Rice University, L1-Related Optimization Project

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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 - 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.

  • 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.