2012/09/19 by Stefania Petra, Petra, Stefania, Christoph Schnörr +3
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.1209.4316
openalex publication_date 2012/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze representative ill-posed scenarios of tomographic PIV with a focus on conditions for unique volume reconstruction. Based on sparse random seedings of a region of interest with small particles, the corresponding systems of linear projection equations are probabilistically analyzed in order to determine (i) the ability of unique reconstruction in terms of the imaging geometry and the critical sparsity parameter, and (ii) sharpness of the transition to non-unique reconstruction with ghost particles when choosing the sparsity parameter improperly. The sparsity parameter directly relates to the seeding density used for PIV in experimental fluids dynamics that is chosen empirically to date. Our results provide a basic mathematical characterization of the PIV volume reconstruction problem that is an essential prerequisite for any algorithm used to actually compute the reconstruction. Moreover, we connect the sparse volume function reconstruction problem from few tomographic projections to major developments in compressed sensing.