I just came across a CS solver written in R as shown in this presentation: Compressive Sampling with R: A Tutorial by Mehmet Suzen. The R1Magic package is here. A reference manual is here.

YALL1 now include a group sparsity solving capability. Let us look at what he can do. From the webpage:

YALL1 package now includes:

- , a solver for sparse reconstruction: Version 1.3, Apr 07, 2011.
YALL1 BasicYALL1 Basic

- , a solver for group/joint sparse reconstruction: Version 1.0, June 09, 2011. Wiki
YALL1 Group

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||_{2}^{2}(L1/L2con) min ||Wx||_{w,1}, s.t. ||Ax - b||_{2}<= δ

(BP+) min ||x||_{w,1}s.t. Ax = b and 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||_{2}^{2}s.t. x >= 0

(L1/L2con+) min ||x||_{w,1}, s.t. ||Ax - b||_{2}<= δ, x >= 0

where

- is an
Am-by-nmatrix withm<< n,

- the solution
x(or its representationWx) is supposed to be (approximately) sparse,

- the data and solution can be
realorcomplex,(If complex, then no non-negativity constraint is allowed)

- a unitary sparsifying basis
Wis optional,Go to discussions and Q&As.

- the 1-norm can be optionally weighted by a nonnegative vector
w.

Supported Features

- Multiple types of
A

- explicit matrix

- ensembles of fast transforms such as FFT, DCT, wavelets

- Both real and complex data

- Both sparse and compressible signals
YALL1 Group

- Non-negative signals

The group sparsity code solves the following model

(GroupBP) min sum_{i}w_{i}||x_g_{i}||_{2}s.t. Ax = b

where g_{1}, g_{2}, … are groups of coordinates and w_{1},w_{2}, … are their weights.

Joint sparsity is a special case of group sparsity for recovering X = [x_{1},x_{2}, ..., x_{l}] where the x_{i}‘s share a common sparse support.

(JointBP) min sum_{i}w_{i}||X_{i,:}||_{2}s.t. AX = B.

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
notneed to cover all coordinatesContributors

- Easy to modify for the support of complex numbers and your signals

Yin Zhang*, Wei Deng, Junfeng Yang, and Wotao Yin.

* The original author of YALL1 (beta 1 – 6).

Tech report

YALL1 Basic: Alternating Direction Algorithms for L1 Problems in Compressive Sensing, Rice CAAM Report TR09-37, 2009.

YALL1 Group/Joint Sparsity: Group Sparse Optimization by Alternating Direction Method, Rice CAAM Report TR11-06, 2011.

Download

YALL1 is nowopen-source. It is distributed under the terms of the GNU General Public License. [Proceed to the download page]

Credit Video: ESA/DLR/FU Berlin (G. Neukum), via the Planetary Society blog.

Phobos ( a moon of Mars) slips past Jupiter, On June 1 2011, Mars express watched as Phobos (the inner and larger of Mars' two moons) slipped past distant Jupiter. Mars Express is studying Phobos to help the Russian Phobos-Grunt mission prepare to land on the moon and grab a sample for return to Earth. Credit: ESA/DLR/FU Berlin (G. Neukum)

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