Software List
- ISD -- Iterative Support Detection for Compressive Sensing [link]
- TVAL3 -- TV minimization by Augmented Lagrangian and ALternating direction ALgorithms [link]
- RecPF -- RecPF: Reconstruction from Partial Fourier data [link]
- FTVd -- color or grasy-scale image deblurring package [link]
- PGC --- graph-cut solver [link]
- FPC -- shrinkage-based algorithm for L_1-miminization [link]
- Bregman Iterative Algorithm built on FPC [link]
Descriptions
- FTVd: a Fast Total Variation based image deblurring algorithm [link]
- PGC, a Preflow-Push based Graph-Cut Solver [link]
- FPC, a fixed-point continuation algorithm for L1-miminization [link]
- A Bregman Iterative Algorithm for constrained L1-Minimization [link]
This is a Matlab package for recovering images, gray scale or color, from blurry and noisy observations based on solving one of the following 2 problems:
min TV(u) + (p/2) ||h*u -f||2 or min TV(u) + p ||h*u -f||1, 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. The noise can be either Gaussian or impulsive like salt-and-pepper.
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).
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 - fk||2,
for given matrix A and vector fk. Our approach is especially useful for many compressed sensing applications where matrix-vector operations involving A and AT can be computed by fast transforms.