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Influence of Signal-to-Noise Ratio and Point Spread Function

Influence of Signal-to-Noise Ratio and Point Spread...

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Influence of Signal-to-Noise Ratio and Point Spread Function on Limits of Super-Resolution Tuan Q. Pham 1 , Lucas J. van Vliet 1 , Klamer Schutte 2 1 Quantitative Imaging Group, Delft University of Technology, Lorentzweg 1, 2628 CJ, Delft, The Netherlands 2 TNO Physics and Electronics Laboratory, P.O. Box 96864, 2509 JG, The Hague, The Netherlands ABSTRACT This paper presents a method to predict the limit of possible resolution enhancement given a sequence of low- resolution images. Three important parameters influence the outcome of this limit: the total Point Spread Function (PSF), the Signal-to-Noise Ratio (SNR) and the number of input images. Although a large number of input images captured by a system with a narrow PSF and a high SNR are desirable, these conditions are often not achievable simultaneously. To improve the SNR, cameras are designed with near optimal quantum efficiency and maximum fill-factor. However, the latter widens the system PSF, which puts more weight on the deblurring part of a super-resolution (SR) reconstruction algorithm. This paper analyzes the contribution of each input parameters to the SR reconstruction and predicts the best attainable SR factor for given a camera setting. The predicted SR factor agrees well with an edge sharpness measure computed from the reconstructed SR images. A sufficient number of randomly positioned input images to achieve this limit for a given scene can also be derived assuming Gaussian noise and registration errors. Keywords: super-resolution limit, fill-factor, under-sampling, deconvolution limit, registration error. 1. INTRODUCTION Super-resolution (SR) is a technique that uses multiple low-resolution (LR) images to produce images of a higher resolution (HR). Since its conception 20 years ago, 24 the topic has received a huge public interest due to its potential to increase performance of existing camera systems without the need for dedicated hardware. 2 Numerous algorithms have been proposed. 3, 6, 10 For optical systems, the reported performance of SR in practical situations is rather limited, reaching four-times resolution enhancement at its best. Strange enough, recently reports on resolution improvements are typically worse than what have been reported in the past (a SR factor of 1.6 in 2004 11 compared to a factor of 4 in 2000 12 ). This does not imply a poor research progress but rather a new challenge due to advances in sensor development that have caused significant changes in LR data characteristics. In particular, a smaller pixel size with a higher fill-factor results in a lower Signal-to-Noise Ratio (SNR) and a wider Point Spread Function (PSF) with respect to sampling pitch. The SNR and PSF characteristics have been influenced mainly by recent advancement in micro-electronics.
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