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arxiv: 2606.00122 · v1 · pith:M2MSXUFSnew · submitted 2026-05-28 · 📡 eess.IV · cs.NA· math.NA

Mathematical framework for perception-driven parameter choice in image denoising

Saara Isoranta , Emilia L.K. Bl{\aa}sten , L\'ilian Ferreira de Freitas , Jukka H\"akkinen , Markus Juvonen , Samuli Siltanen This is my paper

Pith reviewed 2026-06-29 00:48 UTC · model grok-4.3

classification 📡 eess.IV cs.NAmath.NA
keywords image denoisingperception-driven parameter choicepsychometric scalingHaarPSItotal variation denoisinghuman visual perceptioncomparison testsparameter discretization
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The pith

Psychometric scaling of human comparisons yields a HaarPSI threshold for choosing denoising parameters

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper combines mathematical image processing with psychological measurement to select denoising parameters that align with human visual perception instead of relying solely on numerical error metrics. Researchers generate multiple versions of the same photograph denoised under total variation regularization at different parameter values, then run direct comparison tests with human observers. Psychometric scaling of the resulting judgment data identifies a specific HaarPSI value that functions as a threshold for dividing the continuous parameter range into discrete steps. This produces openly available image collections already calibrated to perceived quality differences and supplies a reusable experimental template for other perception-driven imaging tasks.

Core claim

Conducting human comparison tests on total variation denoised images with varying parameters and applying psychometric scaling produces a HaarPSI threshold that discretizes the parameter grid according to perceived similarity, yielding calibrated image sets and a framework for further comparison-based experiments in perception-driven imaging.

What carries the argument

Psychometric scaling of pairwise human similarity judgments on denoised images to calibrate HaarPSI as a discretization threshold for total variation denoising parameters.

If this is right

  • Total variation denoising parameters can be discretized using the derived HaarPSI threshold to produce results that better match human visual assessment.
  • The resulting psychometrically scaled image collections are available for direct use in additional perception-driven imaging experiments.
  • The comparison-test-plus-scaling procedure supplies a template that can be repeated for other denoising algorithms or imaging modalities.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same calibration process could be applied to parameter selection in deblurring, inpainting, or other restoration tasks to align outputs with perception.
  • Automated systems might eventually use the calibrated HaarPSI threshold to pick denoising strength on the fly for new images without manual tuning.
  • Testing the threshold across many different base images would reveal whether it remains stable or varies with image content type.

Load-bearing premise

The judgments collected from human participants in the comparison tests accurately reflect perceived differences that matter for the practical quality of denoised images.

What would settle it

A replication study with new participants that returns a substantially different HaarPSI threshold whose image groupings contradict independent visual quality rankings would show the scaling method does not reliably capture perception.

Figures

Figures reproduced from arXiv: 2606.00122 by Emilia L.K. Bl{\aa}sten, Jukka H\"akkinen, L\'ilian Ferreira de Freitas, Markus Juvonen, Saara Isoranta, Samuli Siltanen.

Figure 1
Figure 1. Figure 1: Two inverse problems solved with total variation (TV) regularization [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The effect different parameter values have on the same measured [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: One of the anchor images used in the last test block. This image was [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The photographic images used as bases for the datasets in this study. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The photographs from which the images in figure 4 are cropped. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: We start with an initial grid consisting of set values, then construct an [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Two consecutive samples from set 2. The images 23 and 24 have a [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Images 1 and 23 of set 1 [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Images 1 and 32 of set 2 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Images 1 and 22 of set 3. The test was conducted online https://compare.blasten.eu 2 [31], built and administrated by our research team. The image pairs were displayed side 1https://doi.org/10.5281/zenodo.18457707 2Available at the time of writing this article 14 [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: A smaller section of each image in set 1 has been magnified here [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The magnified sub–images of set 2. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The magnified sub–images of set 3. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: A screen capture of the test environment [31]. In experiments like these, comfort of the participants has to be taken into account, as well as the explicit issue of growing bored. After a certain point in a test with an infinite amount of questions, observers lose their interest in the images which greatly affects their answers. The effects of boredom (in behavioral studies) have been researched quite rec… view at source ↗
Figure 15
Figure 15. Figure 15: The psychometric curve of set 1. Every blue dot in the image is [PITH_FULL_IMAGE:figures/full_fig_p022_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The psychometric curves of sets 2 and 3. [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Psychometrically scaled set 1 [PITH_FULL_IMAGE:figures/full_fig_p025_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Psychometrically scaled set 3. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_18.png] view at source ↗
read the original abstract

