Documentation for SPECTrecon

Overview

This Julia module provides SPECT forward and back projectors for parallel-beam collimators, accounting for attenuation and depth-dependent collimator response. (Compton scatter within the object is not modeled.)

Designed for use with the Michigan Image Reconstruction Toolbox (MIRT) and similar frameworks.

The method implemented here is based on the 1992 paper by GL Zeng & GT Gullberg "Frequency domain implementation of the three-dimensional geometric point response correction in SPECT imaging" (IEEE Tr. on Nuclear Science, 39(5-1):1444-53, Oct 1992) (DOI).

The forward projection method works as follows.

• The emission image and the attenuation map are rotated (slice by slice) to the desired view angle using either 2D bilinear interpolation or a 3-pass rotation method based on linear interpolation.
• Each (rotated) plane is convolved with the given point spread function (PSF) of the collimator and summed, accounting for attenuation using the "central ray" approximation.

The back-projection method is the exact adjoint of the forward projector.

See the "Examples" for details.