Stanley Osher – Optimization Online

Learning Circulant Sensing Kernels

Published: 2012/08/13

Convex Optimization, Data-Mining, Quadratic Programming circulant matrix, compressed sensing, dictionary learning, sensing kernel learning, sensing operator learning, toeplitz matrix

In signal acquisition, Toeplitz and circulant matrices are widely used as sensing operators. They correspond to discrete convolutions and are easily or even naturally realized in various applications. For compressive sensing, recent work has used random Toeplitz and circulant sensing matrices and proved their efficiency in theory, by computer simulations, as well as through physical … Read more

Error Forgetting of Bregman Iteration

Published: 2012/05/01

Stanley Osher

Wotao Yin

Convex Optimization, Nonsmooth Optimization bregman iteration, error forgetting, l1-minimization, piece-wise linear function, polyhedral function, sparse optimization

This short article analyzes an interesting property of the Bregman iterative procedure, which is equivalent to the augmented Lagrangian method after a change of variable, for minimizing a convex piece-wise linear function J(x) subject to linear constraints Ax=b. The procedure obtains its solution by solving a sequence of unconstrained subproblems of minimizing J(x)+1/2||Ax-b^k||^2, where b^k … Read more