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Anatomically constrained volumetric smoothing enhances fMRI reliability while avoiding smoothing artifacts.

Code ↔ Paper

3 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 3 matches
  1. [1] § Methods › Constrained smoothing ↔ csmooth/optimization.py, lines 8–42 · score 0.63 · heat kernel smoothing, full width, iteratively, optimized, FWHM
  2. [2] § Methods › Constrained smoothing › Equivalent parameter estimation and smoothing ↔ csmooth/optimization.py, lines 8–42 · score 0.61 · Heat kernel smoothing, full width, optimization, nodes, signal, graphs
  3. [3] § Methods › Constrained smoothing › Equivalent parameter estimation and smoothing ↔ csmooth/smooth.py, lines 292–360 · score 0.54 · graph signal, Gaussian kernel, computationally, smoothing kernel, nodes, component

Paper

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The authors' code

Python · 114 lines · 5.4 KB · Apache-2.0 · 2 matches

  1. import numpy as np
  2. import time
  3. from csmooth.fwhm import estimate_fwhm
  4. from csmooth.heat import heat_kernel_smoothing
  5. from csmooth.utils import logger
  8. def graph_smoothing_with_gradient_descent(data, edge_src, edge_dst, edge_distances, fwhm,
  9. max_iterations=100, stop_threshold=0.01, initial_tau=None, learning_rate=1.0,
  10. decay_rate=0.99, random_seed=42):
  11. """
  12. Smooth a signal based on a graph targeting a specific fwhm.
  13. This function uses gradient descent to find the optimal smoothing parameter
  14. to achieve the target fwhm.
  15. First, a random noise image is generated. Then, the signal is smoothed using the initial tau.
  16. The fwhm of the smoothed signal is estimated. The gradient of the fwhm with respect to tau is computed.
  17. The tau is updated using the gradient and learning rate. This process is repeated until the fwhm is close
  18. enough to the target fwhm or the maximum number of iterations is reached.
  19. The final value of tau is used to smooth the original signal.
  20. :param data: signal data to be smoothed.
  21. :param edge_src: source nodes of the graph edges.
  22. :param edge_dst: destination nodes of the graph edges.
  23. :param edge_distances: distances of the graph edges.
  24. :param fwhm: target full width at half maximum in mm.
  25. :param max_iterations: maximum number of iterations for gradient descent.
  26. :param stop_threshold: threshold for stopping the gradient descent.
  27. :param initial_tau: initial value for the smoothing parameter. If None, 2*fwhm is used as the initial value.
  28. :param learning_rate: learning rate for gradient descent.
  29. :param decay_rate: decay rate for the learning rate.
  30. :param random_seed: random seed for generating the random noise image. By default, 42.
  31. :param patience: number of iterations to wait before stopping if the fwhm does not improve.
  32. :return: smoothed signal
  33. """
  35. tua = find_optimal_tau(fwhm=fwhm, edge_src=edge_src, edge_dst=edge_dst,
  36. edge_distances=edge_distances, shape=data.shape, initial_tau=initial_tau,
  37. max_iterations=max_iterations, stop_threshold=stop_threshold,
  38. learning_rate=learning_rate, decay_rate=decay_rate, random_seed=random_seed)
  39. smoothed_signal = heat_kernel_smoothing(signal_data=data, tau=tua, edge_src=edge_src,
  40. edge_dst=edge_dst, edge_distances=edge_distances)
  42. return smoothed_signal, tua
  44. def find_optimal_tau(fwhm, edge_src, edge_dst, edge_distances, shape, initial_tau=None,
  45. max_iterations=100, stop_threshold=0.005, learning_rate=3.0, decay_rate=0.99,
  46. random_seed=42, error_threshold=0.5, patience=20):
  48. # TODO: add momentum to the gradient descent
  50. start_time = time.time()
  52. initial_patience = patience
  54. if initial_tau is None:
  55. initial_tau = 2 * fwhm
  56. tau = initial_tau
  58. np.random.seed(random_seed)
  59. random_noise = np.random.randn(*shape)
  60. mae = np.inf
  61. current_fwhm = np.nan
  62. best_tau = tau
  63. best_mae = np.inf
  64. best_fwhm = current_fwhm
  65. for i in range(max_iterations):
  66. smoothed_noise = heat_kernel_smoothing(signal_data=random_noise, tau=tau, edge_src=edge_src,
  67. edge_dst=edge_dst, edge_distances=edge_distances)
  68. current_fwhm = estimate_fwhm(edge_src=edge_src, edge_dst=edge_dst,
  69. edge_distances=edge_distances, signal_data=smoothed_noise)
  70. logger.debug(f"Iteration {i}: current fwhm: {current_fwhm:.2f}, target fwhm: {fwhm:.2f} tau: {tau:.2f}")
  71. previous_mae = mae
  72. mae = np.abs(current_fwhm - fwhm)
  73. if mae < best_mae:
  74. best_mae = mae
  75. best_tau = tau
  76. best_fwhm = current_fwhm
  77. if mae < stop_threshold:
  78. break
  79. if i == max_iterations - 1:
  80. logger.warning(f"Maximum iterations reached ({max_iterations}). ")
  81. break
  83. gradient = current_fwhm - fwhm
  84. previous_tau = tau
  85. tau -= learning_rate * gradient
  86. if tau <= 0:
  87. logger.info(f"Tau became non-positive. Reducing tau to half of previous value.")
  88. tau = previous_tau / 2
  89. elif mae > previous_mae:
  90. logger.warning(f"MAE increased from {previous_mae:.4f} to {mae:.4f}.")
  91. patience -= 1
  92. if patience <= 0:
  93. logger.warning(f"Patience of {initial_patience} iterations exceeded. Stopping gradient descent.")
  94. break
  95. else:
  96. logger.warning(f"Continuing gradient descent with reduced learning rate.")
  97. learning_rate /= 2
  98. else:
  99. learning_rate *= decay_rate
  100. patience = initial_patience # reset patience if we made progress
  102. if mae > error_threshold:
  103. raise ValueError(f"Failed to achieve target fwhm within error threshold: {error_threshold:.3f}. "
  104. f"Final fwhm: {current_fwhm:.2f}, target fwhm: {fwhm:.2f}, "
  105. f"tau: {tau:.2f}.")
  107. end_time = time.time()
  109. logger.info(f"Gradient descent completed.")
  110. logger.info(f"Final tau: {best_tau:.2f}, "
  111. f"achieved fwhm: {best_fwhm:.2f}, "
  112. f"target fwhm: {fwhm:.2f}, "
  113. f"time taken: {(end_time - start_time) / 60:.2f} minutes")
  114. return best_tau

