2020/05/28 by Simon Arridge, Arridge, Simon, Pascal Fernsel +3 · 1 citation
Engineering · Medicine · #15A23 #15A69 #65K10 #Advanced MRI Techniques and Applications #FOS: Electrical engineering #FOS: Mathematics #Image and Video Processing (eess.IV) #Numerical Analysis (math.NA) #Optical Imaging and Spectroscopy Techniques #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2005.14042
openalex publication_date 2020/05/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
A primary interest in dynamic inverse problems is to identify the underlying\ntemporal behaviour of the system from outside measurements. In this work we\nconsider the case, where the target can be represented by a decomposition of\nspatial and temporal basis functions and hence can be efficiently represented\nby a low-rank decomposition. We then propose a joint reconstruction and\nlow-rank decomposition method based on the Nonnegative Matrix Factorisation to\nobtain the unknown from highly undersampled dynamic measurement data. The\nproposed framework allows for flexible incorporation of separate regularisers\nfor spatial and temporal features. For the special case of a stationary\noperator, we can effectively use the decomposition to reduce the computational\ncomplexity and obtain a substantial speed-up. The proposed methods are\nevaluated for two simulated phantoms and we compare the obtained results to a\nseparate low-rank reconstruction and subsequent decomposition approach based on\nthe widely used principal component analysis.\n