Quantum median filter for Total Variation image denoising

In this new computing paradigm, named quantum computing, researchers from all over the world are taking their first steps in designing quantum circuits for image processing, through a difficult process of knowledge transfer. This effort is named Quantum Image Processing, an emerging research field pushed by powerful parallel computing capabilities of quantum computers. This work goes in this direction and proposes the challenging development of a powerful method of image denoising, such as the Total Variation (TV) model, in a quantum environment. The proposed Quantum TV is described and its sub-components are analysed. Despite the natural limitations of the current capabilities of quantum devices, the experimental results show a competitive denoising performance compared to the classical variational TV counterpart.