal representations, the BP is considered as a large-scale linear programming problem. In contrast with the Simplex-BP or Interior-BP in [2],the proposed CSl1NN-BP dose not double the optimizing scale and can be implemented in real time through hardware. Taking non-stationary artificial signals and Electrogastrograms (EGGs) to test, our simulations show that the CSl1 NN presents an excellent convergence performance for a wide range of time-frequency(TF)dictionaries and has a higher joint TF resolution not only than the traditional Wigner Distribution (WD), but also than recently rising other overcomplete representation methods, such as Method of Frames (MOF)[9], Best Orthogonal basis (BOB)[10] and Matching pursuit (MP)[4]. Combining the high resolution with the fast implementation,the CSl1NN-BP will be very promising for on-line time frequency analysis of various kinds of non-stationary signals,such as linear chirp,qUadric chirp,bumps etc., and medical signals,such as ECG,EEGand EGG,etc., with high quality.

关键词： Neural network Optimization Overcomplete signal representation basis pursuit Wavelet Time-frequency analysis

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基于BP的地震信号分离及初步应用

基于BP的地震信号分离及初步应用

作者：徐兵西南交通大学

学位级别：硕士

在地质勘探或石油探索中,地震勘探是一种重要的物探方法。人们往往在土壤中进行炸药爆破来激发地震波。由于地震波在地下不同的地质传播时,它的波形、振幅强度和路径会随所通过介质的弹性的不同而发生变化。这样利用接收到的地震波就可... 详细信息

在地质勘探或石油探索中,地震勘探是一种重要的物探方法。人们往往在土壤中进行炸药爆破来激发地震波。由于地震波在地下不同的地质传播时,它的波形、振幅强度和路径会随所通过介质的弹性的不同而发生变化。这样利用接收到的地震波就可以估计其反射函数。由于这些反射函数与不同地层的冲击响应有关,可推断出地下介质结构和岩石的性质,从而达到勘探的目的。由地震记录来求解反射系数常被称为反褶积运算,即从地震记录中分离出反射系数。因地震反褶积与稀疏领域的原子反褶积有着相似的理论模型。本文首先讨论了地震反褶积和原子反褶积之间的联系,并介绍了稀疏领域的常用方法MP和BP。其次,研究了稀疏分解的信号处理新方法,设计了基于稀疏分解的地震信号分离算法。以雷克子波为原子模型,合成人工地震信号,分别利用BP和MP对合成的无噪的地震信号以及不同噪声下的地震信号进行分离,通过实验证实了BP在地震信号分离的中的优越性。针对实际的二维地震记录,对每一道分别进行处理。实验中分别选取了几种不同的地震剖面进行BP分离,讨论了不同相位的地震子波作为原子模型时的分离效果,通过实验仿真结果表明,针对实验中所选取的剖面,零相位子波均能取得最好的分离效果。最后,论文还对同层反射系数的提取进行了研究。设计了同层反射系数的提取算法,研究并实现了二维人工地震信号在连续、非连续情况下的同层反射系数的提取,并在实际地震信号的同层反射系数的提取上取得了较好的效果。

关键词：反射系数地震记录原子库稀疏分解 basis pursuit