CDI

Coherent Diffractive Imaging

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Standard reconstruction benchmark — forward model perfectly known, no calibration needed. Score = 0.5 × clip((PSNR−15)/30, 0, 1) + 0.5 × SSIM

#	Method	Score	PSNR (dB)	SSIM	Source
🥇	ScorePhase ScorePhase Wei et al., ECCV 2025 35.82 dB SSIM 0.968 Checkpoint unavailable	0.831	35.82	0.968	✓ Certified	Wei et al., ECCV 2025
🥈	DiffusionPhase DiffusionPhase Song et al., NeurIPS 2024 35.48 dB SSIM 0.964 Checkpoint unavailable	0.823	35.48	0.964	✓ Certified	Song et al., NeurIPS 2024
🥉	HolographyViT HolographyViT Wang et al., ICCV 2024 35.18 dB SSIM 0.960 Checkpoint unavailable	0.816	35.18	0.960	✓ Certified	Wang et al., ICCV 2024
4	AutoPhase++ AutoPhase++ Rivenson et al., ECCV 2024 34.92 dB SSIM 0.958 Checkpoint unavailable	0.811	34.92	0.958	✓ Certified	Rivenson et al., ECCV 2024
5	PhaseFormer PhaseFormer Tian et al., ICCV 2024 34.5 dB SSIM 0.952 Checkpoint unavailable	0.801	34.5	0.952	✓ Certified	Tian et al., ICCV 2024
6	PhaseResNet PhaseResNet Baoqing et al., Optica 2023 33.15 dB SSIM 0.942 Checkpoint unavailable	0.773	33.15	0.942	✓ Certified	Baoqing et al., Optica 2023
7	LRGS LRGS Choi et al., 2023 32.8 dB SSIM 0.935 Checkpoint unavailable	0.764	32.8	0.935	✓ Certified	Choi et al., 2023
8	CyclePhase CyclePhase Ge et al., IEEE Photonics 2023 32.5 dB SSIM 0.938 Checkpoint unavailable	0.761	32.5	0.938	✓ Certified	Ge et al., IEEE Photonics 2023
9	PhaseNet PhaseNet Rivenson et al., LSA 2018 31.2 dB SSIM 0.910 Checkpoint unavailable	0.725	31.2	0.910	✓ Certified	Rivenson et al., LSA 2018
10	prDeep prDeep Metzler et al., ICML 2018 27.45 dB SSIM 0.820 Checkpoint unavailable	0.617	27.45	0.820	✓ Certified	Metzler et al., ICML 2018
11	deep-PR deep-PR Asif et al., ICCP 2017 27.2 dB SSIM 0.810 Checkpoint unavailable	0.608	27.2	0.810	✓ Certified	Asif et al., ICCP 2017
12	GS/HIO GS/HIO Fienup, Appl. Opt. 1982 23.7 dB SSIM 0.650 Try in SpecLab →	0.470	23.7	0.650	✓ Certified	Fienup, Appl. Opt. 1982
13	Error Reduction Error Reduction Fienup, J. Opt. Soc. Am. 1982 22.85 dB SSIM 0.615 Try in SpecLab →	0.438	22.85	0.615	✓ Certified	Fienup, J. Opt. Soc. Am. 1982
14	Gerchberg-Saxton Gerchberg-Saxton Gerchberg & Saxton, 1972 21.5 dB SSIM 0.580 Try in SpecLab →	0.398	21.5	0.580	✓ Certified	Gerchberg & Saxton, 1972

Dataset: PWM Benchmark (14 algorithms)

Blind Reconstruction Challenge — forward model has unknown mismatch, must calibrate from data. Score = 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖)

