### Ioannis Dassios (University of Edinburgh)

#### Second-order methods for sparse signal reconstruction

*Wednesday 23 October 2013 at 15.30, JCMB 6206*

##### Abstract

In this talk we consider a family of optimization problems which arise in the
field of signal reconstruction, i.e. L1 and Total-Variation (TV) regularized
Least-Squares (LS), L1-Analysis and combinations. There has been a
considerable effort for the development of first-order algorithms for L1 and TV
regularized LS. State-of-the-art implementations such as SPGL1 and TwIST can
solve large-scale problems in few seconds on a PC. However, the broader family
of problems studied in this talk challenge these methods. We solve this family
of problems in two steps. First, appropriate smoothing of the problems is
applied, second, a class of Newton-type algorithms is employed, embedded in a
continuation framework for further acceleration. Moreover, we present
perturbation analysis of the optimal solution obtained by the smoothed problem
as a function of a smoothing parameter.

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