Benchmarking learned algorithms for computed tomography image reconstruction tasks

Maximilian B. Kiss; Ander Biguri; Zakhar Shumaylov; Ferdia Sherry; K. Joost Batenburg; Carola-Bibiane Schönlieb; Felix Lucka

doi:10.3934/ammc.2025001

Article Contents

March 2025, Volume 3, 1-43. Doi: 10.3934/ammc.2025001

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Benchmarking learned algorithms for computed tomography image reconstruction tasks

1.
Computational Imaging, Centrum Wiskunde & Informatica, The Netherlands
2.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, United Kingdom
3.
Leiden Institute for Advanced Computer Science, Leiden University, The Netherlands

^*Corresponding author: Maximilian B. Kiss
^*Corresponding author: Maximilian B. Kiss

^# These authors contributed equally to this work.

Received: September 2024

Revised: January 2025

Early access: February 2025

Published: March 2025

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Abstract

Computed tomography (CT) is a widely used non-invasive diagnostic method in various fields, and recent advances in deep learning have led to significant progress in CT image reconstruction. However, the lack of large-scale, open-access datasets has hindered the comparison of different types of learned methods. To address this gap, we use the 2DeteCT dataset, a real-world experimental computed tomography dataset, for benchmarking machine learning based CT image reconstruction algorithms. We categorize these methods into post-processing methods, learned/unrolled iterative methods, learned regularizer methods, and plug-and-play methods, and provide a pipeline for easy implementation and evaluation. Using key performance metrics, including SSIM and PSNR, our benchmarking results showcase the effectiveness of various algorithms on tasks such as full data reconstruction, limited-angle reconstruction, sparse-angle reconstruction, low-dose reconstruction, and beam-hardening corrected reconstruction. With this benchmarking study, we provide an evaluation of a range of algorithms representative for different categories of learned reconstruction methods on a recently published dataset of real-world experimental CT measurements. The reproducible setup of methods and CT image reconstruction tasks in an open-source toolbox enables straightforward addition and comparison of new methods later on. The toolbox also provides the option to load the 2DeteCT dataset differently for extensions to other problems and different CT reconstruction tasks.

Keywords:

Mathematics Subject Classification: Primary: 68T05, 68T07; Secondary: 65R32.

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Figure 1. CT Image Reconstruction Tasks

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Figure 2. Qualitative analysis of all evaluated methods for slice 182 of the test dataset in comparison to the "gold standard" iterative reference reconstruction of the 2DeteCT dataset (green box)

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Table 1. A summary of publicly available CT datasets, supported tasks, their size, and their raw data availability. ($ \checkmark$) = possible through data generation

Dataset	CT Image Reconstruction Tasks				Size (>100 samples)	Raw Data
Dataset	Low-Dose	Limited-Angle	Sparse-Angle	Beam-hardening reduction	Size (>100 samples)	Raw Data
Mayo [56,57]	$ \checkmark$	($ \checkmark$)	($ \checkmark$)	✗	✗ [56] / $ \checkmark$ [57]	✗
LoDoPaB [51]	$ \checkmark$	($ \checkmark$)	($ \checkmark$)	✗	$ \checkmark$	✗
ICASSP GC8 [13]	$ \checkmark$	($ \checkmark$)	($ \checkmark$)	✗	$ \checkmark$	✗
Walnut CBCT [72]	✗	$ \checkmark$	$ \checkmark$	✗	✗	$ \checkmark$
2DeteCT [45]	$ \checkmark$	$ \checkmark$	$ \checkmark$	$ \checkmark$	$ \checkmark$	$ \checkmark$

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Table 2. Method Categorizations

Article	Categorization
Zhang et al., 2020 [94]	Amount of expert knowledge involved: handcrafted, hybrid approaches, mostly learned
Ye et al., 2023 [93]	Point of learned processing: pre-processing, post-processing, and raw-to-image
Ravishankar et al., 2019 [68]	Domain of application: image-domain, hybrid-domain, AUTOMAP [98], sensor-domain
Arridge et al., 2019 [5]	Methodological: Post-processing Methods, Learned / Unrolled Iterative Methods, Learned Regularizer Methods, Plug-and-Play Methods

