Bounded perturbation resilience of projected scaled gradient methods

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, … Read more

String-Averaging Expectation-Maximization for Maximum Likelihood Estimation in Emission Tomography

We study the maximum likelihood model in emission tomography and propose a new family of algorithms for its solution, called String-Averaging Expectation-Maximization (SAEM). In the String-Averaging algorithmic regime, the index set of all underlying equations is split into subsets, called “strings,” and the algorithm separately proceeds along each string, possibly in parallel. Then, the end-points … Read more

A Note on the Behavior of the Randomized Kaczmarz Algorithm of Strohmer and Vershynin

In a recent paper by Strohmer and Vershynin (J. Fourier Anal. Appl. 15:262–278, 2009) a “randomized Kaczmarz algorithm” is proposed for solving consistent systems of linear equations {ai, x = bi }m i=1. In that algorithm the next equation to be used in an iterative Kaczmarz process is selected with a probability proportional to ai2. … Read more