Software

• FPC_AS, a successor of FPC for L₁-miminization [link]
• PGC, a Preflow-Push based Graph-Cut Solver [link]


• FPC, a fixed-point continuation algorithm for L₁-miminization [link]

FPC is a simple and robust algorithm for finding sparse solutions that approximately satisfy the underdetermined linear equations Ax = b. Although it was designed with compressed sensing recovery problems in mind, FPC is applicable to any problem expressible in the form

min ||x||₁ + f(x).

• A Bregman Iterative Algorithm for constrained L₁-Minimization [link]

This is a simple and extremely efficient iterative methods for solving the Basis Pursuit problem

min ||x||₁, subject to Ax = b,
which is used in compressed sensing. This method is based on Bregman iterative regularization and it gives a very accurate solution after solving only a very small number of instances of the unconstrained problem

min p||x||₁ + (1/2)||Ax - f^k||²,
for given matrix A and vector f^k. Our approach is especially useful for many compressed sensing applications where matrix-vector operations involving A and A^T can be computed by fast transforms.

• FTVd, a fast total variation based image deblurring algorithm [link]

This is a simple but efficient algorithm for recovering images from blurry and noisy observations based on solving the problem

min TV(u) + (p/2) ||h*u -f||²,
where f is an input blurry and noise image, u is the output image, h is a blurring kernel, and p>0 is a regularization parameter.