Abstract

In this work, we consider a homotopic principle for solving large-scale and dense underdetermined problems and its applications in image processing and classification. We solve the face recognition problem where the input image contains corrupted and/or lost pixels. The approach involves two steps: first, the incomplete or corrupted image is sub-ject to an inpainting process, and secondly, the restored image is used to carry out the classification or recognition task. Addressing these two steps involves solving large scale minimization problems. To that end, we propose to solve a sequence of linear equality constrained multiquadric problems that depends on a regularization parameter that con-verges to zero. The procedure generates a central path that converges to a point on the solution set of the underde-termined problem. In order to solve each subproblem, a conjugate gradient algorithm is formulated. When noise is pre-sent in the model, inexact directions are taken so that an approximate solution is computed faster. This prevents the ill conditioning produced when the conjugate gradient is required to iterate until a zero residual is attained.