Regularization of Inverse Signal Recovery Problems

Regularization and Inverse Problems

An overview is given of Bayesian inversion and regularization procedures. In particular, the conceptual basis of the maximum entropy method (MEM) is discussed, and extensions to positive/negative and complex data are highlighted. Other deconvolution methods are also discussed within the Bayesian context, focusing mainly on the comparison of Wiener filtering, Massive Inference and the Pixon meth...

Singular Regularization of Inverse Problems

This thesis comments on the use of Bregman distances in the context of singular regularization schemes for inverse problems. According to previous works the use of Bregman distances in combination with variational frameworks, based on singular regularization energies, leads to improved approximations of inverse problems solutions. The Bregman distance has become a powerful tool for the analysis...

Sparsity regularization in inverse problems

Windowed Spectral Regularization of Inverse Problems

Regularization is used in order to obtain a reasonable estimate of the solution to an ill-posed inverse problem. One common form of regularization is to use a filter to reduce the influence of components corresponding to small singular values, perhaps using a Tikhonov least squares formulation. In this work, we break the problem into subproblems with narrower bands of singular values using spec...

Reduced Complexity Regularization of Geophysical Inverse Problems

Shuchin Aeron Department of Electrical Engineering