L1-L2 Optimization in Signal and Image Processing
Résumé
Sparse, redundant representations offer a powerful emerging model for signals. This model approximates a data source as a linear combination of few atoms from a prespecified and over-complete dictionary. Often such models are fit to data by solving mixed ¿1-¿2 convex optimization problems. Iterative-shrinkage algorithms constitute a new family of highly effective numerical methods for handling these problems, surpassing traditional optimization techniques. In this article, we give a broad view of this group of methods, derive some of them, show accelerations based on the sequential subspace optimization (SESOP), fast iterative soft-thresholding algorithm (FISTA) and the conjugate gradient (CG) method, present a comparative performance, and discuss their potential in various applications, such as compressed sensing, computed tomography, and deblurring.
Mots clés
computed tomography
convex optimization problems
fast iterative soft-thresholding algorithm
iterative-shrinkage algorithms
numerical methods
redundant representations
sequential subspace optimization
signal-image processing
conjugate gradient methods
image restoration
image segmentation
iterative methods
optimisation