A Fast Algorithm for Selective Signal Extrapolation with Arbitrary Basis Functions

TL;DR

This paper introduces a highly efficient algorithm for signal extrapolation that works with arbitrary basis functions, significantly reducing computational costs while maintaining accuracy and outperforming existing methods.

Contribution

The paper presents a novel, faster algorithm for Selective Extrapolation applicable to any basis functions, including numerically defined ones, surpassing existing transform-based methods.

Findings

Algorithm is several decades faster than original

Outperforms existing fast transform domain algorithms

Works with arbitrary, numerically defined basis functions

Abstract

Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by generating a model of the signal to be extrapolated as weighted superposition of basis functions. Unfortunately, this algorithm is computationally very expensive and, up to now, efficient implementations exist only for basis function sets that emanate from discrete transforms. Within the scope of this contribution, a novel efficient solution for Selective Extrapolation is presented for utilization with arbitrary basis functions. The proposed algorithm mathematically behaves identically to the original Selective Extrapolation, but is several decades faster. Furthermore, it is able to outperform existent fast transform domain algorithms which are limited to basis function sets that belong to the corresponding transform. With that, the novel algorithm allows for an efficient use of arbitrary basis functions, even if they are only numerically defined.