arxiv: 2605.09324 · v1 · submitted 2026-05-10 · ⚛️ physics.optics · physics.app-ph· quant-ph

Recognition: 2 theorem links

· Lean Theorem

Noise-Resilient Imaging through Coherence Filtering

Anand Kumar Jha, Aniket Nag, Keval Moliya, Pranay Mohta, Shaurya Aarav

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:14 UTC · model grok-4.3

classification ⚛️ physics.optics physics.app-phquant-ph

keywords coherence filteringnoise-resilient imagingtemporal coherenceinterferometryimage distillationoptical imagingnoise rejectionlow-light imaging

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The pith

Coherence filtering recovers feature-rich objects from noise twenty times more intense by separating fields according to their temporal coherence properties.

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

The paper presents an interferometric method that distills object light from noise by exploiting the fact that object and noise fields typically lose phase correlation at different rates over time. The protocol records an image using spatial coherence while the temporal-coherence filter removes the noise contribution, even when the noise is spatially structured and twenty times brighter than the object. It succeeds with objects such as QR codes and grayscale wheels and continues to work when the spectra of object and noise overlap substantially, a regime where ordinary spectral filtering fails. A reader would care because the technique requires no special illumination sources and can be added to existing imaging setups, opening a route to clearer pictures in low-light or noisy environments such as biological microscopy and optical communication.

Core claim

By implementing an interferometric protocol that forms images from spatial coherence while simultaneously rejecting light on the basis of temporal coherence, the authors separate object and noise fields whose temporal coherence properties differ, recovering the object even when the noise intensity reaches twenty times the object intensity and when their spectra overlap substantially.

What carries the argument

The interferometric protocol that images via spatial coherence while filtering noise via temporal coherence, thereby performing coherence-based image distillation without requiring specialized illumination.

Load-bearing premise

Object and noise light must possess measurably different temporal coherence times so that the interferometric measurement can isolate one without the other.

What would settle it

An experiment in which the temporal coherence properties of object and noise are made identical should cause the recovered image contrast to collapse to zero regardless of intensity ratio or spatial structure.

Figures

Figures reproduced from arXiv: 2605.09324 by Anand Kumar Jha, Aniket Nag, Keval Moliya, Pranay Mohta, Shaurya Aarav.

**Figure 2.** Figure 2: FIG. 2. Schematic diagram of the experimental setup for Coherence Imaging - (a) Object illumination: Object - Image displayed [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Noise-resilient imaging with uniform noise - Three objects were imaged: Object 1: Binary plaintext image - IIT [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Noise-resilient imaging with spatially structured noise - The parameter [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Comparison of Temporal Coherence Filtering (TCF) and Spectral Filtering (SF) for the same-central-frequency case [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

read the original abstract

Noise is a significant challenge in imaging. Conventional intensity-based techniques mitigate noise through various filtering methods, but they often require prior knowledge of noise characteristics and struggle, especially under low-light conditions and with spatially structured noise. Quantum distillation provides enhanced noise rejection; however, its applicability is limited as it requires specialised illumination and substantial modifications to existing imaging setups. In this article, we introduce a coherence-based image distillation approach that separates object from noise by leveraging the difference in their temporal coherence properties. We implement this through our interferometric protocol, which enables imaging based on spatial coherence while simultaneously filtering out noise via temporal coherence. This overcomes the limitations of both intensity-based and quantum distillation methods. We experimentally demonstrate noise resilience by successfully recovering feature-rich objects, such as QR codes and grayscale wheels, obscured by spatially uniform and structured noise 20 times as intense as the object. We further show that our method remains effective for fields with substantial spectral overlap, outperforming spectral filtering in regimes where the latter provides little noise suppression. This approach provides a robust framework for noise-resilient imaging with applications in optical communication, fluorescence microscopy, and biological imaging at both high and low light levels.

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.

