Research Training Group 2088

Project B6: Parameter Identification and Sparse Approximation Using Prony-Like Methods

In recent years, Prony methods have been successfully applied to different inverse problems in parameter identification as, e.g., for localization of particles in inverse scattering, for parameter estimation of guided waves, and for deconvolution of ultrasonic signals. The original Prony method aims at reconstructing a sum of exponentials with (unknown) complex parameters from a given small amount of (possibly noisy) measurement values.

From the viewpoint of sparse approximation, the Prony method can also be seen as an approach to non-linear data approximation by a small number of measurements.

The project aims at generalizations of Prony's method, a further analysis of the relations of Prony-like methods to other approaches for parameter estimation problems as well as the application of these relations to improve approximation algorithms in the uni- and multivariate case.

Methods: matrix decompositions (SVD, QR), semi-definite programming, nonlinear approximation, greedy algorithms
Applications:sparse data representation, parameter identification

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