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| | | | | . Your ALgorithms for L1 |
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YALL1 is an Matlab/Octave package for solving eight different L1-norm minimization problems. For more details, see http://www.dirigibleFlightcraft.com/YALL1/. Download the latest version via git:
git clone http://github.com/lynaghk/YALL1/
and use it by adding yall1.m to your Matlab or Octave path:
path(path, '/home/yourname/YALL1')
An example of using YALL1 for basis pursuit (min ||x||_1 such that Ax = b):
%random measurement matrix
n = 1000; %rows
m = 300; %columns
A = randn(m,n);
%signal we will try to reconstruct later
k = 15; %how many non-zero coefficients in signal of interest
xs = zeros(n,1);
p = randperm(n); %pick random coefficients to set
xs(p(1:k)) = randn(k,1);
b = A*xs;
%orthogonalize A and transform our signal b into the new basis
[Q, R] = qr(A',0);
A = Q'; b = R'\b;
opts.tol = 5e-8; %set reconstruction stopping tolerance
[x,Out] = yall1(A, b, opts);
fprintf('L2 norm error: %e\n', norm(x-xs))
The original package is available at http://yall1.blogs.rice.edu/
This version is slightly modified for Octave compatibility.
YALL1: Your ALgorithms for L1
COPYRIGHT (c) 2010 Yin Zhang, Junfeng Yang, and Wotao Yin.
YALL1 is distributed under the terms of the GNU General Public License 3.0. http://www.gnu.org/copyleft/gpl.html
Permission to use, copy, modify, and distribute this software for any purpose without fee is hereby granted, provided that this entire notice is included in all copies of any software which is or includes a copy or modification of this software and in all copies of the supporting documentation for such software. This software is being provided "as is", without any express or implied warranty. In particular, the authors do not make any representation or warranty of any kind concerning the merchantability of this software or its fitness for any particular purpose.