Welcome
YALL1 package now includes:
- YALL1 Basic, a solver for sparse reconstruction: Version 1.4, July 15, 2011.
- YALL1 Group, a solver for group/joint sparse reconstruction: Version 1.2, June 28, 2011.
YALL1 Basic
solves the following L1-minimization problems:
(BP) min ||Wx||w,1, s.t. Ax = b
(L1/L1) min ||Wx||w,1 + (1/ν)||Ax - b||1
(L1/L2) min ||Wx||w,1 + (1/2ρ)||Ax - b||22
(L1/L2con) min ||Wx||w,1, s.t. ||Ax - b||2 <= δ
(BP+) min ||x||w,1, s.t. Ax = b, x >= 0
(L1/L1+) min ||x||w,1 + (1/ν)||Ax - b||1, s.t. x >= 0
(L1/L2+) min ||x||w,1 + (1/2ρ)||Ax - b||22, s.t. x >= 0
(L1/L2con+) min ||x||w,1, s.t. ||Ax - b||2 <= δ, x >= 0
where
- A is an m-by-n matrix with m << n,
- the solution x (or its representation Wx) is supposed to be (approximately) sparse,
- the data and solution can be real or complex, (If complex, then no non-negativity constraint is allowed)
- a unitary sparsifying basis W is optional,
- the 1-norm can be optionally weighted by a nonnegative vector w.
Go to discussions and Q&As.
Supported Features
- Multiple types of A
- explicit matrix
- ensembles of fast transforms such as FFT, DCT, wavelets
- ensembles of convolution or circulant matrices
- Both real and complex data
- Both sparse and compressible signals
- Non-negative signals
YALL1 Group
The group sparsity code solves the following model
(GroupBP) min sum_i wi ||x_gi||2 s.t. Ax = b
(GroupBP+) min sum_i wi ||x_gi||2 s.t. Ax = b, x >= 0
where g1, g2, … are groups of coordinates and w1,w2, … are their weights.
Joint sparsity is a special case of group sparsity for recovering X = [x1,x2, …, xl] where the xi‘s share a common sparse support.
(JointBP) min sum_i wi ||X_i,:||2 s.t. AX = B.
(JointBP+) min sum_i wi ||X_i,:||2 s.t. AX = B, x>= 0.
Supported Features
- Multiple types of A
- explicit matrix
- ensembles of fast transforms such as FFT, DCT, wavelets
- general function handle
- Groups can overlap
- The union of groups does not need to cover all coordinates
- Easy to modify for the support of complex numbers and your signals
Contributors
Yin Zhang*, Wei Deng, Junfeng Yang, and Wotao Yin.
* The original author of YALL1 (beta 1 – 6).
Citation:
YALL1 basic models and tests: J. Yang and Y. Zhang. Alternating direction algorithms for L1-problems in compressive sensing, SIAM Journal on Scientific Computing, 33, 1-2, 250-278, 2011. [arXiv]
YALL1 basic solver code: Y. Zhang, J. Yang, and W. Yin. YALL1: Your ALgorithms for L1, online at yall1.blogs.rice.edu, 2011.
YALL1 group/joint sparsity: W. Deng, W. Yin, and Y. Zhang, Group Sparse Optimization by Alternating Direction Method, Rice CAAM Report TR11-06, 2011. [pdf]
Download
YALL1 is now open-source. It is distributed under the terms of the GNU General Public License. [Proceed to the download page]