Maximum likelihood interpolation for aliasing-aware image restoration

Here we propose an efficient estimation method to interpolate new samples in a blurred and aliased observation, in such a way that (1) aliasing artifacts in an ulterior restoration are mitigated, and (2) thanks to aliasing we may recover some spatial frequencies beyond the Nyquist frequency (super-resolution). The only requirement is having a good approximation of the blurring kernel in high resolution (HR). The method consists of two sequential steps: (1) to perform a Maximum Likelihood Interpolation, according to a Gaussian model; and (2) to apply a standard deconvolution to the interpolated image, using the HR blurring kernel in both steps. Simulations show strong improvements with respect to first deconvolving the unprocessed observation and then doing a standard interpolation with splines, and also with respect to first doing a standard interpolation and then deconvolving.