Nonparametric Blind Super-resolution

Super resolution (SR) algorithms typically assume that the blur kernel is known (either the Point Spread Function \´PSF\´ of the camera, or some default low-pass filter, e.g. a Gaussian). However, the performance of SR methods significantly deteriorates when the assumed blur kernel deviates from the true one. We propose a general framework for "blind" super resolution. In particular, we show that: (i) Unlike the common belief, the PSF of the camera is the wrong blur kernel to use in SR algorithms. (ii) We show how the correct SR blur kernel can be recovered directly from the low-resolution image. This is done by exploiting the inherent recurrence property of small natural image patches (either internally within the same image, or externally in a collection of other natural images). In particular, we show that recurrence of small patches across scales of the low-res image (which forms the basis for single-image SR), can also be used for estimating the optimal blur kernel. This leads to significant improvement in SR results.