Blind superresolution from undersampled blurred measurements

Andrew E Yagle

doi:10.1117/12.504471

24 December 2003 Blind superresolution from undersampled blurred measurements

Andrew E Yagle

Proceedings Volume 5205, Advanced Signal Processing Algorithms, Architectures, and Implementations XIII; (2003) https://doi.org/10.1117/12.504471
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

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.

Citation Download Citation

Andrew E Yagle "Blind superresolution from undersampled blurred measurements", Proc. SPIE 5205, Advanced Signal Processing Algorithms, Architectures, and Implementations XIII, (24 December 2003); https://doi.org/10.1117/12.504471

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