MF-LRTC: Multi-filters guided low-rank tensor coding for image restoration

Image prior information is a determinative factor to tackling with the ill-posed problem. In this paper, we present multi-filters guided low-rank tensor coding (MF-LRTC) model for image restoration. The appeal of constructing a low-rank tensor is obvious in many cases for data that naturally comes from different scales and directions. The MF-LRTC takes advantages of the low-rank tensor coding to capture the sparse convolutional features generated by multi-filters representation. Using such a low-rank tensor coding would reduce the redundancy between feature vectors at neighboring locations and improve the efficiency of the overall sparse representation. In this work, we are committed to achieving this goal by convoluting the target image with Filed-of-Experts (FoE) filters to formulate multi-feature images. Then similarity-grouped cube set extracted from the multi-features images is regarded as a low-rank tensor. The resulting non-convex model is addressed by an efficient ADMM technique. The potential effectiveness of this tensor construction strategy is demonstrated in image restoration including image deblurring and compressed sensing (CS) applications.