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 process-
ing, through a difficult process of knowledge transfer. This effort is named quantum
image processing, an emerging research field pushed by powerful parallel comput-
ing 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 counterpar
