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.
Packages needed here.
using Sinograms: SinoPar, rays, plan_fbp, fbp, fbp_sino_filter
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.
isinteractive() ? jim(:prompt, true) : prompt(:draw);
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.
ig = ImageGeom(MaskCircle(); dims=(128,126), deltas = (2mm,2mm) )
Use SinoPar to define the sinogram geometry.
rg = SinoPar( ; nb = 130, d = 2mm, na = 100)
Ellipse parameters for Shepp-Logan phantom:
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:
sino = radon(rays(rg), ob)
jim(axes(rg), 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.
plan = plan_fbp(rg, ig)
fbp_image = fbp(plan, sino)
A narrow color window is needed to see the soft tissue structures:
clim = (0.9, 1.1) .* μ
jim(axes(ig), fbp_image, "FBP image"; clim)
For comparison, here is the ideal phantom image
true_image = phantom(axes(ig)..., ob, 2)
jim(axes(ig)..., true_image, "True phantom image"; clim)
For fun, here is the filtered sinogram:
sino_filt = fbp_sino_filter(sino, plan.filter)
jim(axes(rg), sino_filt; title="Filtered sinogram", xlabel="r", ylabel="ϕ")
This notebook was generated using Literate.jl.