R. Sanchez, M. Argáez and P. Guillen. “Sparse Representation via l₁-Minimization for Underdetermined Systems in Classification of Tumors with Gene Expression Data. IEEE 33rd Annual International Conference Proceedings of the Engineering in Medicine and Biology Society, Boston, 30 August-3 September 2011, pp. 3362- 3366.

has been cited by the following article:

• TITLE: Face Recognition from Incomplete Measurements via l1-Optimization

  AUTHORS: Miguel Argaez, Reinaldo Sanchez, Carlos Ramirez

  KEYWORDS: Sparse Representation; l1Minimization; Face Recognition; Sparse Recovery; Interior Point Methods;Sparse Regularization

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.2 No.4, December 20, 2012

  ABSTRACT: In this work, we consider a homotopic principle for solving large-scale and dense l1underdetermined 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 subject 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 l1minimization problems. To that end, we propose to solve a sequence of linear equality constrained multiquadric problems that depends on a regularization parameter that converges to zero. The procedure generates a central path that converges to a point on the solution set of the l1underdetermined problem. In order to solve each subproblem, a conjugate gradient algorithm is formulated. When noise is present 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.