A hybrid regularization model for linear inverse problems

Abstract

For the ill-posed linear inverse problem, we propose a hybrid regularization model, which possesses the characters of both the Tikhonov regularization and the TV regularization to some extent. Through transformation, this hybrid regularization model is reformulated as an equivalent minimization problem. Then
we present a modified iterative shrinkage-thresholding algorithm (MISTA) to solve it. The numerical experiments show the effectiveness and the superiority of  both the regularization model and the algorithm.