The application of an oblique-projected Landweber method to a model of supervised learning

This report brings together a novel approach to some computer vision problems and a particular algorithmic development of the Landweber iterative algorithm. The algorithm solves a class of high-dimensional, sparse, and constrained least-squares problems, which arise in various computer vision learning tasks, such as object recognition and object pose estimation. The algorithm has recently been applied to these problems, but it has been used rather heuristically. In this report we describe the method and put it on firm mathematical ground. We consider a convexly constrained weighted least-squares problem and propose for its solution a projected Landweber method which employs oblique projections onto the closed convex constraint set. We formulate the problem, present the algorithm and ∗To whom correspondence should be addressed