reconstruction.md

PET Reconstruction

You do not need to understand reconstruction or attenuation correction to participate, however, having an intuition of the first reconstruction steps can be a significant advantage when designing your pseudo-CT algorithm and loss function.

Introduction

In PET, the radioactive tracer (FDG, a glucose analogue) emits positrons that immediately annihilate with nearby electrons, releasing two 511 keV photons traveling in exactly opposite directions. The detector rings record both photons simultaneously — a coincidence event — telling us which straight line through the patient the emission occurred on, but not where along that line¹. Tallying all such lines produces a sinogram, the raw projection data from which the activity image is reconstructed. However, some photons are absorbed (attenuated) by tissue before reaching the detectors — an effect that is more pronounced for deep structures and dense bone. Attenuation correction compensates for this, and it is what your pseudo-CT enables.

The PET reconstruction algorithm is titled Ordinary Poisson Ordered Subsets Expectation Maximization (OP-OSEM). OP-OSEM is simply a maximum likelihood expectation maximization algorithm where the observed data (the sinograms) are partioned and processed in chunks (subsets) to dramatically accelerate the reconstruction speed. The reconstruction for BIC-MAC performs OP-OPSEM for 5 subsets x 4 iterations = 20 subiterations. Three sinograms are used in OP-OSEM of which the last two must be attenuation corrected: prompts_rd85[.s/.hs], add_nac_rd85[.s/.hs], and mult_nac_rd85[.s/.hs] ²

The reconstruction pipeline for BIC-MAC (src/recon/) uses STIR (Software for Tomographic Image Reconstruction) to perform reconstruction. (see Further Reading for a primer)

¹ A simplification. Modern scanners like the Siemens Quadra used for BIC-MAC can detect the tiny time of flight (TOF) difference between the arriving photons and infer their origin (roughly) on the LOR. Consequently, TOF-enabled sinograms have an extra dimension.

² RD85 means maximum ring difference of 85 and defines how oblique the LORs are allowed to be. The Siemens Quadra allows up to RD322, but RD85 was chosen to reduce the sinogram size.

---

BIC-MAC reconstruction steps

Given a CT (ground-truth or pseudo-CT) and the subject's sinogram data (recon/), the the reconstruction pipeline exectutes the following steps to arrive at a reconstructed attenuation-corrected PET NIfTI image:

1. Superimpose bed pixelated face - The pseudo-CT face is replaced by a pre-saved pixelated face. Likewise, everything outside a ~1cm rim (pillows, bed, hair, air) is replaced by the ground truth image (see ct_face_and_bed.nii.gz and face_and_bed_mask.nii.gz). Consequently, the pseudo-CT algorithm will not benefit from trying to predict these areas. The prediction_mask.nii.gz under ct-label is the inverse mask of face_and_bed_mask.nii.gz and may be used to restrict training to the relevant body region. You can inspect the face-swapped intermediate file (intermediates/ct_face_swapped.nii.gz)

2. HU → μ-map — The pseudo-CT is a volume of Hounsfield units (HU), a relative X-ray density scale where air = −1000 and water = 0. PET reconstruction needs instead the linear attenuation coefficient μ (cm⁻¹) at the 511 keV photon energy of PET annihilation events. The conversion uses a bilinear model (Carney et al. 2006): a steep linear segment maps soft tissue (HU ≤ 47, dominated by water) and a flatter segment maps dense materials like bone (HU > 47). This means that errors in HU are not equally costly in soft tissue and in bone when converting to a mumap. You can inspect the mu_map intermediate file (intermediates/mu_map.nii.gz).

