Laser-Induced Breakdown Spectroscopy (LIBS) 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
🥇	DiffusionSpectra DiffusionSpectra Zhang et al., 2024 33.86 dB SSIM 0.960 Checkpoint unavailable	0.794	33.86	0.960	✓ Certified	Zhang et al., 2024
🥈	SpectraFormer SpectraFormer Spectroscopy transformer, 2024 33.3 dB SSIM 0.955 Checkpoint unavailable	0.782	33.3	0.955	✓ Certified	Spectroscopy transformer, 2024
🥉	Cascade-UNet Cascade-UNet Physics-informed UNet, 2025 33.0 dB SSIM 0.922 Checkpoint unavailable	0.761	33.0	0.922	✓ Certified	Physics-informed UNet, 2025
4	PINN-Spectra PINN-Spectra Physics-informed neural network 31.72 dB SSIM 0.940 Checkpoint unavailable	0.749	31.72	0.940	✓ Certified	Physics-informed neural network
5	ScoreSpectra ScoreSpectra Wei et al., 2025 31.36 dB SSIM 0.935 Checkpoint unavailable	0.740	31.36	0.935	✓ Certified	Wei et al., 2025
6	CDAE CDAE Zhang et al., Sensors 2024 31.5 dB SSIM 0.895 Checkpoint unavailable	0.723	31.5	0.895	✓ Certified	Zhang et al., Sensors 2024
7	U-Net-Spectra U-Net-Spectra Spectral U-Net variant 29.1 dB SSIM 0.902 Checkpoint unavailable	0.686	29.1	0.902	✓ Certified	Spectral U-Net variant
8	SVD SVD Singular Value Decomposition 26.56 dB SSIM 0.847 Try in SpecLab →	0.616	26.56	0.847	✓ Certified	Singular Value Decomposition
9	PnP-DnCNN PnP-DnCNN Zhang et al., 2017 27.9 dB SSIM 0.800 Try in SpecLab →	0.615	27.9	0.800	✓ Certified	Zhang et al., 2017
10	Baseline Correction Baseline Correction Polynomial fitting baseline 24.33 dB SSIM 0.780 Try in SpecLab →	0.545	24.33	0.780	✓ Certified	Polynomial fitting baseline
11	SG-ALS SG-ALS Savitzky-Golay + ALS baseline 24.3 dB SSIM 0.670 Try in SpecLab →	0.490	24.3	0.670	✓ Certified	Savitzky-Golay + ALS baseline

Dataset: PWM Benchmark (11 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
🥇	SpectraFormer + gradient SpectraFormer + gradient Spectroscopy transformer, 2024 Score 0.717 Correct & Reconstruct →	0.717	0.762 31.49 dB / 0.937	0.723 28.74 dB / 0.895	0.665 26.8 dB / 0.853	✓ Certified	Spectroscopy transformer, 2024
🥈	DiffusionSpectra + gradient DiffusionSpectra + gradient Zhang et al., 2024 Score 0.673 Correct & Reconstruct →	0.673	0.766 31.35 dB / 0.935	0.658 26.06 dB / 0.834	0.594 23.87 dB / 0.764	✓ Certified	Zhang et al., 2024
🥉	Cascade-UNet + gradient Cascade-UNet + gradient Physics-informed UNet, 2025 Score 0.667 Correct & Reconstruct →	0.667	0.779 31.84 dB / 0.941	0.635 24.48 dB / 0.785	0.586 22.74 dB / 0.721	✓ Certified	Physics-informed UNet, 2025
4	ScoreSpectra + gradient ScoreSpectra + gradient Wei et al., 2025 Score 0.632 Correct & Reconstruct →	0.632	0.726 28.85 dB / 0.898	0.630 24.67 dB / 0.792	0.541 21.82 dB / 0.682	✓ Certified	Wei et al., 2025
5	SVD + gradient SVD + gradient Singular Value Decomposition Score 0.604 Correct & Reconstruct →	0.604	0.630 24.2 dB / 0.776	0.602 23.6 dB / 0.754	0.581 22.79 dB / 0.723	✓ Certified	Singular Value Decomposition
6	CDAE + gradient CDAE + gradient Zhang et al., Sensors 2024 Score 0.599 Correct & Reconstruct →	0.599	0.757 30.27 dB / 0.921	0.551 21.26 dB / 0.657	0.489 19.11 dB / 0.555	✓ Certified	Zhang et al., Sensors 2024
7	PnP-DnCNN + gradient PnP-DnCNN + gradient Zhang et al., 2017 Score 0.588 Correct & Reconstruct →	0.588	0.693 26.81 dB / 0.853	0.575 22.58 dB / 0.714	0.496 19.32 dB / 0.566	✓ Certified	Zhang et al., 2017
8	PINN-Spectra + gradient PINN-Spectra + gradient Physics-informed neural network Score 0.588 Correct & Reconstruct →	0.588	0.758 30.35 dB / 0.922	0.546 20.99 dB / 0.645	0.460 18.8 dB / 0.540	✓ Certified	Physics-informed neural network
9	SG-ALS + gradient SG-ALS + gradient Savitzky-Golay + ALS baseline Score 0.569 Correct & Reconstruct →	0.569	0.573 22.02 dB / 0.691	0.593 23.02 dB / 0.732	0.542 21.08 dB / 0.649	✓ Certified	Savitzky-Golay + ALS baseline
10	Baseline Correction + gradient Baseline Correction + gradient Polynomial fitting baseline Score 0.560 Correct & Reconstruct →	0.560	0.570 21.76 dB / 0.680	0.572 22.53 dB / 0.712	0.539 21.03 dB / 0.647	✓ Certified	Polynomial fitting baseline
11	U-Net-Spectra + gradient U-Net-Spectra + gradient Spectral U-Net variant Score 0.550 Correct & Reconstruct →	0.550	0.713 27.58 dB / 0.872	0.492 19.26 dB / 0.563	0.444 18.13 dB / 0.506	✓ Certified	Spectral U-Net variant