We approach image denoising from a perception-driven perspective: how can we select the parameters that are best suited for human visual perception? We combine research methods in mathematics and psychology to develop a mathematical framework for measuring perceived similarity. We construct a sample set of differently denoised photographs by using the same base image as input data and by tuning the parameter value in a total variation denoising algorithm. A comparison test is conducted with human participants to survey perceived differences between the images. Analyzing the results with psychometric scaling provides us with a HaarPSI value to use as a threshold in discretizing parameter grids. As a result, we obtain psychometrically scaled, openly available image sets that are ready to use in further experiments in perception-driven imaging, as well as a framework for ensuing experiments involving comparison tests.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a perception-driven framework for choosing parameters in total-variation image denoising. A single base photograph is denoised at multiple regularization strengths; human participants perform pairwise comparison tests on the resulting images; psychometric scaling of the survey data is used to extract a HaarPSI threshold that discretizes the parameter grid. The authors release the scaled image sets and propose the procedure as a template for future perception-driven experiments.

Significance. If the mapping from human judgments to a stable HaarPSI cutoff can be shown to be reproducible, the work supplies both a concrete, openly available test collection and a methodological template that links mathematical image metrics to perceptual data. Such resources are currently scarce in the perception-driven imaging literature.

major comments (2)
  1. [Abstract / Methods (survey and scaling procedure)] The central claim—that psychometric scaling of the comparison-test results directly supplies a usable HaarPSI threshold—rests on an unstated mapping between scaled perceptual distances and computed HaarPSI values. The manuscript does not specify the scaling model (Thurstone, Bradley-Terry, etc.), the number of participants, inter-rater consistency statistics, or the precise thresholding rule applied to the continuous scale. Without these details the threshold cannot be evaluated for stability or generalizability beyond the single base image and algorithm tested.
  2. [Results / Discussion] The assumption that pairwise human judgments of “perceived difference” between total-variation reconstructions accurately reflect quality differences relevant to denoising is load-bearing yet untested. No validation against an independent perceptual quality scale or against objective metrics other than HaarPSI is reported, leaving open the possibility that the derived threshold reflects task-specific artifacts rather than general perceptual utility.
minor comments (2)
  1. [Methods] Clarify whether the same base image is used for all reported experiments or whether additional images were tested; the abstract mentions only one base image.
  2. [Methods] Provide the exact definition or reference for the HaarPSI implementation employed when computing distances between image pairs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on the methodological details and validation aspects. We will revise the manuscript to address the points raised while preserving the core contribution of the perception-driven framework and the released image sets.

read point-by-point responses

  1. Referee: [Abstract / Methods (survey and scaling procedure)] The central claim—that psychometric scaling of the comparison-test results directly supplies a usable HaarPSI threshold—rests on an unstated mapping between scaled perceptual distances and computed HaarPSI values. The manuscript does not specify the scaling model (Thurstone, Bradley-Terry, etc.), the number of participants, inter-rater consistency statistics, or the precise thresholding rule applied to the continuous scale. Without these details the threshold cannot be evaluated for stability or generalizability beyond the single base image and algorithm tested.

    Authors: We agree that these details are required for reproducibility and evaluation of the threshold. The revised manuscript will specify the psychometric scaling model, report the number of participants, include inter-rater consistency statistics, and describe the exact thresholding rule used to obtain the HaarPSI cutoff from the scaled distances. revision: yes

  2. Referee: [Results / Discussion] The assumption that pairwise human judgments of “perceived difference” between total-variation reconstructions accurately reflect quality differences relevant to denoising is load-bearing yet untested. No validation against an independent perceptual quality scale or against objective metrics other than HaarPSI is reported, leaving open the possibility that the derived threshold reflects task-specific artifacts rather than general perceptual utility.

