Fundamental limits of reconstruction-based superresolution algorithms under local translation.
Superresolution is a technique that can produce images of a higher resolution than that of the originally captured ones. Nevertheless, improvement in resolution using such a technique is very limited in practice. This makes it significant to study the problem: "Do fundamental limits exist for superresolution?" In this paper, we focus on a major class of superresolution algorithms, called the reconstruction-based algorithms, which compute high-resolution images by simulating the image formation process. Assuming local translation among low-resolution images, this paper is the first attempt to determine the explicit limits of reconstruction-based algorithms, under both real and synthetic conditions. Based on the perturbation theory of linear systems, we obtain the superresolution limits from the conditioning analysis of the coefficient matrix. Moreover, we determine the number of low-resolution images that are sufficient to achieve the limit. Both real and synthetic experiments are carried out to verify our analysis.
Lin
Zhouchen
Z
Microsoft Research, Asia, 5th floor, Sigma Building, Zhichun Road No. 49, Haidian District, Beijing, 100080, P.R. China. zhoulin@microsoft.com
Shum
Heung-Yeung
HY
D000465:Algorithms; D001185:Artificial Intelligence; D003196:Computer Graphics; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods; D016247:Information Storage and Retrieval / Q000379:methods*; D016014:Linear Models; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique