Recent Advances in Iterative Algorithms for Linear Inverse Problems under Non-quadratic Regularization

Description:  Iterative shrinkage/thresholding (IST) algorithms have been recently proposed to handle a class of convex (maybe non-smooth) unconstrained optimization problems arising in image restoration and other linear inverse problems (e.g., total-variation-based or wavelet-based restoration). It happens that the convergence rate of these IST algorithms depends heavily on the condition of the linear observation operator, becoming very slow when this operator is ill-conditioned or ill-posed. In this talk, I will describe two recently introduced approaches which yield algorithms much faster than IST, specially for severely ill-conditioned problems. The first approach, termed 2IST, is a two-step version of IST; I will briefly mention theoretical results concerning its convergence and show experimental evidence showing that it clearly outperforms IST. The second approach is based on a quadratic programming reformulation of the problem (with bound constraints) to which we apply a gradient projection algorithm. In particular, we adopt a variant of a recently proposed "projected Barzilai-Borwein method", which we show to be particularly effective for the problem in hand. Area(s): Date:  2007-06-19 Start Time:   14:30 Speaker:  Mário A. T. Figueiredo, Instituto de Telecomunicações Instituto Superior Técnico Lisboa, Portugal Place:  5.4 Research Groups: -Numerical Analysis and Optimization See more:   <Main>