    Authors: The manuscript centers on direct measurement of perceived similarity through pairwise comparisons to support parameter selection, rather than claiming a general perceptual quality metric. We will revise the discussion to explicitly note this scope, acknowledge the absence of cross-validation against other scales, and outline how the released data sets could support such validation in follow-up studies. revision: partial

Circularity Check

0 steps flagged

No significant circularity; framework rests on new human experiments and psychometric scaling

full rationale

The paper constructs denoised image samples via total-variation denoising, collects fresh pairwise comparison data from human participants, and applies psychometric scaling to those results to obtain a HaarPSI threshold for parameter discretization. This chain is empirical and self-contained: the threshold is not obtained by fitting a parameter to a subset of the same data and relabeling it a prediction, nor by self-citation of a uniqueness theorem, nor by smuggling an ansatz through prior work. No equations or steps reduce the output to the input by construction. The derivation therefore stands on independent perceptual data rather than tautological re-labeling.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim depends on the domain assumption that pairwise human comparisons can be scaled to measure perceived image similarity, with the HaarPSI value acting as a derived threshold parameter from the experimental data.

free parameters (1)
  • HaarPSI threshold value
    Obtained via psychometric scaling of human data to serve as discretization threshold.
axioms (1)
  • domain assumption Psychometric scaling of comparison test data provides a valid measure of perceived similarity between images
    Invoked when analyzing the results of the human participant survey to derive the threshold.

pith-pipeline@v0.9.1-grok · 5689 in / 1255 out tokens · 42205 ms · 2026-06-29T00:48:02.730651+00:00 · methodology

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Works this paper leans on

34 extracted references · 17 canonical work pages

  1. [1]

    Jari Kaipio and Erkki Somersalo.Statistical and Computational Inverse Problems. Vol. 160. Applied Mathematical Sciences. Springer-Verlag, New York, 2005, pp. xvi+339.isbn: 0-387-22073-9

    2005

  2. [2]

    European Congress of Mathematics

    Martin Burger. “European Congress of Mathematics”. In: EMS Press,

  3. [3]

    Variational regularization in inverse problems and machine learning, pp

    Chap. Variational regularization in inverse problems and machine learning, pp. 253–275.doi:10.4171/8ECM/01

    work page doi:10.4171/8ecm/01

  4. [4]

    Variational regularisation for inverse problems with imperfect forward operators and general noise models

    Leon Bungert et al. “Variational regularisation for inverse problems with imperfect forward operators and general noise models”. In:Inverse Prob- lems36.125014 (2020).doi:10.1088/1361-6420/abc531

    work page doi:10.1088/1361-6420/abc531 2020

  5. [5]

    Variational Methods in Imaging

    Otmar Scherzer Markus Grasmair Harald Grossauer Markus Haltmeier and Frank Lenzen. “Variational Methods in Imaging”. In: New York, New York, USA: Springer, 2009. Chap. Variational Regularization Methods for the Solution of Inverse Problems, pp. 53–113.doi:10.1007/978-0-387- 69277-7_3

    work page doi:10.1007/978-0-387- 2009

  6. [6]

    GitHub documentation

    Tristan van Leeuwen and Christoph Brune.Variational formulations for inverse problems. GitHub documentation. A repository containing lecture notes on inverse problems and imaging. This chapter lists common choices for a regularizer. 2026.url:https://tristanvanleeuwen.github.io/ IP_and_Im_Lectures/variational_formulations.html

    2026

  7. [7]

    Least squares methods for ill-posed problems with a pre- scribed bound

    Keith Miller. “Least squares methods for ill-posed problems with a pre- scribed bound”. In:SIAM J. Math. Anal.1 (1970), pp. 52–74

    1970

  8. [8]

    Lawson and Richard J

    Charles L. Lawson and Richard J. Hanson.Solving Least Squares Prob- lems. Reprint by SIAM in 1995. Engelwood Cliffs, New Jersey, USA: Prentica–Hall, 1974

    1995

  9. [9]

    Sparse tomography

    Keijo H¨ am¨ al¨ ainen et al. “Sparse tomography”. In:SIAM Journal on Sci- entific Computing35.3 (2013), B644–B665.doi:10.1137/120876277. 28

    work page doi:10.1137/120876277 2013

  10. [10]

    Multiresolution Parameter Choice Method for To- tal Variation Regularized Tomography

