Department of CAAM
Rice University, Houston, Texas 77005
(Number of access to this page is
since 05/13/2009)
This Matlab code can currently be applied to the following eight (8) L1-minimization problems:
(BP) min ||Wx||w,1 s.t. Ax = b (L1/L1) min ||Wx||w,1 + (1/&nu)||Ax - b||1 (L1/L2) min ||Wx||w,1 + (1/2&rho)||Ax - b||22 (L1/L2con) min ||Wx||w,1, s.t. ||Ax - b||2 <= &delta (BP+) min ||x||w,1 s.t. Ax = b and x >= 0 (L1/L1+) min ||x||w,1 + (1/&nu)||Ax - b||1 s.t. x >= 0 (L1/L2+) min ||x||w,1 + (1/2&rho)||Ax - b||22 s.t. x >= 0 (L1/L2con+) min ||x||w,1, s.t. ||Ax - b||2 <= &delta, x >= 0where A is m by n with m less than n, and the solution x (or its representation Wx) is supposed to be (approximately) sparse. The data (A,b) can be real or complex, and the signal x can also be complex in the cases of no nonnegativity constraint. A unitary sparsifying basis W is allowed and the 1-norm for x (or Wx) can be weighted by a vector w >= 0.
The capacity for solving models (L1/L2con) and (L1/L2con+) has been added to version beta-6 for A*A' = I.
News:
- August 3, 2009: YALL1 version beta-6 is released that can solve 2 more models for A*A' = I (with bug fixing)
- June 17, 2009: YALL1 version beta-5 is released with improved robustness for A*A' =\= I
- May 26, 2009: YALL1 version beta-4 is released, which no longer requires A*A' = I
- May 13, 2009: YALL1 version beta-3 is released, which requires A*A' = I
Downloading:
- Please do not re-distribute without the permission from the author.
- The programs are written in Matlab language (solver in pcode).
- The pcode was generated under Matlab R2008b v.7.7 (it may not run under some early versions).
- A paper on YALL1 algorithms and related issues (to be available).
- Go to the Download Request Page