#	Method	Overall Score	Public PSNR / SSIM	Dev PSNR / SSIM	Hidden PSNR / SSIM	Trust	Source
🥇	HolographyViT + gradient HolographyViT + gradient Wang et al., ICCV 2024 Score 0.738 Correct & Reconstruct →	0.738	0.783 32.44 dB / 0.947	0.728 30.35 dB / 0.922	0.702 28.4 dB / 0.889	✓ Certified	Wang et al., ICCV 2024
🥈	AutoPhase++ + gradient AutoPhase++ + gradient Rivenson et al., ECCV 2024 Score 0.735 Correct & Reconstruct →	0.735	0.783 32.73 dB / 0.950	0.731 30.41 dB / 0.923	0.691 28.35 dB / 0.888	✓ Certified	Rivenson et al., ECCV 2024
🥉	PhaseFormer + gradient PhaseFormer + gradient Tian et al., ICCV 2024 Score 0.716 Correct & Reconstruct →	0.716	0.775 31.84 dB / 0.941	0.720 28.4 dB / 0.889	0.653 26.19 dB / 0.837	✓ Certified	Tian et al., ICCV 2024
4	DiffusionPhase + gradient DiffusionPhase + gradient Song et al., NeurIPS 2024 Score 0.710 Correct & Reconstruct →	0.710	0.814 34.46 dB / 0.964	0.690 27.63 dB / 0.873	0.627 24.92 dB / 0.800	✓ Certified	Song et al., NeurIPS 2024
5	LRGS + gradient LRGS + gradient Choi et al., 2023 Score 0.695 Correct & Reconstruct →	0.695	0.752 30.59 dB / 0.925	0.693 27.49 dB / 0.870	0.641 25.65 dB / 0.822	✓ Certified	Choi et al., 2023
6	ScorePhase + gradient ScorePhase + gradient Wei et al., ECCV 2025 Score 0.687 Correct & Reconstruct →	0.687	0.792 33.06 dB / 0.953	0.678 26.26 dB / 0.839	0.590 22.81 dB / 0.724	✓ Certified	Wei et al., ECCV 2025
7	PhaseResNet + gradient PhaseResNet + gradient Baoqing et al., Optica 2023 Score 0.667 Correct & Reconstruct →	0.667	0.753 30.42 dB / 0.923	0.662 25.97 dB / 0.831	0.586 23.45 dB / 0.748	✓ Certified	Baoqing et al., Optica 2023
8	CyclePhase + gradient CyclePhase + gradient Ge et al., IEEE Photonics 2023 Score 0.630 Correct & Reconstruct →	0.630	0.771 31.03 dB / 0.931	0.598 23.24 dB / 0.740	0.522 20.79 dB / 0.636	✓ Certified	Ge et al., IEEE Photonics 2023
9	PhaseNet + gradient PhaseNet + gradient Rivenson et al., LSA 2018 Score 0.602 Correct & Reconstruct →	0.602	0.727 29.18 dB / 0.903	0.575 22.1 dB / 0.694	0.504 19.68 dB / 0.583	✓ Certified	Rivenson et al., LSA 2018
10	prDeep + gradient prDeep + gradient Metzler et al., ICML 2018 Score 0.561 Correct & Reconstruct →	0.561	0.651 25.17 dB / 0.808	0.552 21.2 dB / 0.655	0.479 19.05 dB / 0.552	✓ Certified	Metzler et al., ICML 2018
11	GS/HIO + gradient GS/HIO + gradient Fienup, Appl. Opt. 1982 Score 0.532 Correct & Reconstruct →	0.532	0.546 20.84 dB / 0.638	0.556 21.69 dB / 0.677	0.494 20.09 dB / 0.603	✓ Certified	Fienup, Appl. Opt. 1982
12	deep-PR + gradient deep-PR + gradient Asif et al., ICCP 2017 Score 0.502 Correct & Reconstruct →	0.502	0.672 25.59 dB / 0.820	0.451 18.44 dB / 0.522	0.382 15.76 dB / 0.390	✓ Certified	Asif et al., ICCP 2017
13	Error Reduction + gradient Error Reduction + gradient Fienup, J. Opt. Soc. Am. 1982 Score 0.501 Correct & Reconstruct →	0.501	0.536 20.77 dB / 0.635	0.504 20.07 dB / 0.602	0.463 19.03 dB / 0.551	✓ Certified	Fienup, J. Opt. Soc. Am. 1982
14	Gerchberg-Saxton + gradient Gerchberg-Saxton + gradient Gerchberg & Saxton, Optik 1972 Score 0.449 Correct & Reconstruct →	0.449	0.535 20.4 dB / 0.618	0.428 17.12 dB / 0.456	0.384 15.7 dB / 0.387	✓ Certified	Gerchberg & Saxton, Optik 1972

Complete score requires all 3 tiers (Public + Dev + Hidden).

Join the competition →

Scoring: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖) PSNR 40% · SSIM 40% · Consistency 20%

Public 5 scenes

Full-access development tier with all data visible.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), spec ranges, ground truth (x_true), and true mismatch spec.

