A Quantum-Classical Hybrid Block-Matching Algorithm in Noisy Environment using Dissimilarity Measure

A block-matching algorithm finds a group of similar image patches inside a search area. Similarity/dissimilarity measures can help to solve this problem. In different practical applications, finding groups of similar image blocks within an ample search area is often necessary, such as video compression, image clustering, vector quantization, and nonlocal noise reduction. In this work, classical image processing is performed using Gaussian noise and image size reduction with a fit of a Low-Pass Filter or Domain Transform. A hierarchical search technique is implemented to encode the images by phase operator. Using phase image coding with the quantum Fourier transform and the Swap test, we propose a dissimilarity measure. Results were obtained with perfect and noisy simulations and in the case of the Swap test with the IBM and Ionq quantum devices.