Average case recovery analysis of tomographic compressive sensing

• Published in: Linear algebra and its applications Vol. 441; pp. 168 - 198
• Main Authors: Petra, Stefania, Schnörr, Christoph
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.01.2014
• Subjects: Algebraic reconstruction; Compressed sensing; Large deviation; Nonnegative least squares; Sparsity; Tail bound; TomoPIV; Underdetermined systems of linear equations; Algebraic reconstruction; 68U10; Sparsity; Nonnegative least squares; 65F22; Tail bound; TomoPIV; Compressed sensing; Underdetermined systems of linear equations; Large deviation
• ISSN: 0024-3795; 1873-1856
• DOI: 10.1016/j.laa.2013.06.034

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 problem instance 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 results improve the state-of-the-art of tomographic imaging in experimental fluid dynamics.