Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm.

Code ↔ Paper

6 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 6 matches · 4 of them tie a paragraph to a whole file, not to given lines: weak matches, whose lines are not tinted

[1] § Methods › Numerical Experiments ↔ sup_figure_04_noise_dps_stepsize/run.sh, the whole file · a weak match · score 0.72 · retrospectively undersampled, foreground mask, coil compressed, coil sensitivities, whitened, training
[2] § Methods › Numerical Experiments ↔ figure_03_diffusion/run.sh, the whole file · a weak match · score 0.72 · retrospectively undersampled, foreground mask, coil compressed, coil sensitivities, whitened, training
[3] § Methods › Data Processing and Network Training ↔ figure_03_diffusion/run.sh, the whole file · a weak match · score 0.55 · foreground mask, coil sensitivities, whitened, training, sigma, compressed
[4] § Methods › Data Processing and Network Training ↔ sup_figure_04_noise_dps_stepsize/run.sh, the whole file · a weak match · score 0.54 · foreground mask, coil sensitivities, whitened, training, sigma, compressed
[5] § Methods › Numerical Experiments ↔ figure_04_noise/run.sh, lines 44–96 · score 0.52 · foreground mask, coil sensitivities, FFT, Wavelet, slice, PSNR
[6] § Methods › Numerical Experiments ↔ sup_figure_05_cc_uncertainty_dps/run.sh, lines 45–112 · score 0.52 · foreground mask, coil sensitivities, FFT, Wavelet, slice, PSNR

Paper

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The authors' code

Shell · 84 lines · 2.3 KB · no license · 2 matches

#!/bin/bash
#Copyright 2025. TU Graz. Institute of Biomedical Imaging.
#Author: Tina Holliber
set -eu
SCRIPT_DIR=$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )
cd $SCRIPT_DIR
WORKDIR=$(mktemp -d 2>/dev/null || mktemp -d -t 'mytmpdir')
trap 'rm -rf "$WORKDIR"' EXIT
cd "$WORKDIR" || exit
WGH="${WGH:-$SCRIPT_DIR/../01_data/12_trained_weights/wgh}"
if [ ! -f ${WGH}.hdr ]; then
echo "ERROR: Weights file $WGH does not exist."
exit 1
fi
DATA=$SCRIPT_DIR/../01_data/02_t2/ksp
# Remove frequency oversampling
bart fft -i -u 1 $DATA c
bart resize -c 0 320 c c2
bart fft -u 1 c2 ksp
bart resize 0 1 c2 c2
bart transpose 0 1 c2 noise
# Noise whitening
bart whiten ksp noise ksp
# Retrospective undersampling patterns
bart ones 2 1 16 - | bart resize -c 1 320 - ac
bart upat -Y320 -y4 -Z1 - | bart saxpy 1 - ac - | bart threshold -B 0.5 - - | bart repmat 0 320 - pat_reg4
bart upat -Y320 -y12 -Z1 - | bart saxpy 1 - ac - | bart threshold -B 0.5 - - | bart repmat 0 320 - pat_reg12
bart join 10 pat_reg4 pat_reg12 pat
bart scale 1 pat $SCRIPT_DIR/pat
# Coil Compression
bart cc -p12 ksp ksp
LOOP="-l$(bart bitmask 10) -r ksp"
# Coil Sensitivity Estimation
bart $LOOP ncalib -M0.001 -i14 --cgiter=10 ksp col imgs
bart rss 8 col nrm
# Image Scaling
bart fft -i -u 3 imgs imgs
bart $LOOP estscaling -p0.99 -x320:320:1 imgs scl
bart fmac scl col col
# Foreground Masking
bart $LOOP ecalib -r16 -A -m1 ksp - | bart rss 8 - msk
bart fmac col msk col
bart fmac nrm msk nrm
# add noise
bart noise -n8 ksp kspn
bart scale 0.333 kspn kspn
bart scale 0.333 col coln
bart join 5 ksp kspn ksp
bart join 5 col coln col
bart slice 5 0 ksp ksp_full
bart fmac pat ksp ksp
export BART_DEBUG_LEVEL=4
bart pics -w1 -r0.000001 -l1 -i100 -e -g ksp_full col imgfull
bart fmac imgfull nrm $SCRIPT_DIR/ref
# Sampling
LOOP="-l$(bart bitmask 5 10) -e $(bart show -d 5 ksp):$(bart show -d 10 ksp) --random-dims=0"
for step in 0.01 0.05 0.1 0.2 0.3 0.4 0.5; do
BART_DEBUG_LEVEL=4 bart $LOOP sample -p --sigma max=10.,min=0.01 -S10 --gamma=$step -K0 -N240 -g --posterior k=ksp,s=col,dps --mask=msk --cunet w=$WGH sample_dps1_$step > sample_dps_$step.log 2>&1
bart fmac sample_dps1_$step nrm sample_dps1_$step
done
bart join 9 sample_dps1_0.01 sample_dps1_0.05 sample_dps1_0.1 sample_dps1_0.2 sample_dps1_0.3 sample_dps1_0.4 sample_dps1_0.5 $SCRIPT_DIR/sample_dps

run.sh at commit 08b6948, no license · at the source

Overview

Authors: Moritz Blumenthal^1,2, Tina Holliber¹, Jonathan I. Tamir^3,4, Martin Uecker^1,5

