18 September 2014 Spectral method for calculating pixel overlap areas applied to multiframe image de-aliasing
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Abstract
Various techniques and algorithms have been developed to improve the resolution of sensor-aliased imagery captured with an under-sampled pixelated image plane. In the literature these de-aliasing algorithms are sometimes included under the broad umbrella of super-resolution. One basic approach to multiframe de-aliasing is the well-known noniterative algorithm termed variable pixel linear reconstruction (VPLR) or “drizzling.” Many modern techniques are based on iterative optimization of a forward model (objective function). Regardless, both iterative and noniterative techniques rely on estimation of frame-to-frame displacements and rotations to subpixel accuracy. Weights are then solved for and used to distribute low-resolution (LR) pixel values to a high-resolution (HR) grid. One approach used in both VPLR and iterative methods to determine weights is to calculate pixel overlap areas. Well-known spatial domain approaches based on computational geometry exist to perform such calculations. Here we present a novel approach based on exactly calculating overlap areas in the spectral domain, which we call the spectral-overlap (SO) method, and include a comparison with the geometric approach of O’Rourke. All spatial spectra in the SO method are calculated analytically once and for all, resulting in expressions devoid of quadratures. Initial studies indicate that this new algorithm executes about 20 times faster than using the O’Rourke algorithm. The speedup is partly explained by the ability to precompute many quantities involved in the SO approach and apply these quantities to the computation of many distinct spatial overlaps. Application of the algorithm to multiframe de-aliasing is demonstrated using simulated imagery.
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Edward Cohen, Edward Cohen, Richard H. Picard, Richard H. Picard, Peter N. Crabtree, Peter N. Crabtree, } "Spectral method for calculating pixel overlap areas applied to multiframe image de-aliasing", Proc. SPIE 9227, Unconventional Imaging and Wavefront Sensing 2014, 922704 (18 September 2014); doi: 10.1117/12.2059221; https://doi.org/10.1117/12.2059221
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