Event Details

Compressive Sensing Using Lp Optimization

Presenter: Jeevan K. Pant, PhD student
Supervisor: Drs. Andreas Antoniou and Wu-Sheng Lu

Date: Tue, April 17, 2012
Time: 13:00:00 - 00:00:00
Place: EOW 430

ABSTRACT

Abstract:

Three problems in compressive sensing, namely,

  • recovery of sparse signals from noise-free measurements,
  • recovery of sparse signals from noisy measurements, and
  • recovery of block-sparse signals from noisy measurements
are investigated.

Three algorithms are developed for the reconstruction of sparse signals from noise-free measurements. The first and second algorithms minimize the approximate L0 and Lp pseudonorms, respectively, in the null space of the measurement matrix using a sequential quasi-Newton algorithm. The third algorithm minimizes the approximate Lp pseudonorm in the null space by using a sequential conjugate-gradient (CG) algorithm.

Two algorithms for the reconstruction of signals from noisy measurements are developed by minimizing an Lp-pseudonorm regularized squared error as the objective function using a sequential optimization procedure.

The well known total variation ( TV ) norm is extended to a nonconvex version called the TVp pseudonorm and an algorithm for the reconstruction of images is developed that involves minimizing a TVp -pseudonorm regularized squared error using a sequential Fletcher-Reeves' CG algorithm.

The reconstruction of block-sparse signals is investigated. The L2/1 norm is extended to a nonconvex version, called the L2/p pseudonorm, and an algorithm based on the minimization of an L2/p-pseudonorm regularized squared error is developed.