Robust shift and add approach to super-resolution

In the last two decades, many papers have been published, proposing a variety of methods for multi-frame resolution enhancement. These methods, which have a wide range of complexity, memory and time requirements, are usually very sensitive to their assumed model of data and noise, often limiting their utility. Different implementations of the non-iterative Shift and Add concept have been proposed as very fast and effective super-resolution algorithms. The paper of Elad & Hel-Or 2001 provided an adequate mathematical justification for the Shift and Add method for the simple case of an additive Gaussian noise model. In this paper we prove that additive Gaussian distribution is not a proper model for super-resolution noise. Specifically, we show that L-p norm minimization (1 less than or equal to p less than or equal to 2) results in a pixelwise weighted mean algorithm which requires the least possible amount of computation time and memory and produces a maximum likelihood solution. We also justify the use of a robust prior information term based on bilateral filter idea. Finally, for the underdetermined case, where the number of non-redundant low-resolution frames are less than square of the resolution enhancement factor, we propose a method for detection and removal of outlier pixels. Our experiments using commercial digital cameras show that our proposed super-resolution method provides significant improvements in both accuracy and efficiency.