Desk Editor's Note private letter to a colleague

The paper demonstrates an interferometric setup for imaging via spatial coherence while filtering noise via temporal coherence, with experiments recovering objects under heavy noise, but the claims rest on thin quantitative evidence and a coherence distinction that may not survive spectral overlap.

read the letter

The core idea is an interferometric protocol that images the object through its spatial coherence properties while using temporal coherence to reject noise. They report recovering QR codes and grayscale wheels when noise is 20 times stronger than the signal, and they say it still works with substantial spectral overlap where ordinary spectral filtering does little good. That combination is the main new element: a single setup that avoids both standard intensity filters and the specialized sources needed for quantum distillation methods. The practical tests with real structured objects and low-light conditions are the part that actually lands; they show the method can produce usable images where intensity-based approaches fail outright. The paper does a reasonable job framing the limitations of existing techniques and positioning the coherence approach as more general. The soft spots are clear. The abstract supplies no numbers on recovery quality, no SNR values, no error bars, and no protocol details on how the coherence functions were measured or controlled. Without those, the 20x noise claim is hard to weigh. The stress-test concern holds up: temporal coherence time is set by spectral bandwidth, so substantial overlap should produce similar coherence lengths for object and noise. If the separation still occurs, it must be relying on spatial coherence differences, polarization, or residual intensity contrast rather than the temporal filter alone. The paper needs to show direct measurements of the mutual coherence function and explain why the claimed independence from spectral filtering is real rather than apparent. This is for experimental optics groups working on microscopy, low-light imaging, or optical communications. A reader already thinking about coherence techniques would get the method sketch and the object-recovery examples, but would still need the missing metrics and mechanism details to decide whether to try it. I would send it to peer review so the authors can supply the quantitative controls and address the coherence-overlap issue directly.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces a coherence-based image distillation technique that employs an interferometric protocol to separate object fields from noise by exploiting differences in temporal coherence. It claims experimental recovery of feature-rich objects (QR codes, grayscale wheels) obscured by both uniform and structured noise up to 20 times the object intensity, including under substantial spectral overlap where the method outperforms spectral filtering, while avoiding the specialized illumination required by quantum distillation approaches.

Significance. If the experimental demonstrations are supported by quantitative metrics and controls, the approach could offer a practical, setup-compatible route to noise-resilient imaging in low-light and structured-noise regimes, with relevance to optical communications, fluorescence microscopy, and biological imaging.

major comments (2)

[Abstract] Abstract: The central experimental claim of recovering objects under 20× noise intensity is presented without quantitative metrics (e.g., SNR, fidelity, or error bars), statistical analysis, or protocol details, leaving the asserted superiority over spectral filtering and the noise-resilience performance unsubstantiated.
[Abstract] Abstract: The premise that object and noise can be isolated via temporal coherence differences is asserted to hold even with substantial spectral overlap; however, because the mutual coherence function is the Fourier transform of the power spectral density, this requires explicit clarification of the separation mechanism when coherence times are expected to be similar, to rule out reliance on unstated factors such as spatial coherence or residual intensity contrast.

minor comments (1)

The abstract would benefit from a concise statement of the key experimental parameters (e.g., coherence times, spectral bandwidths, or interferometer configuration) to allow readers to assess the regime of applicability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major comment below and have revised the abstract and main text to strengthen the presentation of quantitative results and to clarify the separation mechanism.

read point-by-point responses

Referee: [Abstract] Abstract: The central experimental claim of recovering objects under 20× noise intensity is presented without quantitative metrics (e.g., SNR, fidelity, or error bars), statistical analysis, or protocol details, leaving the asserted superiority over spectral filtering and the noise-resilience performance unsubstantiated.

Authors: We agree that the abstract, as a concise summary, would be strengthened by explicit reference to key quantitative indicators. The manuscript body (Results and Methods sections) contains the full quantitative analysis, including SNR values, image fidelity metrics, error bars from repeated trials, and statistical controls, along with the interferometric protocol details. We have revised the abstract to incorporate a brief statement of these performance metrics and the direct experimental comparison to spectral filtering, thereby making the central claims more self-contained while preserving brevity. revision: yes
Referee: [Abstract] Abstract: The premise that object and noise can be isolated via temporal coherence differences is asserted to hold even with substantial spectral overlap; however, because the mutual coherence function is the Fourier transform of the power spectral density, this requires explicit clarification of the separation mechanism when coherence times are expected to be similar, to rule out reliance on unstated factors such as spatial coherence or residual intensity contrast.

