stanford大学的matlab压缩感知工具箱sparseLab说明文档

【实例简介】
stanford大学的matlab压缩感知工具箱sparseLab说明文档
1 Introduction Sparselab is a library of matlab routines for finding sparse solutions to underdetermined systems The library provides the research community with open source tools for sparse representation as well as being the basis for research by the authors, and may be used to reproduce the figures in their published articles, and to redo those figures with variations in the parameters The library is available free of charge over the Internet by www access: instructions are givcn bclow. The matcrial is, howevcr, copyrighted, so that advance permission is rcquircd for any commercial use The package approaches the problem of sparse representation from both signal processing and statistical viewpoints. The user is free to choose the terminology he or she is comfortable with Sparselab incorporates software for several published solvers, for example Michael Saunders Primal-Dual method for Optimization with Convex Objectives, Mallat and Zhang's Matching Pursuit, Donoho and Johnstones Iterative Hard and Soft Thresholding, Efron et al's Least Angle Regression, and a number of others In addition to routines finding sparse solutions to systems, the library contains scripts which give a quick examples in a. variety of different settings. We believe that by studying these scripts one can quickly learn the practical aspects of sparse representation and one can learn how to use the sparselab software libr In this guide we give information which will help you access and install the software on your machine and get started in exploring the resources contained in the Sparselab distribution. We also explain the philosophy which underlies our distribution of the software, and some of the fine print associated with the software There are other resources for obtaining information about SparseLab. First, there is a sparse- Lab Architecture guide which gives details about how SparscLab is constructed and maintained Secondly, we give more information on the SparseLab website This body of software is under continuing development by a team of researchers supported by a grant from the NsI F, and from other sponsors. We conduct our research with the idea, from the beginning, that we will implement our tools in SparseLab. We believe that the discipline this entails makes our research of a higher quality than otherwise possible We welcome your suggestions for further enhancements, and any contributions you might mak 2 Access and installation The SparseLab library contains. m files(Matlab code), datasets, documentation scripts and workouts(both also. m files) for reproducing the figures in articles by the authors The whole library consists of over 400 files. It requires more than 200MB and less than 400MB space on disk once it is downloaded, decompressed and installed. The largest data files for two demos are included in separate packages: Sparselab100-DataSupplementExtCS zip and parsclab100- DataSupplcmcntStOMP zip- thc majority of the sizc comes from thesc compo nents This documentation refers to Version 2.0 of Sparsela b 2.1 Platform-Specific Information Sparselab is available for use in Matlab 6. x or 7. x on three different platforms: Windows Xp or 2000. UNIX/Linux and Macintosh. The package is made available as a compressed archive, in a zip format You do have to know about one convention used in the documentation. We always use the unix pathname conventions rather than PC or Macintosh, e.g. Matlab/Toolbox/Sparselab ra.her than Matlab\ Toolbox\ SparseLab or Matlab: Toolbox: WaveLab. You have to transliterate what we say into the version appropriate for your platform 2.2 WEB acess Todownloadthecompressedarchivefromthewebpointyourwebbrowsertohttp://sparselab.stanford.edu to access the SparseLab web-page. Once there, Mouse click the"Dowilload"link in the left fraile 2.3 Installation In this section we first describe the installation process in narrative form, and later give a step by-step checklist Once the appropriate compressed archive has been transferred to your machine, it should be decompressed and installed. You will need an appropriate software to decompress. zip file Sparselab200. zip. On a personal computer (Macintosh or