ORCID iDs: Moritz Blumenthal, Tina Holliber, Martin Uecker

Institute of Biomedical Imaging Graz University of Technology Graz Austria
Department of Radiology Boston Children's Hospital, Harvard Medical School Boston USA
Chandra Family Department of Electrical Engineering University of Texas at Austin Austin USA
Department of Diagnostic Medicine, Dell Medical School University of Texas at Austin Austin USA
BioTechMed‐Graz Graz Austria

Institutions: Boston Children's Hospital (United States); Harvard University (United States); Graz University of Technology (Austria); The University of Texas at Austin (United States); BioTechMed-Graz (Austria)

Journal: Magnetic resonance in medicine, volume 96, issue 3, pages 1323-1332

Dates: received 10 December 2025; accepted 22 April 2026; published online 10 May 2026; in print September 2026

Type: Other · Language: English

License: CC BY

Identifiers: DOI 10.1002/mrm.70416 · PMID 42108406 · PMCID PMC13327450 · OpenAlex W4417143449

Open access: hybrid, a free copy (OpenAlex)

Preprint: arxiv:2512.05791

Status: code verified

Categories: structural MRI / diffusion (modality), human (organism), methods / tools (subfield)

Methods: Spectral & time-frequency, Machine learning, Smoothing, state filtering, decompositions

Keywords: Bayesian reconstruction, diffusion posterior sampling, image reconstruction, MRI, parallel imaging

MeSH: Algorithms*, Brain*, Diffusion Magnetic Resonance Imaging*, Image Processing, Computer-Assisted*, Magnetic Resonance Imaging*, Bayes Theorem, Humans, Image Enhancement, Reproducibility of Results (* major topic)

Journal subjects: Technical Note, Imaging Methodology

Topic: Advanced Neuroimaging Techniques and Applications (Radiology, Nuclear Medicine and Imaging, Medicine), according to OpenAlex

Funding: National Science Foundation (CCF‐2239687); Austrian Science Fund (Fonds zur Förderung der Wissenschaftlichen Forschung) (10.55776/F100800)

Citations: not cited yet (Europe PMC); 35 references in the paper

Abstract

Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k‐space data. However, sampling methods such as diffusion posterior sampling (DPS) or likelihood annealing suffer from long reconstruction times and the need for parameter tuning. The purpose of this work is to develop a robust sampling algorithm with fast convergence.

Theory and Methods: In the reverse diffusion process used for sampling the posterior, the exact likelihood is multiplied with the diffused prior at all noise scales. To overcome the issue of slow convergence, preconditioning is used. The method is trained on fastMRI data and tested on retrospectively undersampled brain data of a healthy volunteer.

Results: For posterior sampling in Cartesian and non‐Cartesian accelerated MRI the new approach outperforms annealed sampling and DPS in terms of reconstruction speed and sample quality.

Conclusion: The proposed exact likelihood with preconditioning enables rapid and reliable posterior sampling across various MRI reconstruction tasks without the need for parameter tuning.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 6 matches between paragraphs and lines of code.

gitlab.tugraz.at/ibi/mrirecon/papers/dps-pula

License: none: the authors keep all their rights

State: the link answers, verified on 28 September 2026

Evidence: files inventoried

Commit: 08b6948239e96dbd5867e2ac9b7cd8a9a79a7112, 23 March 2026

Languages: Shell (30), Python (6)

Size: 83 files, 36 scripts

Software Heritage: not archived

Found in: “Data Availability Statement”

Holds: README

Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation

Tools: NumPy (5 files), Matplotlib (3 files), h5py (1 file), Numba (1 file)