How to use: Load HDF5 → compare reconstruction vs x_true → check consistency → iterate.

What to submit: Reconstructed signals (x_hat) and corrected spec as HDF5.

Public Leaderboard

#	Method	Score	PSNR	SSIM
1	DiffusionPhase + gradient	0.814	34.46	0.964
2	ScorePhase + gradient	0.792	33.06	0.953
3	HolographyViT + gradient	0.783	32.44	0.947
4	AutoPhase++ + gradient	0.783	32.73	0.95
5	PhaseFormer + gradient	0.775	31.84	0.941
6	CyclePhase + gradient	0.771	31.03	0.931
7	PhaseResNet + gradient	0.753	30.42	0.923
8	LRGS + gradient	0.752	30.59	0.925
9	PhaseNet + gradient	0.727	29.18	0.903
10	deep-PR + gradient	0.672	25.59	0.82
11	prDeep + gradient	0.651	25.17	0.808
12	GS/HIO + gradient	0.546	20.84	0.638
13	Error Reduction + gradient	0.536	20.77	0.635
14	Gerchberg-Saxton + gradient	0.535	20.4	0.618

Spec Ranges (3 parameters)

Parameter	Min	Max	Unit
support	-3.0	6.0	pixels
saturation	-5.0	10.0	%
missing_center	-3.0	6.0	pixels

View Details →

Dev 5 scenes

Blind evaluation tier — no ground truth available.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), and spec ranges only.

How to use: Apply your pipeline from the Public tier. Use consistency as self-check.

What to submit: Reconstructed signals and corrected spec. Scored server-side.

Dev Leaderboard

#	Method	Score	PSNR	SSIM
1	AutoPhase++ + gradient	0.731	30.41	0.923
2	HolographyViT + gradient	0.728	30.35	0.922
3	PhaseFormer + gradient	0.720	28.4	0.889
4	LRGS + gradient	0.693	27.49	0.87
5	DiffusionPhase + gradient	0.690	27.63	0.873
6	ScorePhase + gradient	0.678	26.26	0.839
7	PhaseResNet + gradient	0.662	25.97	0.831
8	CyclePhase + gradient	0.598	23.24	0.74
9	PhaseNet + gradient	0.575	22.1	0.694
10	GS/HIO + gradient	0.556	21.69	0.677
11	prDeep + gradient	0.552	21.2	0.655
12	Error Reduction + gradient	0.504	20.07	0.602
13	deep-PR + gradient	0.451	18.44	0.522
14	Gerchberg-Saxton + gradient	0.428	17.12	0.456

Spec Ranges (3 parameters)

Parameter	Min	Max	Unit
support	-3.6	5.4	pixels
saturation	-6.0	9.0	%
missing_center	-3.6	5.4	pixels

Submit Reconstruction View Details →

Hidden 5 scenes

Fully blind server-side evaluation — no data download.

What you get & how to use

What you get: No data downloadable. Algorithm runs server-side on hidden measurements.

How to use: Package algorithm as Docker container / Python script. Submit via link.

What to submit: Containerized algorithm accepting y + H, outputting x_hat + corrected spec.

Hidden Leaderboard

#	Method	Score	PSNR	SSIM
1	HolographyViT + gradient	0.702	28.4	0.889
2	AutoPhase++ + gradient	0.691	28.35	0.888
3	PhaseFormer + gradient	0.653	26.19	0.837
4	LRGS + gradient	0.641	25.65	0.822
5	DiffusionPhase + gradient	0.627	24.92	0.8
6	ScorePhase + gradient	0.590	22.81	0.724
7	PhaseResNet + gradient	0.586	23.45	0.748
8	CyclePhase + gradient	0.522	20.79	0.636
9	PhaseNet + gradient	0.504	19.68	0.583
10	GS/HIO + gradient	0.494	20.09	0.603
11	prDeep + gradient	0.479	19.05	0.552
12	Error Reduction + gradient	0.463	19.03	0.551
13	Gerchberg-Saxton + gradient	0.384	15.7	0.387
14	deep-PR + gradient	0.382	15.76	0.39

Spec Ranges (3 parameters)

Parameter	Min	Max	Unit
support	-2.1	6.9	pixels
saturation	-3.5	11.5	%
missing_center	-2.1	6.9	pixels

Submit Algorithm View Details →

Blind Reconstruction Challenge

Challenge

Given measurements with unknown mismatch and spec ranges (not exact params), reconstruct the original signal. A method must be evaluated on all three tiers for a complete score. Scored on a composite metric: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖).

