2020/01/06 by Chang Min Hyun, Seong Hyeon Baek, Hyun, Chang Min +7 · 2 citations
Computer Science · Engineering · Mathematics · Medicine · #Algorithm #Artificial intelligence #Computer science #Deep learning #FOS: Computer and information sciences #FOS: Electrical engineering #Image and Video Processing (eess.IV) #Inverse #Inverse problem #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine learning #Mathematics #Medical Imaging Techniques and Applications #Medical imaging #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Underdetermined system #cs.LG #eess.IV #electronic engineering #information engineering #stat.ML
paper · pdf · doi:10.48550/arxiv.2001.01432
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2020/01/06 · arxiv created 2020/06/26 · arxiv updated 2020/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, with the significant developments in deep learning techniques,\nsolving underdetermined inverse problems has become one of the major concerns\nin the medical imaging domain. Typical examples include undersampled magnetic\nresonance imaging, interior tomography, and sparse-view computed tomography,\nwhere deep learning techniques have achieved excellent performances. Although\ndeep learning methods appear to overcome the limitations of existing\nmathematical methods when handling various underdetermined problems, there is a\nlack of rigorous mathematical foundations that would allow us to elucidate the\nreasons for the remarkable performance of deep learning methods. This study\nfocuses on learning the causal relationship regarding the structure of the\ntraining data suitable for deep learning, to solve highly underdetermined\ninverse problems. We observe that a majority of the problems of solving\nunderdetermined linear systems in medical imaging are highly non-linear.\nFurthermore, we analyze if a desired reconstruction map can be learnable from\nthe training data and underdetermined system.\n