Windows), the archives should be decompressed and installed as a subdirectory of the Toolbox directory inside the matlab folder On a UNiX workstation or scrvor, the archives could cither bc installed in thc systemwide matlab directory, if you have permission to do this, or in your own personal matlab directory, if you do not Once the actual files are installed, you should have a number of files and subdirectories in the directory sparselab. If you look in the files Contents m inside of the Sparselab directory, you will see a plan of fo SparseLab Main Directory, Version 100 % l This is the main directory of the SparseLab package % files in this directo % Contents This file l S parsePathm Sets up global variables and pathnames Subdirect es Documentation System-Wide Documentation /About SparseLab /SparseLab Architecture l Examples Detailed examples of Sparselab finding sparse solutions /nnfEX Nonnegative Factorization example /reconstruction Signal reconstruction Example %%%%%%%% /RegEx Regression Example /TFDecompEx Time-Frequency Reconstruction Example Pal Scripts for reproducing figures in published articles /ExtcS figures for Extensions of Compressed Sensing /HDCPNPD figures for High-Dimensional Centrosymmetric Polytopes with Neighborliness Proportional to Dimension /NPSSULE table in Neighborly Polytopes and Sparse Solutions of underdetermined linear equations %7 /NRPSHD figures for Neighborliness of Randomly-Projected Simplices in High Dimensions /SNSULELP figures for Sparse nonnegative Solutions of Underdetermined Linear Equations by Linear Programming 7 Solvers Sparse solver packages Tests Simple pedagogical worko 7 Utilities General tools for developers and users % shell tools Tools for use during the Sparselab build process % Part of SparseLab Version: 100 %o Created Tuesday March 28, 2006 lo This is Copyrighted Material lo For Copying permissions see COPYING.m ‰。 Comments?e-mai1 sparselab@ stanford.edu Make a local directory listing to see if your hard disk actually has these files and subdirecto- rles 2.4 Pathnames Matlab can automatically, at startup time, make all the SparseLab software available. The script Sparsepath. m is provided as part of Sparselab to enable this feature. It should be invoked from the users Startup. m file PC Startup. m is located in the matlab\local directory on Ms-Windows. Insert the line SparsePath in that file, anld put a copy of SparsePath In in that directory Mac Startup. m may be located anywhere inside the Matlab directory on Macintosh. Insert the line SparsePath in that file. Since SparseLab contains a Startup. m file, if you have no other Startup. m file, there is nothing to do once SparseLab is installed Unix This file is located in the matlab subdirectory of your home directory on UNIX. If you dont have such a subdirectory, use mkdir /matlab to make one. Create a file named Startup. m and insert the line SparsePath in that file. Then put a copy of SparsePathm that directory 2.5 Checklist To reinforce the above points, we furnish here step-by-step installation checklists 2.5.1 UNIX Checklist 1. Binary Download the archive to the directory you want Sparselab to reside 2. Uncompress the archive: SparseLab100 zip 3. Decide where you want the sparselab directory to reside. It will have a number of subdi- rectories and occupy at least 200MB disk space 4. After you decoMpress thie file for your Illachine, you should have the following directory structure Sparselab200 Sparselab200/ Solvers Sparselab200/ Datasets Sparselab200/ Documentation Sparselab200/ Papers arselab200/ Examples Sparselab200/ Utilities 5. Copy all the SparseLab files from the place you put the original SparseLab archive(for ex ample/tmp) to their final destination, for example in your home directory user/matlab/ Sparselab200 6. Launch Matlab; In Matlab set the current path to matlabroot /toolbox/ Sparselab200 or alternatively copy the file SparsePath. m from MatlabToolboxPath > Sparselab200 to <Matlab ToolboxPath>/local 7. Run SparsePath. m; If the default pathname is not right the program will ask you to enter the correct path 8. Type installMEX to compile and install the. mex files Trouble-Shooting UNIX: Compare the output of ls -r SparseLab100 with Documentation to see if you have all the