optimization.py at commit c423680, under Apache-2.0 · at the source

Overview

Authors: David G. Ellis1, Michele R. Aizenberg1
  1. Department of Neurosurgery, University of Nebraska Medical Center, Omaha, NE, United States
Institutions: University of Nebraska Medical Center (United States)
Journal: Frontiers in neuroimaging, volume 5, article 1753534
Dates: received 24 November 2025; accepted 23 March 2026; published online 1 May 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.3389/fnimg.2026.1753534 · PMID 42146843 · PMCID PMC13175814 · OpenAlex W7160043380
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: fMRI (modality), methods / tools (subfield)
Methods: Spectral & time-frequency, Statistics, Connectivity, Graphs, fMRI & imaging
Keywords: fMRI, spatial smoothing, anatomically constrained smoothing, task activation, functional connectivity, volumetric smoothing artifacts
Topic: Functional Brain Connectivity Studies (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Citations: not cited yet (Europe PMC); 39 references in the paper

Abstract

Introduction: Smoothing fMRI data prior to analysis is a fundamental and widely used technique to increase sensitivity. Unconstrained smoothing can also reduce the spatial specificity of the analysis by introducing artifacts in the data. This study tested the effects of smoothing on the reliability and accuracy of both task fMRI and resting state data. The effects of unconstrained smoothing were compared to those of an anatomically constrained smoothing method, which prevents smoothing across the white and gray matter surfaces of the cortex.

Methods: Unconstrained Gaussian smoothing and anatomically constrained smoothing were applied to simulated data, a sensory task fMRI dataset, a precision fMRI motor task mapping dataset, and a resting state fMRI dataset. Smoothing-related artifacts were tested for and compared between the smoothing methods, and the effects of the smoothing methods on the reliability and accuracy were measured.

