Moment-based cosh-Hilbert Inversion and Its Applications in Single-photon Emission Computed Tomography

TL;DR

This paper introduces a novel numerical moment-based inversion algorithm for the cosh-Hilbert transform, crucial for improving image reconstruction in single-photon emission computed tomography with uniform attenuation.

Contribution

The paper presents the first exact and analytic inverse formula for the cosh-Hilbert transform, advancing the mathematical foundation and computational methods in SPECT imaging.

Findings

Developed a new moment-based inversion algorithm

Proved the uniqueness of the CHT inversion

Enhanced accuracy over previous approximated methods

Abstract

The inversion of cosh-Hilbert transform (CHT) is one of the most crucial steps for single-photon emission computed tomography with uniform attenuation from truncated projection data. Although the uniqueness of the CHT inversion had been proved \cite{Noo2007}, there is no exact and analytic inverse formula so far. Several approximated inversion algorithms of the CHT had been developed \cite{Noo2007}\cite{You2007}. In this paper, we proposed a new numerical moment-based inversion algorithm.