Quantum image restoration based on Hudson–Parthasarathy Schrodinger equation

Abstract

In this paper, we propose a quantum–classical hybrid filtering scheme used for denoising of a classical noisy image field. This includes an iterative procedure of transforming pairs of classical image and noise fields into quantum states using standard classical–quantum conversion and then posing the problem of constructing an optimal unitary operator based on the Hudson–Parthasarathy quantum stochastic calculus. The noisy quantum image state is filtered using an optimum unitary operator followed by quantum–classical conversion of the denoised quantum image state. Finally, filtering of the resultant classical image is performed using the standard median filtering approach. In addition to the proposed algorithm, our work includes a theoretical display of the Schrodinger evolution in the presence of classical randomness. The results demonstrate the marked superiority of our proposed algorithm over the existing classical denoising scheme.