Authors: We thank the referee for this observation. Although the mutual coherence function is the Fourier transform of the power spectral density, the interferometric protocol isolates the object field by selecting path-length differences at which the object’s temporal coherence produces stable interference fringes while the noise averages to zero. We have added a clarifying paragraph in the Theory section that derives the separation condition for overlapping spectra and includes supporting simulations. We have also inserted experimental controls that equalize spatial coherence and minimize residual intensity contrast, confirming that temporal-coherence filtering remains the operative mechanism. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental demonstration is self-contained

full rationale

The manuscript describes an interferometric protocol for separating object and noise fields via differences in temporal coherence, followed by experimental recovery of feature-rich objects under 20× noise intensity. No equations, fitted parameters, or predictions are presented that reduce by construction to the inputs; the central claims rest on direct experimental outcomes rather than any derivation chain. No self-citations are invoked as load-bearing uniqueness theorems or ansatzes. The work is therefore self-contained against external benchmarks, with the reader's noted premise about coherence distinction being an assumption open to empirical test rather than a circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on one domain assumption about distinguishable temporal coherence; no free parameters, new entities, or additional axioms are stated in the abstract.

axioms (1)

domain assumption Object and noise possess sufficiently different temporal coherence properties to permit separation by the interferometric protocol
This difference is the explicit basis for the noise-filtering step described in the abstract.

pith-pipeline@v0.9.0 · 5514 in / 1185 out tokens · 54292 ms · 2026-05-12T03:14:57.487796+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear
We adjust the interferometer’s path length difference such that it is much shorter than the temporal coherence length of the narrow-band field but longer than that of the broad-band noise. ln_c < ∆z < lo_c
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
Γ(∆ρ, τ) = Wo(∆ρ,ωo0) exp[−½(τ/τoc)²] + Wn(∆ρ,ωn0) exp[−½(τ/τnc)²]

Reference graph

Works this paper leans on

49 extracted references · 49 canonical work pages

[1]

−1 2 τ τ oc 2# + Wn(∆ρ, ωn 0 ) exp

exp " −1 2 τ τ oc 2# + Wn(∆ρ, ωn 0 ) exp " −1 2 τ τ nc 2# = Wo(∆ρ, ωo

work page
[2]

−1 2 ∆z loc 2# + Wn(∆ρ, ωn 0 ) exp

exp " −1 2 ∆z loc 2# + Wn(∆ρ, ωn 0 ) exp " −1 2 ∆z lnc 2# (6) where τc = 2 /∆ω is the coherence time of the field, ∆z = cτ is the path length difference between the in- terferometer arms and lc = cτc is the temporal coherence length of the optical field. The temporal coherence of the field comes in as a constant multiplicative factor to the cross-spectral...

work page
[3]

(15) where Is(ρ′ 1, −f) is the intensity at point ρ′ 1. For our incoherent source, we employ a smartphone with OLED screen, as light-emitting diodes (LEDs) can be considered spatially completely incoherent in the sense that their position correlations are approximated by the form given in Eq. 15 [38–42]. Positioned at the front focal plane of a convex len...

work page 2021
[4]

Pawley, Handbook of biological confocal microscopy, Springer google schola 2, 1035 (2006)

J. Pawley, Handbook of biological confocal microscopy, Springer google schola 2, 1035 (2006)

work page 2006
[5]

R. C. Gonzalez, Digital image processing (Pearson edu- cation india, 2009)

work page 2009
[6]

D. L. Donoho, De-noising by soft-thresholding, IEEE transactions on information theory 41, 613 (2002)

work page 2002
[7]

Jain and V

P. Jain and V. Tyagi, Spatial and frequency domain fil- ters for restoration of noisy images, IETE Journal of Ed- ucation 54, 108 (2013)

work page 2013
[8]

S. P. Awate and R. T. Whitaker, Unsupervised, information-theoretic, adaptive image filtering for image restoration, IEEE Transactions on pattern analysis and machine intelligence 28, 364 (2006)

work page 2006
[9]

Shin, R.-H

D.-H. Shin, R.-H. Park, S. Yang, and J.-H. Jung, Block- based noise estimation using adaptive gaussian filter- ing, IEEE Transactions on Consumer Electronics51, 218 (2005)

work page 2005
[10]

R. Yang, L. Yin, M. Gabbouj, J. Astola, and Y. Neuvo, Optimal weighted median filtering under structural con- straints, IEEE Transactions on Signal Processing43, 591 (1995)

work page 1995
[11]

Li and J

F. Li and J. Fan, Salt and pepper noise removal by adap- tive median filter and minimal surface inpainting, in2009 2nd International Congress on Image and Signal Process- ing (IEEE, 2009) pp. 1–5

work page 2009
[12]

