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Previously, Ratliff et al. and Sakoglu et al. developed algebraic nonuniformity correction (NUC) algorithms (the latter developed a matrix-based version with regularization capabilities) which mitigate fixed-pattern nonuniformity (noise) that is notoriously present in infrared image sequences/videos, by utilizing global translational motion of the scene or the imaging camera system. Infrared imagery, like almost any other two-dimensional (2-D) imagery, have been traditionally sampled and acquired using a rectangular grid, therefore the developed NUC algorithms work on this traditional rectangular grid mitigating the most dominant, bias/offset portion of the nonuniformity. On the other hand, it is well-known that hexagonal sampling grid captures more information in sampled data/imagery when compared to traditional rectangular sampling, and a hexagonal addressing scheme for hexagonally-sampled imagery, namely array set addressing scheme, was recently developed by Rummelt et al. in order to be able to convert imagery between the two different coordinate systems and to perform various mathematical and image processing operations. In this work, we derive the bilinear interpolation equations between two image frames for hexagonally-sampled infrared imagery with bias/offset nonuniformity under the 2-D global motion of the scene or the camera, and apply the 2-D algebraic NUC algorithm to hexagonally-sampled imagery. We present a simulation of MWIR infrared imagery with hexagonally-sampled pixel array, with global motion of the scene and with bias/offset nonuniformity, and we test the efficiency of the NUC algorithm on the simulated infrared imagery (based on real MWIR infrared imagery) and compare the performance of the hexagonally-sampled pixel array imagery NUC results to those of the traditional rectangularly-sampled pixel array imagery.
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