### Software

- FPC_AS, a successor of FPC for
*L*_{1}-miminization [link] - PGC, a Preflow-Push based Graph-Cut Solver [link]
- FPC, a fixed-point continuation algorithm for
*L*_{1}-miminization [link] - A Bregman Iterative Algorithm for constrained
*L*_{1}-Minimization [link] - FTVd, a fast total variation based image deblurring algorithm [link]

FPC is a simple and robust algorithm for finding sparse solutions that approximately satisfy the underdetermined linear equationsAx=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).

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

min || x||_{1}, subject toAx=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 matrixAand vectorf. Our approach is especially useful for many compressed sensing applications where matrix-vector operations involving^{k}AandA^{T}can be computed by fast transforms.

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},

wherefis an input blurry and noise image,uis the output image,his a blurring kernel, andp>0 is a regularization parameter.