CS: TVAL3 TV minimization by Augmented Lagrangian and ALternating direction ALgorithms, and YALL1

Chengbo Li, Wotao Yin, and Yin Zhang just released

TVAL3: TV minimization by Augmented Lagrangian and ALternating direction ALgorithms


From the page:

This solver can currently be applied to the following TV-minimization problems:


(Isotropic/Anisotropic TV) min TV(u) s.t. Au = b

(Isotropic/Anisotropic TV+) min TV(u) s.t. Au = b and u \gt 0

(Isotropic/Anisotropic TVL2) min TV(u) + (μ/2)||Au - b||22

(Isotropic/Anisotropic TVL2+) min TV(u) + (μ/2)||Au - b||22 s.t. u \gt 0

where A is m by n with m less than n representing the measurement matrix, b is a dense vector representing the observation, and the solution u is supposed to be (approximately) sparse or piecewise linear. The data (A,b) can be real or complex, and the signal u can also be complex in cases of no nonnegativity constraint. Besides, A*A'=I is not required.

You can download the code here.

In related news, YALL1 version beta-5 was released yesterday with improved robustness for A*A' =\= I.

Both reconstruction softwares will be added to the reconstruction section of the Compressive Sensing Big Picture page.

Credit: NASA, LRO/LCROSS on the launch pad via Damaris' blog.