3. Smooth μ-map — A 4 mm FWHM Gaussian blur is applied to the μ-map before any sinogram operations. This is standard clinical practice to reduce the effect of CT noise and slight patient movement. Consequently, very fine structural detail in your pseudo-CT may be blurred away before it ever influences the PET sinogram, and by extension, the PET-based metrics. You can inspect the smoothed mu_map intermediate file (intermediates/mumap_smoothed.nii.gz)

4. Resample to STIR — Resamples the μ-map onto STIR's z-axis grid (ring spacing 3.29 mm), snapping the origin to the STIR coordinate system. A technical prerequisite for STIR's forward projection. The intermediate files are (intermediates/mumap_stir[.hv/.ahv/.v])

5. Compute ACF sinogram — The μ-map is forward projected along every line of response (LOR) in the PET scanner geometry, computing the total integrated attenuation each annihilation photon pair experiences along that path. The result is the attenuation correction factor (ACF) sinogram, which has the same shape as the other PET sinograms, except from the fact that it lacks a TOF-dimension. The intermediate files are(intermediates/acf[.hs/.v])

6.–7. Apply ACF to sinograms — The ACF sinogram is multiplied into both the multiplicative sinogram and the additive sinogram. This encodes the predicted attenuation into the reconstruction inputs. The intermediate files are (intermediates/add[.hs/.s] and intermediates/mult[.hs/.s])

8. OSEM reconstruction — OP-OSEM is run for 20 subiterations (5 subsets, 4 iterations). The result is smoothed by a 4 mm FWHM Gaussian post-filter to reduce noise. The intermediate files are (intermediates/pet_20[.ahv/.hv/.v]).

9. Convert to NIfTI — Writes the reconstructed PET volume as a NIfTI file with the correct origin, accounting for the scanner bed position and gantry offset stored in recon/offset.json. The final output is pet.nii.gz

Intermediate outputs are written to output_dir/intermediates/. The pipeline skips steps whose outputs already exist, so it resumes automatically from a partial run.

---

Warning

Running reconstruction requires ~20 GB of RAM and takes 20–120 minutes depending on CPU speed. The intermediates/ folder uses ~50 GB of additional disk space — consider deleting it after a successful reconstruction.

Running the Pipeline

Option 1: Docker (recommended)

A pre-built image with STIR and all dependencies is available.

docker pull ghcr.io/bic-mac-challenge/recon:latest

docker run --rm \
  -v /path/to/sub-000/recon:/data/recon \
  -v /path/to/ct.nii.gz:/data/ct/ct.nii.gz \
  -v /path/to/output:/data/output \
  ghcr.io/bic-mac-challenge/recon:latest

The reconstructed PET is written to /data/output/pet.nii.gz. A full debug log is written to /data/output/intermediates/recon.log.

Environment variables:

Variable	Default	Effect
OVERWRITE	0	Set to 1 to ignore existing intermediates and rerun from scratch
VERBOSE	0	Set to 1 to stream STIR subprocess output to the terminal

docker run --rm \
  -e OVERWRITE=1 \
  -e VERBOSE=1 \
  -v /path/to/sub-000/recon:/data/recon \
  -v /path/to/ct.nii.gz:/data/ct/ct.nii.gz \
  -v /path/to/output:/data/output \
  ghcr.io/bic-mac-challenge/recon:latest

Option 2: Direct Python (requires local STIR)

python src/recon/main.py \
  --recon_dir <subject_recon_dir> \
  --ct <ct.nii.gz> \
  --output_dir <output_dir> \
  [-w] [-v]

Argument	Description
--recon_dir	Subject's recon/ directory (contains sinograms, offset.json, face mask)
--ct	CT NIfTI file in Hounsfield units
--output_dir	Directory where pet.nii.gz and intermediates/ will be written
-w / --overwrite	Rerun from scratch, ignoring existing intermediates
-v / --verbose	Stream STIR subprocess output to the terminal

---

Expected recon/ Contents

recon/
├── add_nac_rd85.hs / .s       # additive sinogram (scatter + randoms)
├── mult_nac_rd85.hs / .s      # multiplicative sinogram (normalisation, decay)
├── prompts_rd85.hs / .s       # raw prompt coincidences
├── offset.json                # bed position and gantry offset
├── ct_face_and_bed.nii.gz     # ground-truth CT values at face + scanner bed
└── face_and_bed_mask.nii.gz   # binary face + scanner bed mask

Only subjects in the full train/ split and the val/ split include recon/ data (see the main README).

---

Further Reading

• Carney et al. (2006) — "Method for Transforming CT Images for Attenuation Correction in PET/CT Scanners", Medical Physics. The bilinear HU→μ model used in this pipeline.
• Cherry, Sorenson & Phelps — Physics in Nuclear Medicine (4th ed., 2012)