IMAL   13325
INSTITUTO DE MATEMATICA APLICADA DEL LITORAL "DRA. ELEONOR HARBOURE"
Unidad Ejecutora - UE
artículos
Título:
Image restoration with a half-quadratic approach to mixed weighted smooth and anisotropic bounded variation regularization
Autor/es:
IBARROLA, FRANCISCO; RUBEN D SPIES
Revista:
SOP Transactions on Applied Mathematics
Editorial:
Scientific Online
Referencias:
Año: 2014 vol. 1 p. 59 - 75
ISSN:
2373-8472
Resumen:
The problem of restoring a signal or image is often tantamount to approximating the solution ofa linear inverse ill-posed problem. In order to find such an approximation one might regularizethe problem by penalizing variations on the estimated solution. Among the wide variety ofmethods available to perform this penalization, the most commonly used is the Tikhonov-Phillipsregularization, which is appropriate when the sought signal or image is expected to be smooth,but it results unsuitable whenever preservation of discontinuities and edges is an importantmatter. Nonetheless, there are other methods with edge preserving properties, such as boundedvariation (BV) regularization. However, these methods tend to produce piecewise constantsolutions showing the so called "staircasing effect" and their numerical implementations entailgreat computational effort and cost. In order to overcome these obstacles, we consider a mixedweighted Tikhonov and anisotropic BV regularization method to obtain improved restorationsand we use a half-quadratic approach to construct highly efficient numerical algorithms. Severalnumerical results in signal and image restoration problems are presented.