A Quantum Richardson–Lucy image restoration algorithm based on controlled rotation operation and Hamiltonian evolution

The problems of the real-time and high-precision image processing, even the powerful classical computers and their algorithms, are not satisfactory solution. With the emerging quantum technology, quantum image representation that shines can ease these solutions. The quantum Richardson–Lucy algorithm is proposed on controlled rotation operation and Hamiltonian evolution. To begin with, a flexible representation of the quantum image model is used as the basis of image representation, and the amplitude is manipulated by controlled rotation gate. Then, the controlled rotation operation is completed, and then, the algorithm only needs the quantum state on the first quantum register, and the algorithm constructs an quantum gate by Hamiltonian evolution on the register, which is to realize the quantum gate Richardson–Lucy function. Finally, the quantum state after controlled rotation is further operated by the quantum gate constructed by non-sparse Hamiltonian evolution technique, and all quantum states storing color information are reduced to clear quantum images. The simulation results show that the algorithm has the best effect on motion blur, and the peak signal-to-noise ratio can reach 31.3985 under small blur degree. The processing result of Gaussian noise is worse than that of pure motion blur, with a peak signal-to-noise ratio of 26.5232.