Sparse Image and Video Recovery Using Gradient Projection for Linearly Constrained Convex Optimization

OF THE CAPSTONE PROJECT Sparse Image and Video Recovery Using Gradient Projection for Linearly Constrained Convex Optimization by Daniel Thompson May 2011 University of California, Merced Abstract This project concerns the reconstruction of a signal, which corresponds to either an image or a temporally-varying scene. Signal recovery can be accomplished through finding a sparse solution to an `2-`1 minimization problem, which can be solved efficiently by gradient projection. In imaging applications, the signal of interest corresponds to nonnegative pixel intensities. Hence, additional nonnegativity constraints are placed upon the `2-`1 minimization problem. This results in a more difficult problem to solve, but one with a higher potential for accurate reconstructions. This work focuses on a gradient projection approach for sparse signal recovery that incorporates nonnegativity constraints in the minimization problem. For video recovery we exploit inter-frame correlations to improve upon the näıve approach of solving each frame independently. Numerical results are presented for both an image and video experiment to demonstrate the effectiveness of this approach.This project concerns the reconstruction of a signal, which corresponds to either an image or a temporally-varying scene. Signal recovery can be accomplished through finding a sparse solution to an `2-`1 minimization problem, which can be solved efficiently by gradient projection. In imaging applications, the signal of interest corresponds to nonnegative pixel intensities. Hence, additional nonnegativity constraints are placed upon the `2-`1 minimization problem. This results in a more difficult problem to solve, but one with a higher potential for accurate reconstructions. This work focuses on a gradient projection approach for sparse signal recovery that incorporates nonnegativity constraints in the minimization problem. For video recovery we exploit inter-frame correlations to improve upon the näıve approach of solving each frame independently. Numerical results are presented for both an image and video experiment to demonstrate the effectiveness of this approach.