In this project, we develop algorithms for qualitative inverse problems, such as radar imaging or ultrasound imaging. The scientific contributions will be twofold: Firstly, reduce the computational burden associated with classical imaging algorithms through the use of reduced-order modeling. Secondly, develop imaging algorithms that image free of artifacts at the resolution limit. Two methods are investigated in this project. First, the use of convolution neural networks to remove imaging artifacts introduced by imaging algorithms (multiple removals and point-spread function convolution). And, second, to leverage recent advances in the field of data-driven reduced order modeling for imaging applications. Students will work on this project in the context of the course 1TD307 Projects in computational science, and Advanced Course on Topics in Scientific Computing I/II.