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

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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	Cascade-UNet + gradient	0.779	31.84	0.941
2	DiffusionSpectra + gradient	0.766	31.35	0.935
3	SpectraFormer + gradient	0.762	31.49	0.937
4	PINN-Spectra + gradient	0.758	30.35	0.922
5	CDAE + gradient	0.757	30.27	0.921
6	ScoreSpectra + gradient	0.726	28.85	0.898
7	U-Net-Spectra + gradient	0.713	27.58	0.872
8	PnP-DnCNN + gradient	0.693	26.81	0.853
9	SVD + gradient	0.630	24.2	0.776
10	SG-ALS + gradient	0.573	22.02	0.691
11	Baseline Correction + gradient	0.570	21.76	0.68

Spec Ranges (4 parameters)

Parameter	Min	Max	Unit
laser_energy_fluctuation	-2.0	4.0	-
matrix_effect	-6.0	12.0	-
self_absorption_correction	-4.0	8.0	-
crater_to_crater_variation	-3.0	6.0	-

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	SpectraFormer + gradient	0.723	28.74	0.895
2	DiffusionSpectra + gradient	0.658	26.06	0.834
3	Cascade-UNet + gradient	0.635	24.48	0.785
4	ScoreSpectra + gradient	0.630	24.67	0.792
5	SVD + gradient	0.602	23.6	0.754
6	SG-ALS + gradient	0.593	23.02	0.732
7	PnP-DnCNN + gradient	0.575	22.58	0.714
8	Baseline Correction + gradient	0.572	22.53	0.712
9	CDAE + gradient	0.551	21.26	0.657
10	PINN-Spectra + gradient	0.546	20.99	0.645
11	U-Net-Spectra + gradient	0.492	19.26	0.563

Spec Ranges (4 parameters)

Parameter	Min	Max	Unit
laser_energy_fluctuation	-2.4	3.6	-
matrix_effect	-7.2	10.8	-
self_absorption_correction	-4.8	7.2	-
crater_to_crater_variation	-3.6	5.4	-

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	SpectraFormer + gradient	0.665	26.8	0.853
2	DiffusionSpectra + gradient	0.594	23.87	0.764
3	Cascade-UNet + gradient	0.586	22.74	0.721
4	SVD + gradient	0.581	22.79	0.723
5	SG-ALS + gradient	0.542	21.08	0.649
6	ScoreSpectra + gradient	0.541	21.82	0.682
7	Baseline Correction + gradient	0.539	21.03	0.647
8	PnP-DnCNN + gradient	0.496	19.32	0.566
9	CDAE + gradient	0.489	19.11	0.555
10	PINN-Spectra + gradient	0.460	18.8	0.54
11	U-Net-Spectra + gradient	0.444	18.13	0.506

Spec Ranges (4 parameters)

Parameter	Min	Max	Unit
laser_energy_fluctuation	-1.4	4.6	-
matrix_effect	-4.2	13.8	-
self_absorption_correction	-2.8	9.2	-
crater_to_crater_variation	-2.1	6.9	-

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

Spec DAG — Forward Model Pipeline

M → R → D

M Modulation

R Rotation

D Detector

Mismatch Parameters

Symbol	Parameter	Description	Perturbed
l_e	laser_energy_fluctuation	Laser energy fluctuation (-)	2.0
m_e	matrix_effect	Matrix effect (-)	6.0
s_c	self_absorption_correction	Self-absorption correction (-)	4.0
c_v	crater_to_crater_variation	Crater-to-crater variation (-)	3.0

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.