    Kati Niinim¨ aki et al. “Multiresolution Parameter Choice Method for To- tal Variation Regularized Tomography”. In:SIAM Journal on Imaging Sciences9.3 (2016), pp. 938–974.doi:10.1137/15M1034076

    work page doi:10.1137/15m1034076 2016

  11. [11]

    On the solution of functional equations by the method of regularization

    Vladimir A. Morozov. “On the solution of functional equations by the method of regularization”. In:Doklady Akademii Nauk SSSR167.3 (1966), pp. 510–512

    1966

  12. [12]

    Morozov’s discrepancy prin- ciple for Tikhonov regularization of severly ill-posed problems in finite- dimensional subspaces

    Sergei Pereverzyev and Eberhard Schock. “Morozov’s discrepancy prin- ciple for Tikhonov regularization of severly ill-posed problems in finite- dimensional subspaces”. In:Numerical Functional Analysis and Optimiza- tion21.7 (2000)

    2000

  13. [13]

    Sparsity-promoting Bayesian inversion

    Ville Kolehmainen et al. “Sparsity-promoting Bayesian inversion”. In:In- verse Problems28.2 (2012).doi:10.1088/0266-5611/28/2/025005

    work page doi:10.1088/0266-5611/28/2/025005 2012

  14. [14]

    Karl Pearson. “On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling”. In: The Philosophical Magazine50 (1900), pp. 157–175

    1900

  15. [15]

    The Chi-square test of independence

    Mary L. McHugh. “The Chi-square test of independence”. In:Biochemia Medica23.2 (2013), pp. 143–149

    2013

  16. [16]

    Blog post ongeeksforgeeks.org

    Alind Gupta.Chi–Square Test for Feature Selection - Mathematical Ex- planation. Blog post ongeeksforgeeks.org. A post explaining how this test can be mathematically applied to feature selection, such as parame- ter selection. 2025.url:https://www.geeksforgeeks.org/machine- learning/chi-square-test-for-feature-selection-mathematical- explanation/

    2025

  17. [17]

    Nonlinear total varia- tion based noise removal algorithms

    Stanley Osher Leonid I. Rudin and Emad Fatemi. “Nonlinear total varia- tion based noise removal algorithms”. In:Physica D60.1-4 (1992), pp. 259– 268.doi:10.1016/0167-2789(92)90242-F. 29

    work page doi:10.1016/0167-2789(92)90242-f 1992

  18. [18]

    A First–Order Primal–Dual Algo- rithm for Convex Problems with Applications to Imaging

    Thomas Pock Antonin Chambolle. “A First–Order Primal–Dual Algo- rithm for Convex Problems with Applications to Imaging”. In:Journal of Mathematical Imaging and Vision(40(1) 2010), pp. 120–145.url:http: //dx.doi.org/10.1007/s10851-010-0251-1

    work page doi:10.1007/s10851-010-0251-1 2010

  19. [19]

    Efficient Algorithms for Global Optimization Meth- ods in Computer Vision

    Kristian Bredies. “Efficient Algorithms for Global Optimization Meth- ods in Computer Vision”. In: Berlin: Springer Berlin Heidelberg, 2014. Chap. Recovering piecewise smooth multichannel images by minimization of convex functionals with total generalized variation penalty, pp. 44–77

    2014

  20. [20]

    A Law of Comparitive Judgment

    L. L. Thurstone. “A Law of Comparitive Judgment”. In:Psychological Review34 (1929), pp. 273–286

    1929

  21. [21]

    Winchester, Massachusetts, USA: Imcotek Press, 2000

    Peter Engeldrum.Psychometric Scaling: A Toolkit for Imaging Systems Development. Winchester, Massachusetts, USA: Imcotek Press, 2000

    2000

  22. [22]

    The Perception of Similarity, Dif- ference and Opposition

    Ivana Bianchi and Roberto Burro. “The Perception of Similarity, Dif- ference and Opposition”. In:Journal of Intelligence11.9 (2023).doi: 10.3390/jintelligence11090172

    work page doi:10.3390/jintelligence11090172 2023

  23. [23]

    Models for paired comparisons

    U. B¨ ockenholt. “Models for paired comparisons”. In:Encyclopedia of So- cial Measurement(2005), pp. 735–740.doi:10.1016/B0- 12- 369398- 5/00454-0

    work page doi:10.1016/b0- 2005

  24. [24]

