Sparsity-constrained inversion with tomographic applications

该项目的重点是在离散和连续环境下，稀疏约束正则化方法的贝叶斯方法和确定性方法之间的异同。稀疏性方法假设背景的模型是已知的，并且只需要重建与背景的偏差，例如夹杂或缺陷，偏差应该在适当的基或框架中用很少的系数来有效地表示。在理论方面，现有知识的极限将被扩大到包括非线性逆问题、非高斯噪声模型以及连续和离散反演框架之间的联系。在计算方面，将开发新的、健壮的、高效的稀疏性提升的反演算法。在应用方面，首先用简单的测试用例和模拟数据对所提出的反演方法进行了检验，然后用与生物发光和有限数据X射线层析成像相关的测量数据进行了检验。

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.