Controlled Total Variation regularization for image deconvolution
Résumé
To resolve the image deconvolution problem, the
total variation (TV) minimization approach has been proved
to be very efficient. However, we observe that this approach
has an over-minimizing TV effect in the sense that it gives a
solution whose TV is usually smaller than that of the original
image. This effect is due to the pre-pondering role of the TV
in the the corresponding minimization problem and prevents
from finding the exact solution of the deconvolution problem
when such a solution exists. We propose a modified version of
the gradient descent algorithm, which leads to an exact solution
of the deconvolution problem if it exists and to a satisfactory
approximative solution if there is no exact one. The idea consists
in introducing a control on the contribution of the TV in the
classical gradient descent algorithm. The new algorithm has the
advantage that the restored image has the TV closer to that
of the original image, compared to the classical gradient descent
approach. Numerical results show that our method is competitive
compared to some recent ones.