Parallel-beam tomography¶

This page describes parallel-beam tomographic image reconstruction using the Julia package Sinograms.jl.

This page was generated from a single Julia file: 03-parallel-beam.jl.

Setup¶

Packages needed here.

In [ ]:

using Sinograms: SinoPar, rays, plan_fbp, fbp
using ImageGeoms: ImageGeom, fovs, MaskCircle
using ImagePhantoms: SheppLogan, shepp_logan, radon, phantom
using Unitful: mm
using MIRTjim: jim, prompt

The following line is helpful when running this file as a script; this way it will prompt user to hit a key after each figure is displayed.

In [ ]:

isinteractive() ? jim(:prompt, true) : prompt(:draw);

Parallel-beam sinogram of Shepp-Logan phantom¶

For illustration, we start by synthesizing a parallel-beam sinogram of the Shepp-Logan phantom.

For completeness, we use units (from Unitful), but units are optional.

Use ImageGeom to define the image geometry.

In [ ]:

ig = ImageGeom(MaskCircle(); dims=(128,126), deltas = (2mm,2mm) )

Use SinoPar to define the sinogram geometry.

In [ ]:

sg = SinoPar( ; nb = 130, d = 2mm, na = 100)

Ellipse parameters for Shepp-Logan phantom:

In [ ]:

μ = 0.01 / mm # typical linear attenuation coefficient
ob = shepp_logan(SheppLogan(); fovs = fovs(ig), u = (1, 1, μ))

Radon transform of Shepp-Logan phantom:

In [ ]:

sino = radon(rays(sg), ob)
jim(axes(sg), sino; title="Shepp-Logan sinogram", xlabel="r", ylabel="ϕ")

# Image reconstruction via FBP

Here we start with a "plan", which would save work if we were reconstructing many images.

In [ ]:

plan = plan_fbp(sg, ig)
fbp_image, sino_filt = fbp(plan, sino)

A narrow color window is needed to see the soft tissue structures:

In [ ]:

clim = (0.9, 1.1) .* μ
jim(axes(ig), fbp_image, "FBP image"; clim)

For comparison, here is the ideal phantom image

In [ ]:

true_image = phantom(axes(ig)..., ob, 2)
jim(axes(ig)..., true_image, "True phantom image"; clim)

This notebook was generated using Literate.jl.