A novel perspective on denoising using quantum localization with application to medical imaging

Abstract: Background noise in many fields such as medical imaging poses significant challenges for accurate diagnosis, prompting the development of denoising algorithms. Traditional methodologies, however, often struggle to address the complexities of noisy environments in high dimensional imaging systems. This paper introduces a novel quantum-inspired approach for image denoising, drawing upon principles of quantum and condensed matter physics. Our approach views medical images as amorphous structures akin to those found in condensed matter physics and we propose an algorithm that incorporates the concept of mode resolved localization directly into the denoising process. Notably, unlike previous studies that considered localization as a hindrance, our approach considers quantum localization as a fundamental component of image reconstruction which is used to differentiate between noisy and non-noisy modes based on diffusivity and localization measurements. This perspective eliminates the need for hyperparameter tuning, making the proposed method a standalone algorithm which can be implemented with minimal manual intervention and can perform automatic filtering of noise regardless of noise level. Through numerical validation, we showcase the effectiveness of our approach in addressing noise-related challenges in imaging and especially medical imaging, underscoring its relevance for possible quantum computing applications.