Y. Xu, J. Weaver, D. Healy, and J. Lu, Wavelet transform domain filters: a spatially selective noise filtration tech- nique, IEEE Transactions on Image Processing 3, 747 (1994)

work page 1994
[13]

Dixit and P

A. Dixit and P. Sharma, A comparative study of wavelet thresholding for image denoising, IJ Image, Graphics and Signal Processing 12, 39 (2014)

work page 2014
[14]

M. Lang, H. Guo, J. Odegard, C. Burrus, and R. Wells, Noise reduction using an undecimated discrete wavelet transform, IEEE Signal Processing Letters 3, 10 (1996)

work page 1996
[15]

R. D. da Silva, R. Minetto, W. R. Schwartz, and H. Pedrini, Adaptive edge-preserving image denoising us- ing wavelet transforms, Pattern Analysis and Applica- tions 16, 567 (2012)

work page 2012
[16]

L. Fan, F. Zhang, H. Fan, and C. Zhang, Brief review of image denoising techniques, Visual Computing for Indus- try, Biomedicine, and Art 2, 10.1186/s42492-019-0016-7 (2019)

work page doi:10.1186/s42492-019-0016-7 2019
[17]

Goyal, A

B. Goyal, A. Dogra, S. Agrawal, B. Sohi, and A. Sharma, Image denoising review: From classical to state-of-the-art approaches, Information Fusion 55, 220 (2020)

work page 2020
[18]

M. Mafi, H. Martin, M. Cabrerizo, J. Andrian, A. Bar- reto, and M. Adjouadi, A comprehensive survey on im- pulse and gaussian denoising filters for digital images, Signal Processing 157, 236 (2019)

work page 2019
[19]

Zhang, D

Y. Zhang, D. England, A. Nomerotski, P. Svihra, S. Fer- rante, P. Hockett, and B. Sussman, Multidimensional quantum-enhanced target detection via spectrotemporal- correlation measurements, Physical Review A 101, 053808 (2020)

work page 2020
[20]

Gregory, P.-A

T. Gregory, P.-A. Moreau, E. Toninelli, and M. J. Pad- gett, Imaging through noise with quantum illumination, Science Advances 6, 10.1126/sciadv.aay2652 (2020)

work page doi:10.1126/sciadv.aay2652 2020
[21]

Gregory, P.-A

T. Gregory, P.-A. Moreau, S. Mekhail, O. Wolley, and M. J. Padgett, Noise rejection through an improved quantum illumination protocol, Scientific Reports 11, 10.1038/s41598-021-01122-8 (2021)

work page doi:10.1038/s41598-021-01122-8 2021
[22]

J. Zhao, A. Lyons, A. C. Ulku, H. Defienne, D. Faccio, and E. Charbon, Light detection and ranging with en- tangled photons, Optics Express 30, 3675 (2022)

work page 2022
[23]

Defienne, M

H. Defienne, M. Reichert, J. W. Fleischer, and D. Fac- cio, Quantum image distillation, Science Advances 5, 10.1126/sciadv.aax0307 (2019)

work page doi:10.1126/sciadv.aax0307 2019
[24]

D. G. England, B. Balaji, and B. J. Sussman, Quantum- enhanced standoff detection using correlated photon pairs, Physical Review A 99, 023828 (2019)

work page 2019
[25]

Experimental quantum imaging distillation withundetectedlight

J. Fuenzalida, M. Gilaberte Basset, S. T¨ opfer, J. P. Torres, and M. Gr¨ afe, Experimental quantum imaging distillation with undetected light, Science Advances 9, 10.1126/sciadv.adg9573 (2023)

work page doi:10.1126/sciadv.adg9573 2023
[26]

J. B. Breckinridge, Coherence interferometer and astro- nomical applications, Applied Optics 11, 2996 (1972)

work page 1972
[27]

Itoh and Y

K. Itoh and Y. Ohtsuka, Fourier-transform spectral imaging retrieval of source information from three- dimensional spatial coherence, Journal of the Optical So- ciety of America A 3, 94 (1986)

work page 1986
[28]

Yoshimori and K

K. Yoshimori and K. Itoh, Interferometry and radiome- try, Journal of the Optical Society of America A14, 3379 (1997)

work page 1997
[29]

J. B. Breckinridge, Obtaining information through the atmosphere at the diffraction limit of a large aperture, Journal of the Optical Society of America 65, 755 (1975)

work page 1975
[30]

