Weighted total generalized variation for compressive sensing reconstruction

Total generalized variation (TGV) is a generalization of total variation (TV). This method has gained more and more attention in image processing due to its capability of reducing staircase effects. As the existence of high order regularity, TGV tends to blur edges, especially when noise is excessive. In this paper, we propose an iterative weighted total generalized variation (WTGV) model to reconstruct images with sharp edges and details from compressive sensing data. The weight is iteratively updated using the latest reconstruction solution. The splitting variables and alternating direction method of multipliers (ADMM) are employed to solve the proposed model. To demonstrate the effectiveness of the proposed method, we present some numerical simulations using partial Fourier measurement for natural and MR images. Numerical results show that the proposed method can avoid staircase effects and keep fine details at the same time.