Mathematical model development of super-resolution image Wiener restoration

In super-resolution (SR), a set of degraded low-resolution (LR) images are used to reconstruct a higher-resolution image that suffers from acquisition degradations. One way to boost SR images visual quality is to use restoration filters to remove reconstructed images artifacts. We propose an efficient method to optimally allocate the LR pixels on the high-resolution grid and introduce a mathematical derivation of a stochastic Wiener filter. It relies on the continuous-discrete-continuous model and is constrained by the periodic and nonperiodic interrelationships between the different frequency components of the proposed SR system. We analyze an end-to-end model and formulate the Wiener filter as a function of the parameters associated with the proposed SR system such as image gathering and display response indices, system average signal-to-noise ratio, and inter-subpixel shifts between the LR images. Simulation and experimental results demonstrate that the derived Wiener filter with the optimal allocation of LR images results in sharper reconstruction. When compared with other SR techniques, our approach outperforms them in both quality and computational time.