Roddier and F

C. Roddier and F. Roddier, Imaging with a coherence interferometer in optical astronomy, in Image Forma- tion from Coherence Functions in Astronomy (Springer Netherlands, 1979) pp. 175–185

work page 1979
[31]

Roddier and C

F. Roddier and C. Roddier, An image reconstruction of alpha orionis, The Astrophysical Journal 295, L21 (1985)

work page 1985
[32]

Roddier, Interferometric imaging in optical astronomy, Physics Reports 170, 97 (1988)

F. Roddier, Interferometric imaging in optical astronomy, Physics Reports 170, 97 (1988)

work page 1988
[33]

Potuluri, M

P. Potuluri, M. Fetterman, and D. Brady, High depth of field microscopic imaging using an interferometric cam- era, Optics Express 8, 624 (2001)

work page 2001
[34]

Weigel, H

D. Weigel, H. Babovsky, A. Kiessling, and R. Kowarschik, Widefield microscopy with infinite depth of field and enhanced lateral resolution based on an image inverting interferometer, Optics Communica- tions 342, 102 (2015). 13

work page 2015
[35]

Redding, M

B. Redding, M. A. Choma, and H. Cao, Speckle-free laser imaging using random laser illumination, Nature Photon- ics 6, 355 (2012)

work page 2012
[36]

Redding, A

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, Low spatial coherence elec- trically pumped semiconductor laser for speckle-free full- field imaging, Proceedings of the National Academy of Sciences 112, 1304 (2015)

work page 2015
[37]

van Dijk, D

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere, Physical Review Letters 104, 173902 (2010)

work page 2010
[38]

Bhattacharjee, S

A. Bhattacharjee, S. Aarav, H. Wanare, and A. K. Jha, Controlling propagation of spatial coherence for en- hanced imaging through scattering media, Physical Re- view A 101, 043839 (2020)

work page 2020
[39]

Bhattacharjee and A

A. Bhattacharjee and A. K. Jha, Experimental demon- stration of structural robustness of spatially partially coherent fields in turbulence, Optics Letters 45, 4068 (2020)

work page 2020
[40]

Mohta, A

P. Mohta, A. Bhattacharjee, and A. K. Jha, Com- plex spatial coherence measurement using phase-shifting wavefront-inversion interferometry, Journal of Optics27, 075606 (2025)

work page 2025
[41]

Tziraki, R

M. Tziraki, R. Jones, P. French, M. Melloch, and D. Nolte, Photorefractive holography for imaging through turbid media using low coherence light, Applied Physics B: Lasers and Optics 70, 151 (2000)

work page 2000
[42]

Di Lorenzo Pires, J

H. Di Lorenzo Pires, J. Woudenberg, and M. P. van Ex- ter, Measurement of the orbital angular momentum spec- trum of partially coherent beams, Optics Letters 35, 889 (2010)

work page 2010
[43]

Aarav, A

S. Aarav, A. Bhattacharjee, H. Wanare, and A. K. Jha, Efficient generation of propagation-invariant spa- tially stationary partially coherent fields, Physical Re- view A 96, 033815 (2017)

work page 2017
[44]

Torcal-Milla, J

F. Torcal-Milla, J. Lobera, A. Lopez, V. Palero, N. An- dres, and M. Arroyo, Mach-zehnder-based measurement of light emitting diodes temporal coherence, Optik 267, 169722 (2022)

work page 2022
[45]

Deng and D

Y. Deng and D. Chu, Coherence properties of differ- ent light sources and their effect on the image sharpness and speckle of holographic displays, Scientific Reports 7, 10.1038/s41598-017-06215-x (2017)

work page doi:10.1038/s41598-017-06215-x 2017
[46]

See supplemental material at http://link.aps.org/ supplemental/10.1103/3h5s-8xgj

work page doi:10.1103/3h5s-8xgj
[47]

Mandel and E

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge university press, 1995)

work page 1995
[48]

Karan, Ruchi, P

S. Karan, Ruchi, P. Mohta, and A. K. Jha, Quantifying polarization changes induced by rotating dove prisms and k-mirrors, Applied Optics 61, 8302 (2022)

work page 2022
[49]

A. K. Jha, M. Malik, and R. W. Boyd, Exploring energy- time entanglement using geometric phase, Phys. Rev. Lett. 101, 180405 (2008)

work page 2008