Infuence oF Signal-to-Noise Ratio and Point Spread ±unction
on Limits oF Super-Resolution
Tuan Q. Pham
, Lucas J. van Vliet
, Klamer Schutte
Quantitative Imaging Group, Delft University of Technology, Lorentzweg 1, 2628 CJ, Delft,
TNO Physics and Electronics Laboratory, P.O. Box 96864, 2509 JG, The Hague, The
This paper presents a method to predict the limit of possible resolution enhancement given a sequence of low-
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 ±ll-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.
super-resolution limit, ±ll-factor, under-sampling, deconvolution limit, registration error.
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,
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.
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
compared to a factor of 4 in 2000
). This does not imply a poor research progress but rather a new
challenge due to advances in sensor development that have caused signi±cant changes in LR data characteristics.
In particular, a smaller pixel size with a higher ±ll-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.