6Graph Spectral Image Restoration

Jiahao PANG1 and Jin ZENG2

1InterDigital Inc., New York, USA

2SenseTime Research, Shenzhen, China

6.1. Introduction

Digital images are vulnerable to various degradations during acquisition, editing, compression, transmission and so on. For instance, capturing a night view with a smartphone camera will likely result in a noisy image(Yuan et al. 2007), while storing digital images in the widely used Joint Photographic Experts Group(JPEG) format inevitably leads to compression artifacts(Xiong et al. 1997). However, the quality of digital images is vital, not only to the esthetic aspect of human perception, but also to the subsequent consumption in machine tasks(e.g. recognition and segmentation). Consequently, for decades, a huge body of research has been devoted to digital image restoration; yet, it remains a crucial topic in signal processing and computer vision(Katsaggelos 2012). Representative image restoration problems include image denoising, image deblurring, image inpainting and image super-resolution(Gunturk and Li 2012), as illustrated in Figure 6.1. In this chapter, we focus on resolving this category of problems with graph spectral signal processing.

6.1.1. A simple image degradation model

We first introduce a sufficiently general but simple image degradation model(Aubert and Vese 1997; Milanfar 2013; Dong et al. 2012). We denote the original (uncorrupted) image in its vectorized form by x ∈ ℝn and its corrupted version by y ∈ ℝm

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