Image restoration via joint low-rank and external nonlocal self-similarity prior

Recent studies have revealed that joint priors, such as joint sparsity and external nonlocal self-similarity (ENSS) prior and joint low-rank and sparsity prior, are extremely effective in various image inverse problems. Few works, however, make use of both low-rank and ENSS priors. With this in mind, in this paper we propose a new joint prior, namely LRENSS prior, which utilizes low-rank and ENSS priors jointly in a unified framework, and successfully adapt the proposed LRENSS prior to image restoration problems. Specifically, low-rank and ENSS priors are bridged by treating ENSS prior as dictionaries for structural sparse representation. Further, an elegant block coordinate descent method is developed to solve the corresponding optimization problem. The proposed LRENSS prior is validated on image denoising and image deblurring tasks. Experimental results illustrate that the proposed LRENSS prior has better performance than other state-of-the-art algorithms in both qualitative and quantitative assessments.