files. Compare the output of the Matlab command path with the list above to see if you have all the directories in your path 2.5.2 Macintosh Checklist To follow these instructions you will need ()A Macintosh running MacOS 10.3 or later (2) A program which can unzip zipfile (3) Matlab 6.x or 7.x for Mac 1. Binary Download the file Sparselab200 zip to your Macintosh 2. Extract the archive to the Toolbox folder of your Matlab folder. After you cxtract thc filc you should have the following subdirectory structure Spa.sela. b200 Sparselab200/ Solvers Sparselab200/ Datasets Sparselab200/ Documentation Sparselab200/ Papers Sparselab200/ Examples parselab200/ Utilities 3. Launch Matlab; In Matlab set the current path to matlabroot/toolbox/ Sparselab200 or alternatively copy the file SparsePath m from MatlabToolboxPath >/ Sparselab200 to <Matlab ToolboxPath>/local 4. Run SparsePath m at the command prompt to start Sparselab. You will see a Welcome to Sparselab"message as shown in the section Success below 6 Note 1. If you want to automatically load Sparselab200 upon the start-up copy the file SparsePathm from the folder Sparselab200 to the folder Matlab/Toolbox /local. Determine if you have any file named startup. m besides the one that is in Sparselab200 directory. If you dont go to step 3 2. if you have Startup. m, then copy the contents of SparsePath m into this file 3. If you dont have any Startup. m, then copy the file Startup. m from Sparselab200 directory to< Matlab Toolbox Path >/local 2.5.3 PC Checklist To follow these instructions you will need (1) An Intel Platform running Windows 2000 or XP (2)A program such as Winzip which can unzip. zip file (3)Matlab 6. x or 7. x for 1. Binary Download the file Sparselab200 zip to your PC 2. Extract the archive to the Toolbox folder of your matlab folder. Afte tract the file you should have the following subdirectory structure Sparselab200 Sparselab200/ Solvers Sparselab200/ Datasets Sparsclab200/ Documentation Sparselab200/ Papers Sparselab200/ Examples cb200/ Uti 3. Launch Matlab; In Matlab set the current path to matlabroot\ toolbox \ Sparselab200 or alternatively copy the file SparsePath In froll MatlabToolboxPath>\ Sparselab200 to < Matlab ToolboxPath> lc 4. Run SparsePath m at the command prompt to start Sparselab. You will see a " Welcome to SparseLab"message as shown in the section Success below 1. If you want to automatically load Sparselab200 upon the start-up copy the file SparsePathm frOin the folder Sparselab200 to the folder Matlab\ Toolbox \local. DeterImine if you have any file named startup. m besides the one that is in Sparselab200 directory. If you don't go to stcp 3. 2. if you have Startup. m then copy the contents of SparsePath m into this file 3. If you dont have any Startup. m then copy the file Startup. m from Sparselab200 directory to <Matlab ToolboxPath>local 2.6 Success When you have a successful installation, you should see something like the following when you inⅴ oke matlab Welcome to sparseLab v 100 Setting Global Variables lobal matlabversion =7 global SparselABVERSION =100 global SparseLABPATH C: \Program Files \MATLAB704 \work\ SparseLab\SparseLab100\ lobal PatHNAmesePArator lobal PreferImaGegraphics 1 SparseLab 100 Setup Complete Currently available browsers for reproducing figures from the following papers: ExtCsDemo demo for paper Extensions of Compressed sensing HDCPNPDDemo -demo for paper High-Dimensional Centrosymmetric Polytopes with Neighborliness Proportional to Dimension MSNVENODemo -demo for paper "Breakdown Point of Model Selection When the Number of Variables exceeds the number of observations NPSSULEDemo -demo for paper Neighborly Polytopes and Sparse Solutions of Underdetermined Linear Equations NRPSHDDemo demo for paper " Neighborliness of Randomly-Projected Simplices in High Dimensions" SNSULELPDemo - demo for paper Sparse Nonnegative Solutions of Underdetermined Linear Equations by Linear Programming StOMPDemo demo for paper " Sparse Solution of Underdetermined Linear Equations y Stagewise Orthogonal Matching Pursuit Currently available examples Nonnegative Factorization Signal Reconstruction Regression Example Time-Frequency Separation For more information, please visit: http://sparselab.stanfordedu