Theoretical analysis on reconstruction-based super-resolution for an arbitrary PSF

This study presents and proves a condition number theorem for super-resolution (SR). The SR condition number theorem provides the condition number for an arbitrary space-invariant point spread function (PSF) when using an infinite number of low resolution images. A gradient restriction is also derived for maximum likelihood (ML) method. The gradient restriction is presented as an inequality which shows that the power spectrum of the PSF suppresses the spatial frequency component of the gradient of ML cost function. A Box PSF and a Gaussian PSF are analyzed with the SR condition number theorem. Effects of the gradient restriction on super-resolution results are shown using synthetic images.