Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Rethinking the Pipeline of Demosaicing, Denoising and Super-Resolution

Incomplete color sampling, noise degradation, and limited resolution are the three key problems that are unavoidable in modern camera systems. Demosaicing (DM), denoising (DN), and super-resolution (SR) are core components in a digital image processing pipeline to overcome the three problems above, respectively. Although each of these problems has been studied actively, the mixture problem of DM, DN, and SR, which is a higher practical value, lacks enough attention. Such a mixture problem is usually solved by a sequential solution (applying each method independently in a fixed order: DM $\to$ DN $\to$ SR), or is simply tackled by an end-to-end network without enough analysis into interactions among tasks, resulting in an undesired performance drop in the final image quality. In this paper, we rethink the mixture problem from a holistic perspective and propose a new image processing pipeline: DN $\to$ SR $\to$ DM. Extensive experiments show that simply modifying the usual sequential solution by leveraging our proposed pipeline could enhance the image quality by a large margin. We further adopt the proposed pipeline into an end-to-end network, and present Trinity Enhancement Network (TENet). Quantitative and qualitative experiments demonstrate the superiority of our TENet to the state-of-the-art. Besides, we notice the literature lacks a full color sampled dataset. To this end, we contribute a new high-quality full color sampled real-world dataset, namely PixelShift200. Our experiments show the benefit of the proposed PixelShift200 dataset for raw image processing.Comment: Code is available at: https://github.com/guochengqian/TENe