Availability: 1 check, the latest on 28 September 2026: the link answers

28 September 2026: the link answers

37 files

00_scripts/replace.sh, Shell, 21 lines
00_scripts/runtime.sh, Shell, 10 lines
01_data/01_t1/run.sh, Shell, 40 lines
01_data/02_t2/run.sh, Shell, 40 lines
01_data/03_radial/run.sh, Shell, 47 lines
01_data/11_train_data/convert_fastMRI.py, Python, 37 lines
01_data/11_train_data/prep.sh, Shell, 47 lines
01_data/11_train_data/run.sh, Shell, 56 lines
01_data/12_trained_weights/run.sh, Shell, 28 lines
02_train_fastMRI/train_cunet.sh, Shell, 33 lines
figure_01_analytic/2D_analytical.py, Python, 155 lines
figure_01_analytic/2D_sampling.py, Python, 179 lines
figure_01_analytic/pdf_score_func.py, Python, 151 lines
figure_01_analytic/run.sh, Shell, 18 lines
figure_01_analytic/sampling_algo.py, Python, 77 lines
figure_02_comparison/fig.sh, Shell, 101 lines
figure_02_comparison/run.sh, Shell, 119 lines
figure_03_diffusion/fig.sh, Shell, 25 lines
figure_03_diffusion/run.sh, Shell, 66 lines, 2 matches
figure_04_noise/fig.sh, Shell, 87 lines
figure_04_noise/run.sh, Shell, 140 lines, 1 match
figure_05_noncart/fig.sh, Shell, 42 lines
figure_05_noncart/run.sh, Shell, 111 lines
run_all.sh, Shell, 22 lines
run_supporting.sh, Shell, 25 lines
sup_figure_01_comparison_dps/fig.sh, Shell, 62 lines
sup_figure_01_comparison_dps/run.sh, Shell, 106 lines
sup_figure_02_cg/fig.py, Python, 93 lines
sup_figure_02_cg/fig.sh, Shell, 62 lines
sup_figure_02_cg/run.sh, Shell, 94 lines
sup_figure_04_noise_dps_stepsize/fig.sh, Shell, 36 lines
sup_figure_04_noise_dps_stepsize/run.sh, Shell, 84 lines, 2 matches
sup_figure_05_cc_uncertainty_dps/fig.sh, Shell, 74 lines
sup_figure_05_cc_uncertainty_dps/run.sh, Shell, 112 lines, 1 match
sup_figure_06_noncart_dps/fig.sh, Shell, 24 lines
sup_figure_06_noncart_dps/run.sh, Shell, 100 lines
README.md, Text, 49 lines

At the source: gitlab.tugraz.at/ibi/mrirecon/papers/dps-pula

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
36 scripts, each with its path and the digest of its content;
6 matches between paragraphs of the paper and lines of the code (method lexical-v1);
neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

Datasets cited

zenodo:17739731, at Zenodo; found in “Data Availability Statement”

Data Availability Statement

In the spirit of reproducible research, the code to reproduce the results of this paper is available at https://gitlab.tugraz.at/ibi/mrirecon/papers/dps‐pula (https://gitlab.tugraz.at/ibi/mrirecon/papers/dps-pula) (Version v0.2). All reconstructions have been performed with BART (v1.0.00), available at https://codeberg.org/mrirecon/bart. The data used in this study is available at Zenodo (DOI: 10.5281/zenodo.17739731 (https://doi.org/10.5281/zenodo.17739731)).

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 2, 28 September 2026

Publisher: n/a → Wiley

Version 1, 28 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 5 keywords, 9 MeSH terms, 2 funders, 19 references.

Cite

This paper

Blumenthal, M., Holliber, T., Tamir, J. I., & Uecker, M. (2026). Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm. Magnetic resonance in medicine, 96(3), 1323-1332. https://doi.org/10.1002/mrm.70416

BibTeX

@article{blumenthal2026fast, author = {Blumenthal, Moritz and Holliber, Tina and Tamir, Jonathan I. and Uecker, Martin}, title = {{Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm}}, journal = {Magnetic resonance in medicine}, year = {2026}, month = may, volume = {96}, number = {3}, pages = {1323--1332}, publisher = {Wiley}, issn = {0740-3194}, doi = {10.1002/mrm.70416}, url = {https://doi.org/10.1002/mrm.70416}, pmid = {42108406}, pmcid = {PMC13327450} }

RIS

TY - JOUR AU - Blumenthal, Moritz AU - Holliber, Tina AU - Tamir, Jonathan I. AU - Uecker, Martin TI - Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm T2 - Magnetic resonance in medicine J2 - Magn Reson Med PY - 2026 DA - 2026/05/10 VL - 96 IS - 3 SP - 1323 EP - 1332 SN - 0740-3194 PB - Wiley DO - 10.1002/mrm.70416 UR - https://doi.org/10.1002/mrm.70416 LA - en ER -

CSL-JSON

{ "id": "10.1002/mrm.70416", "type": "article-journal", "title": "Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm", "container-title": "Magnetic resonance in medicine", "author": [ { "family": "Blumenthal", "given": "Moritz" }, { "family": "Holliber", "given": "Tina" }, { "family": "Tamir", "given": "Jonathan I." }, { "family": "Uecker", "given": "Martin" } ], "container-title-short": "Magn Reson Med", "volume": "96", "issue": "3", "page": "1323-1332", "DOI": "10.1002/mrm.70416", "PMID": "42108406", "PMCID": "PMC13327450", "ISSN": "0740-3194", "publisher": "Wiley", "URL": "https://doi.org/10.1002/mrm.70416", "language": "en", "issued": { "date-parts": [ [ 2026, 5, 10 ] ] } }

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