Sparsity-constrained inversion with tomographic applications

• Applicants: Professor Dr. Martin Burger; Professor Dr. Peter Maaß
• Subject Area: Mathematics
• Term: from 2011 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 190846722

The proposed project focuses on similarities and differences between Bayesian and deterministicapproaches to sparsity-constrained regularization methods, both in discrete and continuoussettings. The sparsity approach assumes that a model for the background is known and thatonly deviations from the background, such as inclusions or defects, have to be reconstructed.The deviations should be efficiently represented with few coefficients in a suitable basis orframe. Regarding theory, the limits of current knowledge will be pushed to cover nonlinearinverse problems, non-Gaussian noise models and connections between continuous and discreteinversion frameworks. Regarding computation, new, robust and efficient sparsity-promotinginversion algorithms will be developed. Regarding applications, the proposed inversion methodsare tested first with simple test cases and simulated data and later with measured data relatedto bioluminescence and limited-data X-ray tomography.

• DFG Programme: Research Grants
• International Connection: China, Finland
• Participating Persons: Professor Dr. Jianguo Huang; Professor Matti Lassas; Professor Dr. Samuli Siltanen