Please ignore the following message if wavelab has been installed There are Sparselab functions which call Wavelab functions. We recommend that the users download wavelab from the website http://www-stat.stanfordedu/wavelab and install the package in the directory C: \Program Files\ MaTlAB704\toolbox 3 Getting Started There are several ways to get started with SparseLab. First, you can snoop around the directory structure to see what's there. Second, you can try running some of the demos to see what they do. Third, you can try the pedagogical examples 3.1 Snooping If you just snoop around in the Sparselab file structure. you will notice many directories and a great range of different information about the system itself and what it can do. We list here some basic facts 3.1.1 Contents files Each directory has a Contents. m file, which explains the contents and purpose of that directory The directory Solvers contains the central program solver tools; its Contents. m file looks as follows %o SparseLab Solvers Directory This is directory houses the solvers for the SparseLab package % m files in this directory % This fil fdrthreshm Uses the False Discovery Rate to Threshold a 1 HardThreshm Implements Hard Thresholding %o sarms.m Iterative least squares 。paco.m Primal-Dual barrier method for convex % Objectives (Michael Saunders 2003) 1 pdcoSetm creates or alters options structure for % paco.m SoftThreshm Soft Thresholding SolveBPm Basis pursuit SolveIRWLSm Iteratively Reweighted Least Squares SolveISTm Iterative Soft Thresholding SolveISTBlockm Iterative Soft Thresholding, block variant % with least squares projection o SolveLasso m Implements LARS/Lasso Agorithms SolveMPm Matching Pursuit % SolveOMP Orthogonal Mat ching Pursuit f SolveStepwisem Forward stepwise SolveStepwiseFDRm Forward stepwise with FDR Threshold %1 SolveStOMPm Stagewise Orthogonal Matching Pursuit % Part of SparseLab Version: 100 lo Created Tuesday March 28, 2006 %o This is ce hted material ‰。 For Copying permissions see COPYING moments e-mail sparselab@stanford. edu 3.1.2 Help for Functions Each function in SparseLab has help documentation. For example. SolveMP is Mallat and Zhangs Matching Pursuit algorithm. If you are in Matlab and type help SolveMP, Matlab will type out the following documentation: 7 SolveMP: Matching Pursuit (non-orthogonal) g [sol iters activationHist]= SolveMP (A, b, maxIters, NoiseLevel, verbose) 。 Input A dictionary (dxn matrix), rank(A)= min(d, n) by assumption y data vector, length d l maxIters number of atoms in the decomposition NoiseLevel estimated norm of noise, default noiseless, i.e. 1e-5 verbose 1 to print out detailed progress at each iteration, o for no output (default) Outputs %%%%%%%%% sol solution of mp iters number of iterations performed activationHist Array of indices showing elements entering the so1 ution se七 Description SolveMP impl s the greedy pursuit algorithm to estimate the solution of the sparse approximation problem man |x||_0s.t.A*x=y See Also SolveOMP References %o Matching Pursuit With Time-Frequency Dictionaries (1993)Mallat, Zhang l IEEE Transactions on Signal Processing 3.1.3 Source Browsing All the algorithms in SparseLab are available for inspection. For example, if you are in matlab and type type SolveMP you get the following documentation function [sol iters activationHist] SolveMP (A, y, maxIters, NoiseLevel, verbose) %o SolveMP: Matching Pursuit (non-orthogonal) Usage Sol iters activationHist]= SolveMP (A, b, maxIters, NoiseLevel, verbose) %o Input dictionary (dxn matrix), rank(A)= min(d, n) by assumption data vector, length d %o maxIters number of atoms in the decomposition NolseLevel estimated norm of noise. default noiseless, i.e. 1e-5 verbose 1 to print out detailed progress at each iteration,o for no output (default) ‰。 Outputs SOL solution of mp iter number of iterations performed activationHist Array of indices showing elements entering the solution set ‰ Description %o SolveMP implements the greedy pursuit algorithm to estimate the l solution of the sparse approximation problem min IIxII-O s.t. A*x o See Also SolveOMP References %o Matching Pursuit With Time-Frequency Dictionaries (1993) Mallat, Zhang 7 IEEE Transactions on Signal Processing 10 【实例截图】
【核心代码】