A two-stage convolutional sparse prior model for image restoration

Image restoration (IR) from noisy, blurred or/and incomplete observed measurement is one of the important tasks in image processing community. Image prior is of utmost importance for recovering a high quality image. In this paper, we present a two-stage convolutional sparse prior model for efficient image restoration. The multi-view features prior is first obtained by convolving the image with the Fields-of-Experts (FoE) filters and then the resulting multi-view features are represented by convolutional sparse coding (CSC) prior. By taking advantage of the convolutional filters, the proposed two-stage model inherits the strengths of multi-view features and CSC priors. The assembled multi-view features contain high-frequency, redundancy, and large range of feature orientations, which are favor to be represented by CSC and consequently for better image recovery. Augmented Lagrangian and alternating direction method of multipliers are employed to decouple the nonlinear optimization problem in order to iteratively approach the optimum solution. The results of various experiments on image deblurring and compressed sensing magnetic resonance imaging (CS-MRI) reconstruction consistently demonstrate that the proposed algorithm efficiently recovers image and presents advantages over the current leading restoration approaches.