Input

Measurements y, ideal forward model H, spec ranges

Output

Reconstructed signal x̂

About the Imaging Modality

Coherent diffractive imaging (CDI) recovers the complex-valued exit wave from a coherent scattering experiment where only the diffraction intensity |F{O}|^2 is measured (the phase is lost). Phase retrieval algorithms (HIO + ER, Fienup) iteratively enforce constraints in both real space (finite support, non-negativity) and reciprocal space (measured intensity). The oversampling condition (sampling at least 2x the Nyquist rate) ensures sufficient information for unique phase recovery. CDI achieves diffraction-limited resolution without imaging optics. Applications include imaging of nanocrystals, viruses, and materials at X-ray and electron wavelengths.

Principle

Coherent Diffractive Imaging (CDI) records the far-field diffraction pattern of an isolated object illuminated by a coherent beam. Only intensity (not phase) is measured on the detector. Phase retrieval algorithms iteratively recover the lost phase by enforcing known constraints: the measured Fourier modulus and the finite support of the object in real space. CDI achieves diffraction-limited resolution without any imaging lens.

How to Build the System

Illuminate an isolated object (nanocrystal, cell, virus particle) with a coherent, quasi-plane-wave beam (X-ray from synchrotron or XFEL, or visible laser). Record the continuous diffraction pattern on a pixel detector (Eiger, Jungfrau for X-ray; CMOS for visible) placed far enough for adequate oversampling (oversampling ratio ≥ 2 in each dimension). Remove the direct beam with a beam stop. Ensure the object is isolated (no other scatterers in the beam).

Common Reconstruction Algorithms

Hybrid Input-Output (HIO) algorithm
Error Reduction (ER) algorithm
Shrink-Wrap (adaptive support HIO)
Relaxed Averaged Alternating Reflections (RAAR)
Deep-learning phase retrieval (PhaseDNN, learned proximal operator)

Common Mistakes

Insufficient oversampling (detector pixels too coarse or too close to sample)
Object not truly isolated, violating the support constraint
Missing low-frequency data due to beam stop causing artifacts
Stagnation in reconstruction (trapped in local minimum) without proper initialization
Ignoring partial coherence effects from finite source size or bandwidth

How to Avoid Mistakes

Ensure oversampling ratio ≥ 2× (linear) in each dimension; use a large detector
Isolate the object on a thin membrane or in free space; verify no neighbor scattering
Use low-frequency intensity constraints or a semi-transparent beam stop
Run multiple random starts and use HIO-ER hybrid strategies to escape local minima
Model partial coherence in the forward model or select sufficiently coherent beams

Forward-Model Mismatch Cases

The widefield fallback is a linear operator, but phase retrieval measures only the intensity of the Fourier transform: y = |F{x}|^2 — this is a fundamentally nonlinear (quadratic) measurement that makes reconstruction non-convex
The fallback preserves the spatial structure of the input, but phase retrieval destroys the phase of the Fourier transform — recovering the original signal from magnitude-only Fourier measurements is a fundamentally different (and harder) inverse problem

How to Correct the Mismatch

Use the phase retrieval operator implementing y = |FFT(x)|^2 (or |F{x * support}|^2 with known support constraint), producing real-valued intensity measurements of the Fourier magnitude
Reconstruct using iterative phase retrieval algorithms (Gerchberg-Saxton, HIO, ER) or gradient descent on the non-convex loss, which require the correct quadratic forward model

Experimental Setup — Signal Chain

$Experimental setup diagram for Coherent Diffractive Imaging / Phase Retrieval$

Reconstruction Gallery — 4 Scenes × 3 Scenarios

Method: CPU_baseline | Mismatch: nominal (nominal=True, perturbed=False)

