Abstract

Various techniques and algorithms have been developed to improve the resolution of sensor-aliased imagery captured with multiple subpixel-displaced frames on an undersampled pixelated image plane. These dealiasing algorithms are typically known as multiframe superresolution (SR), or geometric SR to emphasize the role of the focal-plane array. Multiple low-resolution (LR) aliased frames of the same scene are captured and allocated to a common high-resolution (HR) reconstruction grid, leading to the possibility of an alias-free reconstruction, as long as the HR sampling rate is above the Nyquist rate. Allocating LR-frame irradiances to HR frames requires the use of appropriate weights. Here we present a novel approach in the spectral domain to calculating exactly weights based on spatial overlap areas, which we call the spectral-overlap (SO) method. We emphasize that the SO method is not a spectral approach but rather an approach to calculating spatial weights that uses spectral decompositions to exploit the array properties of the HR and LR pixels. The method is capable of dealing with arbitrary aliasing factors and interframe motions consisting of in-plane translations and rotations. We calculate example reconstructed HR images (the inverse problem) from synthetic aliased images for integer and for fractional aliasing factors. We show the utility of the SO-generated overlap-area weights in both noniterative and iterative reconstructions with known or unknown aliasing factor. We show how the overlap weights can be used to generate the Green’s function (pixel response function) for noniterative dealiasing. In addition, we show how the overlap-area weights can be used to generate synthetic aliased images (the forward problem). We compare the SO approach to the spatial-domain geometric approach of O’Rourke and find virtually identical high accuracy but with significant enhancements in speed for SO. We also compare the SO weights to interpolated weights and find that the overlap-area weights lead to significantly smaller errors in iterative reconstructions. We consider how the SO method might be extended to account for the influence of the optical transfer function, more complex or space-variant motions, the registration process, and noise.

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