    A Haar Wavelet–Based Perceptual Similarity Index for Image Qual- ity Assessment

    Gitta Kutyniok Rafael Reisenhofer Sebastian Bosse and Thomas Wiegand. “A Haar Wavelet–Based Perceptual Similarity Index for Image Qual- ity Assessment”. In:Signal Processing: Image Communication(61 2018). Matlab and Python algorithms can be found at https://www.math.uni- bremen.de/cda/HaarPSI/, as well as a summary on the use and function of the method., ...

    work page doi:10.1016/j.image.2017.11.001 2018

  25. [25]

    Image quality as- sessment: from error visibility to structural similarity

    H. Sheikh Zhou Wang A. C. Bovik and E. Simoncelli. “Image quality as- sessment: from error visibility to structural similarity”. In:IEEE Transac- tions on Image Processing13.4 (2004), pp. 600–612.doi:10.1109/TIP. 2003.819861. 30

    work page doi:10.1109/tip 2004

  26. [26]

    Leipzig, Germany: Breitkopf und H¨ artel, 1860

    Gustav Fechner.Elemente der psychophysik. Leipzig, Germany: Breitkopf und H¨ artel, 1860

  27. [27]

    A Wavelet Tour of Signal Processing: The Sparse Way

    St´ ephane Mallet. “A Wavelet Tour of Signal Processing: The Sparse Way”. In: Academic Press, 2009. Chap. 2: The Fourier Kingdom, pp. 33–57.doi: 10.1016/B978-0-12-374370-1.X0001-8

    work page doi:10.1016/b978-0-12-374370-1.x0001-8 2009

  28. [28]

    A Matlab code of the Chambolle–Pock algorithm written by Emilia Bl˚ asten and L´ ılian Ferreira de Freitas

    L´ ılian Ferreira de Freitas Emilia Bl˚ asten.TV-Chambolle multicolor func- tion. A Matlab code of the Chambolle–Pock algorithm written by Emilia Bl˚ asten and L´ ılian Ferreira de Freitas. 2022

    2022

  29. [29]

    20287835

    Saara Isoranta Emilia Bl˚ asten L´ ılian Ferreira de Freitas Jukka H¨ akkinen Markus Juvonen and Samuli Siltanen.Psychometrically scaled image sets. Openly available dataset in Zenodo. The repository containing the data constracted over the course of this project. 2026.doi:10.5281/zenodo. 18457707

    work page doi:10.5281/zenodo 2026

  30. [30]

    The fusiform face area: a cortical region specialized for the perception of faces

    Nancy Kanwisher and Galit Yovel. “The fusiform face area: a cortical region specialized for the perception of faces”. In:Philos Trans R Soc Lond B Biol Sci.29.361 (2006), pp. 2109–2128.doi:10.1098/rstb.2006.1934. url:https://pmc.ncbi.nlm.nih.gov/articles/PMC1857737/

    work page doi:10.1098/rstb.2006.1934 2006

  31. [31]

    The neural basis of face pareidolia with human intracerebral recordings

    Beg¨ um Cerraho˘ glu et al. “The neural basis of face pareidolia with human intracerebral recordings”. In:Imaging Neuroscience3 (2025). From MIT Press Direct.doi:https://doi.org/10.1162/imag_a_00518

    work page doi:10.1162/imag_a_00518 2025

  32. [32]

    L´ ılian Ferreira de Freitas.Image Compare!https://compare.blasten. eu. The image comparison test built by L´ ılian Ferreira de Freitas, available online. 2024

    2024

  33. [33]

    Is boredom a source of noise and/or a confound in behavioral science research?

    Wanja Wolff Maria Meier Corinna S. Martarelli. “Is boredom a source of noise and/or a confound in behavioral science research?” In:Humanit Soc Sci Commun11.368 (2024).doi:10.1057/s41599-024-02851-7

    work page doi:10.1057/s41599-024-02851-7 2024

  34. [34]

    fi / en/

    Tutkijoiden y¨ o.Researchers’ night.https : / / tutkijoidenyo . fi / en/. The European Researchers’ night event in Finland, where researchers at four different universities present their research to the public, the inverse 31 problems research unit at University of Helsinki among them. The pro- gramme of UH can be found on this page:https://www.helsinki.f...

    2025