Computational aspects and applications of a new transform for solving the complex exponentials approximation problem
It provides a computational implementation of a previously theoretical transform, making it applicable to real-world signal processing and inverse problems.
The paper develops a practical algorithm for a new transform that solves the complex exponentials approximation problem, demonstrating its effectiveness on NMR spectrometry, time series interpolation/extrapolation, and shape from moments problems.
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has been proposed in a theoretical framework. In this work some computational issues are addressed to make this new tool useful in practice. An algorithm is developed and used to solve a Nuclear Magnetic Resonance spectrometry problem, two time series interpolation and extrapolation problems and a shape from moments problem.