2020/06/06 by Markus Haltmeier, Linh V. Nguyen, Haltmeier, Markus +1
Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2006.03972
openalex publication_date 2020/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their solutions. Therefore, any reasonable solution method requires the use of regularization tools that select specific solutions and at the same time stabilize the inversion process. Recently, data-driven methods using deep learning techniques and neural networks demonstrated to significantly outperform classical solution methods for inverse problems. In this chapter, we give an overview of inverse problems and demonstrate the necessity of regularization concepts for their solution. We show that neural networks can be used for the data-driven solution of inverse problems and review existing deep learning methods for inverse problems. In particular, we view these deep learning methods from the perspective of regularization theory, the mathematical foundation of stable solution methods for inverse problems. This chapter is more than just a review as many of the presented theoretical results extend existing ones.