IMAGE RESTORATION WITH A HALF-QUADRATIC APPROACH TO MIXED WEIGHTED SMOOTH AND ANISOTROPIC BV REGULARIZATION

FRANCISCO IBARROLA; RUBEN SPIES

San Luis

Congreso; Reunión Anual de la Unión Matemática Argentina, UMA; 2014

Unión Matemática Argentina, UMA

The problem of restoring a signal or image is often tantamount to approximating the solution of a linear inverse ill-posed problem. In order to find such approximation one might regularize the problem by penalizing varia tions on the estimated solution. Among the wide variety of methods available to perform this penalization, the most commonly used is the Tikhonov-Phillips regularization, which is appropriate when the sought image is expected to be smooth, but results unsuitable whenever edge preservation is an important matter. Nonetheless, there are other methods with edge preserving properties, such as bounded variation (BV) regularization, onwhich we shall focus here. Implementing this, however, generally entails a great computational cost and tends to produce piecewise constant solutions. In order to overcome these obstacles, we will consider a mixed weighted Tikhonov and anisotropic BV regularization method to perform an improved restoration, and a half-quadratic approach to construct a reduced CPU time algorithm. Several numerical results in signal and image restoration problems will be shown