Many problems in image and video processing may be formulated in the language of constrained optimization. Algorithms for solving general constrained optimization problems may not guarantee solutions or be computationally efficient, particularly if the problem is nonlinear or non-convex. Oftentimes these constrained optimization problems may be relaxed into the form of a convex problem. This allows for the use of convex solvers such as the Augmented Lagrangian method and the Split Bregman iteration. In this thesis, we will study the advantages of incorporating convexity into constrained optimization problems. These problems will be motivated from the standpoint of hyperspectral image processing, particularly the detection and identification of airborne chemicals in gas cloud releases.
|Commitee:||Gao, Tangan, Ziemer, William|
|School:||California State University, Long Beach|
|Department:||Mathematics and Statistics|
|School Location:||United States -- California|
|Source:||MAI 52/05M(E), Masters Abstracts International|
|Keywords:||Convex optimization, Hyperspectral, Image processing|
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