Abstract
We propose a novel infimal convolution type functional based on total generalized variation (TGV) and shearlet transform, which can be easily incorporated into image restoration problems. We employ the TGV functional to represent the piecewise smooth cartoon part of an image and the L1 norm of shearlet transform for the edge-like texture part. The proposed model recovers both fine details and edge features of images satisfactorily. The existence of solutions to our proposed model is proved. We also design a general algorithm using the classical first-order Primal–Dual method for solving our imaging problems. Numerical experiments are carried out to illustrate the ability of the new regularizer in preserving edge-like textures better than some existing variational and sparsity-based methods.
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