Blind superresolution from undersampled blurred measurements
A.E. Yagle · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2003
Superresolution is the problem of reconstructing a single high-resolution image from several blurred and downsampled low-resolution versions of it. We solve this problem for the case of unknown blurring functions. The image and functions must have finite support, and the number of low-resolution images must equal or exceed the number of pixels in each blurring function. Using a 2-D polyphase decomposition of the image, we show that the obvious reformulation as an MIMO blind deconvolution problem fails unless the grid of downsampling is chosen carefully, in which case 2X2 downsampling can be achieved. We also show that irregular sampling allows reconstruction of an MXM high-resolution image from L2 low-resolution images blurred with an LXL blurring function can be achieved with as few as L2 + (M/L)2 pixels in each low-resolution image. Illustrative examples illustrate the points with explicit numbers.