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Table 3. Summary of the acquisition parameters of the 2DeteCT dataset, adapted from [45]. The Thoreaus filter is a compound filter made of Sn 0.1mm, Cu 0.2mm, Al 0.5mm. The SOD and SDD values are based on the motor readings of the FleX-ray scanner which get translated into physical quantities and are subject to alignment errors

Acquisition parameter	Mode 1	Mode 2	Mode 3
Tube voltage	$ {90.0}\ {\rm{ kV}} $	$ {90.0}\ {\rm{ kV}} $	$ {60.0}\ {\rm{ kV}} $
Tube power	$ {3.0}\ {\rm{ W}} $	$ {90.0}\ {\rm{ W}} $	$ {60.0}\ {\rm{ W}} $
Filters used	Thoraeus	Thoraeus	No Filter
Exposure time	$ {50.0}\ {\rm{ms}} $
Binned detector pixel size	$ {149.6} $ µm
Number of binned detector pixels	956
Source to object distance (SOD)	$ {431.020}\ {\rm{mm}} $
Source to detector distance (SDD)	$ {529.000}\ {\rm{mm}} $
Number of projections	3601
Angular increment	$ {0.1}{\deg} $

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Table 4. Evaluated methods

Category	Method (Year and Reference)
Classical Methods	FBP [33], AGD [62], PDHG [16]
Post-Processing Methods	U-Net [71], MSD-Net [67], DnCNN [96]
Learned / Unrolled Iterative Methods	Learned Gradient [2], TV-regularized Learned Gradient,
	Learned Primal Dual [3]
Learned Regularizer Methods	AR [55], TDV [47], ACR [59,60]
Plug-and-Play Methods	DnCNN-PnP [96], DRUNet-PnP [95], GS-PnP [37]

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Table 5. Quantitative analysis of all evaluated methods with respect to PSNR and SSIM on their performance in the CT image reconstruction tasks: Full Data "mode 2", Low-Dose "mode 1", and Beam-Hardening "mode 3"

