{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Fan-beam tomography: short scan\n",
    "\n",
    "This page describes fan-beam tomographic image reconstruction\n",
    "using the Julia package\n",
    "[`Sinograms.jl`](https://github.com/JuliaImageRecon/Sinograms.jl)\n",
    "for a \"short\" scan\n",
    "where the rotation (`orbit`) is 180° plus the fan angle.\n",
    "This case requires\n",
    "[Parker weighting](https://doi.org/10.1118/1.595078).\n",
    "\n",
    "This page focuses on fan-beam with an \"arc\" detector,\n",
    "i.e., 3rd-generation CT systems\n",
    "where the detector is an arc\n",
    "having a focal point\n",
    "at the X-ray source.\n",
    "This geometry is popular\n",
    "in part because it facilitates\n",
    "anti-scatter grids."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Setup"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Packages needed here."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using Plots: plot, gui\n",
    "using Unitful: mm\n",
    "using Sinograms: SinoFanArc, rays, plan_fbp, fbp, sino_geom_plot!\n",
    "using ImageGeoms: ImageGeom, fovs, MaskCircle\n",
    "using ImagePhantoms: SheppLogan, shepp_logan, radon, phantom\n",
    "using MIRTjim: jim, prompt"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "The following line is helpful when running this file as a script;\n",
    "this way it will prompt user to hit a key after each figure is displayed."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "isinteractive() ? jim(:prompt, true) : prompt(:draw);"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Fan-beam sinogram of Shepp-Logan phantom\n",
    "\n",
    "For illustration,\n",
    "we start by synthesizing\n",
    "a fan-beam sinogram\n",
    "of the Shepp-Logan phantom.\n",
    "\n",
    "For completeness,\n",
    "we use units (from Unitful),\n",
    "but units are optional."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Use `ImageGeom` to define the image geometry."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "ig = ImageGeom(MaskCircle(); dims=(128,126), deltas = (2mm,2mm) )"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Use `SinoFanArc` to define the sinogram geometry,\n",
    "with the `:short` option for `orbit` to make a short scan.\n",
    "Note that even though we specify `na = 100`\n",
    "we end up with `na = 67` views\n",
    "because of the `:short` option."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "rg = SinoFanArc( :short, ;\n",
    "    nb = 130, d = 3.2mm, na = 100, dsd = 400mm, dod = 140mm,\n",
    ")"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Examine the geometry to verify the FOV.\n",
    "The `na=67` blue dots show the `:short` scan."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "jim(axes(ig), ig.mask; prompt=false)\n",
    "sino_geom_plot!(rg, ig)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "prompt()"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Ellipse parameters for Shepp-Logan phantom:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "μ = 0.01 / mm # typical linear attenuation coefficient\n",
    "ob = shepp_logan(SheppLogan(); fovs = fovs(ig), u = (1, 1, μ))"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Short arc fan-beam sinogram for Shepp-Logan phantom:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "sino = radon(rays(rg), ob)\n",
    "jim(axes(rg), sino; title=\"Shepp-Logan 'short' sinogram\",\n",
    "    xlabel=\"r\", ylabel=\"ϕ\")"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Image reconstruction via FBP\n",
    "Here we start with a \"plan\",\n",
    "which would save work if we were reconstructing many images."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "plan = plan_fbp(rg, ig)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Examine Parker weights:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "jim(axes(rg), plan.view_weight; title = \"Parker weights\",\n",
    "    xlabel=\"r\", ylabel=\"ϕ\")"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Finally perform FBP:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "fbp_image = fbp(plan, sino);"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "A narrow color window is needed to see the soft tissue structures:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "clim = (0.9, 1.1) .* μ\n",
    "jim(axes(ig), fbp_image, \"FBP image for 'short' arc case\"; clim)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "For comparison, here is the ideal phantom image:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "true_image = phantom(axes(ig)..., ob, 2)\n",
    "jim(axes(ig)..., true_image, \"True phantom image\"; clim)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Here is the difference image.\n",
    "Better sampling would reduce the errors."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "jim(axes(ig)..., fbp_image - true_image, \"Error image\")"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
   ],
   "metadata": {}
  }
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