Regularization graphs—a unified framework for variational regularization of inverse 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

Numerical Regularization for Atmospheric Inverse Problems - Preamble

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Variable-smoothing Regularization Methods for Inverse Problems

Many inverse problems of practical interest are ill-posed in the sense that solutions do not depend continuously on data. To eeectively solve such problems, regularization methods are typically used. One problem associated with classical regularization methods is that the solution may be oversmoothed in the process. We present an alternative \local regularization" approach in which a decomposit...