Abstract
In this work, we present a few explicit and implicit formulations used in the analysis and solution of inverse problems. These formulations have been developed and/or applied by the authors to the solution of different problems with applications in engineering, biophysics and biotechnology. Here emphasis is given to a matrix-based explicit formulation, and to the construction of a generalized family of regularization terms which is used when the inverse problem is formulated implicitly as an optimization problem. The efficacy of the methodologies developed is demonstrated with the results for a few test cases using noiseless and noisy synthetic data.
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