Results: In the experiments with simulated data, unconstrained Gaussian smoothing demonstrated decreased accuracy and increased white matter activation compared to constrained smoothing. In the sensory task activation analysis, both Gaussian and constrained smoothing increased the reliability of the sensory task fMRI activations, but Gaussian smoothing increased the percentage of active voxels in the white matter relative to constrained smoothing (p < 0.001). Relative to constrained smoothing, Gaussian smoothing with FWHM > 3 mm also decreased the accuracy of motor mapping results from individual sessions to the precision maps (p < 0.001). With cluster significance thresholding, mean false positive voxel percentages remained below 5% for both methods across the tested kernel widths. Both Gaussian and constrained smoothing demonstrated a biasing effect on the resting state connectivity of nearby regions and on the graph theory metrics of the functional connectomes.

Conclusion: This study showed that unconstrained Gaussian smoothing spreads activation across cortical boundaries, increases white matter activation, and biases graph theory connectivity metrics. Anatomically constrained smoothing reduced some of these smoothing artifacts while still increasing reliability and may be a reasonable alternative to unconstrained Gaussian smoothing.

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 3 matches between paragraphs and lines of code.

ellisdg/csmooth

License: Apache-2.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: c4236808cb2cf49ebb8c29fe7c27a2384b3530b0, 3 March 2026
Languages: Python (13)
Size: 20 files, 13 scripts
Software Heritage: not archived
Found in: the acknowledgements
Holds: README, license file, environment (Dockerfile, pyproject.toml, requirements.txt, setup.py)
Not found: CITATION.cff, tests, continuous integration, documentation
Tools: NumPy (8 files), NiBabel (4 files), SciPy (4 files), Nilearn (3 files), NetworkX (2 files), TemplateFlow (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
15 files
At the source: github.com/ellisdg/csmooth

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;
  • 13 scripts, each with its path and the digest of its content;
  • 3 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

No dataset and no data link were found in the paper.

Data availability statement

The sensory task fMRI data analyzed in this study can be found at openneuro.org under dataset ds005009 version 1.0.0. The fMRI data for the Midnight Scan Club analyzed in this study can be found at openneuro.org under dataset ds000224 version 1.0.4. Data analyzed in this study from the Human Connectome Project in Aging can be accessed through the National Institute of Mental Health Data Archive at nda.nih.gov. Data collection for the Human Connectome Project in Aging was supported by the National Institute on Aging of the National Institutes of Health under Award Number U01AG052564.

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

Versions

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, pages, dates, 2 authors, 6 keywords, 35 references.

Cite

This paper

Ellis, D. G., & Aizenberg, M. R. (2026). Anatomically constrained volumetric smoothing enhances fMRI reliability while avoiding smoothing artifacts. Frontiers in neuroimaging, 5, 1753534. https://doi.org/10.3389/fnimg.2026.1753534

BibTeX

@article{ellis2026anatomically,
author = {Ellis, David G. and Aizenberg, Michele R.},
title = {{Anatomically constrained volumetric smoothing enhances fMRI reliability while avoiding smoothing artifacts}},
journal = {Frontiers in neuroimaging},
year = {2026},
month = may,
volume = {5},
pages = {1753534},
publisher = {Frontiers Media SA},
issn = {2813-1193},
doi = {10.3389/fnimg.2026.1753534},
url = {https://doi.org/10.3389/fnimg.2026.1753534},
pmid = {42146843},
pmcid = {PMC13175814}
}

RIS

TY - JOUR
AU - Ellis, David G.
AU - Aizenberg, Michele R.
TI - Anatomically constrained volumetric smoothing enhances fMRI reliability while avoiding smoothing artifacts
T2 - Frontiers in neuroimaging
J2 - Front Neuroimaging
PY - 2026
DA - 2026/05/01
VL - 5
SP - 1753534
SN - 2813-1193
PB - Frontiers Media SA
DO - 10.3389/fnimg.2026.1753534
UR - https://doi.org/10.3389/fnimg.2026.1753534
LA - en
ER -

CSL-JSON

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"DOI": "10.3389/fnimg.2026.1753534",
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