A fast proximal splitting algorithm for constrained TGV-regularized image restoration

Fast proximal splitting algorithm for constrained TGV‐regularised image restoration and reconstruction

“…Such degradations cause the loss of important features in an image, such as blurring of edges or textures. Therefore, they need to be undone or reduced prior to performing additional image‐processing tasks and image restoration/reconstruction [1–7] become a basal task in imaging. For simplicity, the degradation process of an image is generally modelled as the following linear problem: where u and f are the original image and the observed image, respectively, both of which possess an domain that is expressed in a vector form; is the matrix operator that models the acquisition processing, which is generally an ill‐posed operator; and is a vector of some type of additive noise such as Gaussian noise or impulse noise.…”

“…In this paper, a fast algorithm is proposed to solve the problem (2), where is the TGV model. The proposed method was first used for image deblurring in [1]. In this paper, we further expand it to MRI reconstruction, which is a famous CS problem.…”