2012/08/29 by Stefania Petra, Petra, Stefania, Christoph Schnörr +1
Engineering · Medicine · #65F22 #68U10 #Electrical and Bioimpedance Tomography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Medical Imaging Techniques and Applications #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1208.5894
openalex publication_date 2012/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The reconstruction of three-dimensional sparse volume functions from few tomographic projections constitutes a challenging problem in image reconstruction and turns out to be a particular instance problem of compressive sensing. The tomographic measurement matrix encodes the incidence relation of the imaging process, and therefore is not subject to design up to small perturbations of non-zero entries. We present an average case analysis of the recovery properties and a corresponding tail bound to establish weak thresholds, in excellent agreement with numerical experiments. Our result improve the state-of-the-art of tomographic imaging in experimental fluid dynamics by a factor of three.