Technical Note: An Efficient Implementation of the Spherical Radon Transform with Cylindrical Apertures

TL;DR

This paper presents a computationally efficient method for implementing the spherical Radon transform with cylindrical apertures by exploiting symmetry and expressing it as a composition of circular Radon transforms, suitable for GPU acceleration.

Contribution

It introduces a novel, efficient implementation of the spherical Radon transform and its adjoint for cylindrical geometries, improving computational speed and consistency in image reconstruction.

Findings

Significantly reduces computation time for SRT with cylindrical apertures

Provides a sparse matrix-based implementation for GPU acceleration

Ensures consistent gradients in optimization-based reconstructions

Abstract

The spherical Radon transform (SRT) is an integral transform that maps a function to its integrals over concentric spherical shells centered at specified sensor locations. It has several imaging applications, including synthetic aperture radar and photoacoustic computed tomography. However, computation of the SRT can be expensive. Efficient implementation of SRT on general purpose graphic processing units (GPGPUs) often utilizes non-matched implementation of the adjoint operator, leading to inconsistent gradients in optimization-based image reconstruction methods. This work details an efficient implementation of the SRT and its adjoint for the case of a cylindrical measurement aperture. Exploiting symmetry of the cylindrical geometry, the SRT can then be expressed as the composition of two circular Radon transforms (CRT). Utilizing this formulation then allows for an efficient implementation of the SRT as a discrete-to-discrete operator utilizing sparse matrix representation.