Deep learning-based solvability of underdetermined inverse problems in medical imaging

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of major concerns medical imaging domain, where are motivated by willingness to provide high resolution images as little data possible, optimizing collection terms minimal acquisition time, cost-effectiveness, and low invasiveness. Typical examples include undersampled magnetic resonance imaging(MRI), interior tomography, sparse-view computed tomography(CT), techniques have achieved excellent performances. However, there is a lack mathematical analysis why method performing well. This study aims explain about causal relationship regarding structure training suitable for learning, solve highly problems. We present particular low-dimensional solution model highlight advantage methods over conventional methods, two approaches use prior information completely different way. also analyze whether can learn desired reconstruction map from three models (undersampled MRI, CT, tomography). paper discusses nonlinearity linear systems conditions (called M-RIP condition).