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arXiv · 1710.09277

Aspects of 2D-Adaptive Fourier Decompositions

You Gao·Tao Qian·Vladimir Temlyakov·Long-fei Cao
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Abstract

As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable influence to the rational approximation of one complex variable and phase retrieving problems, etc. In a recent paper, Qian developed 2D-AFDs for treating square images as the essential boundary of the 2-torus embedded into the space of two complex variables. This paper studies the numerical aspects of multi-dimensional AFDs, and in particular 2D-AFDs, which mainly include (i) Numerical algorithms of several types of 2D-AFDs in relation to image representation; (ii) Perform experiments for the algorithms with comparisons between 5 types of image reconstruction methods in the Fourier category; and (iii) New and sharper estimations for convergence rates of orthogonal greedy algorithm and pre-orthogonal greedy algorithm. The comparison shows that the 2D-AFD methods achieve optimal results among the others.

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You Gao, Tao Qian, Vladimir Temlyakov, Long-fei Cao. 2017-10-24. Aspects of 2D-Adaptive Fourier Decompositions. https://arxiv.org/abs/1710.09277

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