Graph-based joint denoising and super-resolution of generalized piecewise smooth images
Images are often decoded with noise at receiver due to capturing errors and/or signal quantization during compression. Further, it is often necessary to display a decoded image at a higher resolution than the captured one, given available high-resolution (HR) display or a need to zoom-in for detailed examination. In this paper, we address the problems of image denoising and super-resolution (SR) jointly in one unified graph-based framework, focusing on a special class of signals called generalized piecewise smooth (GPWS) images. GPWS images are composed mostly of smooth regions connected by transition regions, and represent an important subclass of images, including cartoon, sub-regions of video frames with captions, graphics images in video games, etc. Like our previous work on piecewise smooth (PWS) images, GPWS images also imply simple-enough graph representations in the pixel domain, so that suitable graph-based filtering techniques can be readily applied. Specifically, leveraging on previous work on graph spectral analysis, for a given pixel block in low-resolution (LR) we first use the second eigenvector of a computed graph Laplacian matrix to identify a hard boundary, and then use the third eigenvector to identify two piecewise smooth regions and a transition region that separates them. The LR hard boundary is then super-resolved into HR via a procedure based on local self-similarity, while graph weights of the LR transition region is mapped to those of the HR transition region via polynomial fitting. Using the computed HR boundary and weights in the transition region, we construct a suitable HR graph corresponding to the LR counterpart, and perform joint denoising / SR using a graph smoothness prior. Experimental results show that our proposed algorithm outperforms two representative separable denoising / SR schemes in both subjective and objective quality.