L1 Homotopy: A MATLAB Toolbox for Homotopy Algorithms in L1 Norm Minimization Problems

 

Introduction:

 

This package is a collection of MATLAB routines for solving some L1 norm minimization problems using homotopy techniques. These problems are usually encountered in the recovery of sparse signals from linear incoherent measurements.

 

This package contains scripts for solving the following optimization problems:

 

·        Basis pursuit denoising (BPDN) / LASSO

·        Dantzig selector

·        L1 decoding

·        Robust L1 decoding

 

In addition to solving these problems for any given set of parameters, we have some dynamic algorithms to update their solution when

 

·        New measurements are sequentially added to the system

·        The unknown signal varies over time and we get a new measurement vector

 

Download:

 

Homotopy package (.zip)

 

User’s guide (.pdf)  (still under preparation)

 

Related papers:

 

·        M. Salman Asif and Justin Romberg, Dynamic updating for L1 minimization, submitted to IEEE Journal of selected topics in signal processing, special issue on compressive sensing.

 

Related softwares and links:

 

·        l1_magic [link]

·        CVX [link]

·        WaveLab [link]

·        GPSR [link]

·        FPC_AS [link]

 

License:

 

L1 Homotopy © 2009  Salman Asif, Justin Romberg

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. <http://www.gnu.org/licenses/>.

 

 

 

         

BPDN homotopy path

 

   

 

Dantzig selector homotopy path

 

Last updated: 06/26/09