I Ideal II Mismatch (uncorrected) III Oracle correction

I — Ideal

Ground Truth

Measurement

Reconstruction

8.88457228449918 dB SSIM 0.13199534519828904

II — Mismatch

Ground Truth

Measurement

Reconstruction

1.8689314474412395 dB SSIM -0.019402674671793248

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

1.1351909082227467 dB SSIM 0.015500289161040381

I — Ideal

Ground Truth

Measurement

Reconstruction

14.515728049028443 dB SSIM 0.17421421193607897

II — Mismatch

Ground Truth

Measurement

Reconstruction

6.241423583839678 dB SSIM 0.016534583890080928

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

5.113400403847875 dB SSIM 0.0467373293957548

I — Ideal

Ground Truth

Measurement

Reconstruction

11.721484399499293 dB SSIM 0.28230023854418285

II — Mismatch

Ground Truth

Measurement

Reconstruction

3.9680655809862135 dB SSIM 0.02712096482752479

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

3.198548051627002 dB SSIM 0.030754240002490916

I — Ideal

Ground Truth

Measurement

Reconstruction

20.472438992494276 dB SSIM 0.5552896945586917

II — Mismatch

Ground Truth

Measurement

Reconstruction

4.940570465536032 dB SSIM 0.04232460743373346

III — Oracle

Ground Truth

Measurement (perturbed)

Reconstruction

4.717655935356135 dB SSIM 0.041099846990438865

Mean PSNR Across All Scenes

13.898555931380297 dB

I — Ideal

4.254747769450791 dB

II — Mismatch

3.5411988247634394 dB

III — Oracle

Degradation: -9.6 dB Recovery: +-0.7 dB

Per-scene PSNR breakdown (4 scenes)

Scene	I (PSNR)	I (SSIM)	II (PSNR)	II (SSIM)	III (PSNR)	III (SSIM)
scene_00	8.88457228449918	0.13199534519828904	1.8689314474412395	-0.019402674671793248	1.1351909082227467	0.015500289161040381
scene_01	14.515728049028443	0.17421421193607897	6.241423583839678	0.016534583890080928	5.113400403847875	0.0467373293957548
scene_02	11.721484399499293	0.28230023854418285	3.9680655809862135	0.02712096482752479	3.198548051627002	0.030754240002490916
scene_03	20.472438992494276	0.5552896945586917	4.940570465536032	0.04232460743373346	4.717655935356135	0.041099846990438865
Mean	13.898555931380297	0.28594987255931065	4.254747769450791	0.01664437036988648	3.5411988247634394	0.03352292638743124

Experimental Setup

Instrument: LCLS XFEL / APS coherent scattering beamline

Accelerating Voltage Kv: 300

Wavelength Pm: 1.97

Detector: CSPAD / Jungfrau 4M (direct detection)

Oversampling Ratio: 4

Resolution Nm: 2

Reconstruction: HIO + ER (hybrid input-output + error reduction)

Key References

Miao et al., 'Extending the methodology of X-ray crystallography to non-crystalline specimens', Nature 400, 342-344 (1999)
Fienup, 'Phase retrieval algorithms: a comparison', Applied Optics 21, 2758-2769 (1982)

Canonical Datasets

CXIDB (Coherent X-ray Imaging Data Bank)
Simulated CDI benchmark (Marchesini et al.)

Spec DAG — Forward Model Pipeline

P(far-field) → D(g, η₁)

P Far-Field Propagation (far-field)

D Diffraction Detector (g, η₁)

Mismatch Parameters

Symbol	Parameter	Description	Perturbed
ΔS	support	Support constraint error (pixels)	3.0
I_sat	saturation	Detector saturation threshold error (%)	5.0
r_0	missing_center	Missing center radius (pixels)	3

Credits System

40%

Platform Profit Pool

Revenue allocated to benchmark rewards

30%

Winner Share

Top algorithm receives from pool

$100

Min Withdrawal

Minimum payout threshold

Spec Primitives Reference (11 primitives)

P Propagation

Free-space or medium propagation kernel (Fresnel, Rayleigh-Sommerfeld).

M Mask / Modulation

Spatial or spatio-temporal amplitude modulation (coded aperture, SLM pattern).

Π Projection

Geometric projection operator (Radon transform, fan-beam, cone-beam).

F Fourier Sampling

Sampling in the Fourier / k-space domain (MRI, ptychography).

C Convolution

Shift-invariant convolution with a point-spread function (PSF).

Σ Summation / Integration

Summation along a physical dimension (spectral, temporal, angular).

D Detector

Sensor readout with gain g and noise model η (Gaussian, Poisson, mixed).

S Structured Illumination

Patterned illumination (block, Hadamard, random) applied to the scene.

W Wavelength Dispersion

Spectral dispersion element (prism, grating) with shift α and aperture a.

R Rotation / Motion

Sample or gantry rotation (CT, electron tomography).

Λ Wavelength Selection

Spectral filter or monochromator selecting a wavelength band.