Method	Metric	CT Image Reconstruction Task
Method	Metric	Full Data	Low-Dose	Beam-Hardening
Classical Methods
FBP	SSIM	0.7463 $ \pm $ 0.0296	0.0838 $ \pm $ 0.0212	0.3367 $ \pm $ 0.0464
FBP	PSNR	35.0285 $ \pm $ 2.0907	18.6437 $ \pm $ 2.0508	14.5594 $ \pm $ 1.9056
AGD	SSIM	0.7753 $ \pm $ 0.0380	0.0727 $ \pm $ 0.0182	0.3483 $ \pm $ 0.0650
AGD	PSNR	35.1006 $ \pm $ 2.2801	17.7062 $ \pm $ 2.0517	14.4294 $ \pm $ 1.9255
PDHG	SSIM	0.7689 $ \pm $ 0.0498	0.6820 $ \pm $ 0.0749	0.4492 $ \pm $ 0.0616
PDHG	PSNR	34.3251 $ \pm $ 1.9703	31.9637 $ \pm $ 1.9824	15.0090 $ \pm $ 1.9094
Post-Processing Methods
FBP+U-Net	SSIM	0.6499 $ \pm $ 0.0681	0.7632 $ \pm $ 0.0780	0.6336 $ \pm $ 0.0760
FBP+U-Net	PSNR	32.6998 $ \pm $ 1.9512	27.6772 $ \pm $ 3.0133	28.0629 $ \pm $ 3.8439
FBP+MSDNet	SSIM	0.8481 $ \pm $ 0.0384	0.7253 $ \pm $ 0.0864	0.7991 $ \pm $ 0.0665
FBP+MSDNet	PSNR	33.2999 $ \pm $ 1.9492	31.6910 $ \pm $ 1.9559	31.4389 $ \pm $ 2.0988
FBP+DnCNN	SSIM	0.8324 $ \pm $ 0.0403	0.7127 $ \pm $ 0.0806	0.6328 $ \pm $ 0.0751
FBP+DnCNN	PSNR	32.2575 $ \pm $ 1.9506	29.7645 $ \pm $ 1.9748	28.2405 $ \pm $ 2.0374
Learned / Unrolled Iterative Methods
LG	SSIM	0.7498 $ \pm $ 0.0708	0.6685 $ \pm $ 0.0772	0.6025 $ \pm $ 0.0747
LG	PSNR	32.4409 $ \pm $ 1.9527	30.4679 $ \pm $ 1.9945	28.4148 $ \pm $ 1.9584
LGTV	SSIM	0.8221 $ \pm $ 0.0532	0.7008 $ \pm $ 0.0797	0.6656 $ \pm $ 0.0774
LGTV	PSNR	33.3312 $ \pm $ 1.9493	30.9991 $ \pm $ 1.9328	29.5372 $ \pm $ 2.0008
LPD	SSIM	0.8447 $ \pm $ 0.0370	0.8282 $ \pm $ 0.0519	0.8352 $ \pm $ 0.0568
LPD	PSNR	33.3086 $ \pm $ 1.9466	32.6685 $ \pm $ 1.9656	33.1382 $ \pm $ 1.9759
Learned Regularizer Methods
AR	SSIM	0.8196 $ \pm $ 0.0385	0.8039 $ \pm $ 0.0505	0.3125 $ \pm $ 0.0479
AR	PSNR	32.3583 $ \pm $ 1.9621	31.0472 $ \pm $ 1.9763	19.5692 $ \pm $ 1.9612
TDV	SSIM	0.7282 $ \pm $ 0.0652	0.6047 $ \pm $ 0.0815	0.5494 $ \pm $ 0.0635
TDV	PSNR	33.1204 $ \pm $ 1.9496	28.2429 $ \pm $ 1.9433	25.7832 $ \pm $ 2.0109
ACR	SSIM	0.8518 $ \pm $ 0.0362	0.8163 $ \pm $ 0.0522	0.6742 $ \pm $ 0.0505
ACR	PSNR	33.7131 $ \pm $ 1.9450	32.2621 $ \pm $ 1.9689	18.5708 $ \pm $ 1.7824
Plug-and-Play Methods
DnCNN-PnP	SSIM	0.8585 $ \pm $ 0.0402	0.7795 $ \pm $ 0.0523	0.5989 $ \pm $ 0.0375
DnCNN-PnP	PSNR	32.8506 $ \pm $ 1.9306	31.3986 $ \pm $ 1.9424	15.4667 $ \pm $ 1.9107
DRUNet-PnP	SSIM	0.8573 $ \pm $ 0.0405	0.7984 $ \pm $ 0.0517	0.5945 $ \pm $ 0.0375
DRUNet-PnP	PSNR	32.8935 $ \pm $ 1.9327	31.5762 $ \pm $ 1.9480	15.4543 $ \pm $ 1.9102
GS-PnP	SSIM	0.7856 $ \pm $ 0.0590	0.7727 $ \pm $ 0.0683	0.5131 $ \pm $ 0.0562
GS-PnP	PSNR	32.5734 $ \pm $ 1.9331	31.7931 $ \pm $ 1.9444	15.3466 $ \pm $ 1.9128

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Table 6. Quantitative analysis of all evaluated methods with respect to PSNR and SSIM on their performance in the CT image reconstruction tasks of Limited-Angle

Method	Metric	CT Image Reconstruction Task
Method	Metric	Limited-Angle 120	Limited-Angle 90	Limited-Angle 60
Classical Methods
FBP	SSIM	0.3418 $ \pm $ 0.0354	0.2369 $ \pm $ 0.0323	0.1557 $ \pm $ 0.0288
FBP	PSNR	22.4188 $ \pm $ 1.9240	19.4251 $ \pm $ 1.9405	16.9057 $ \pm $ 1.9579
AGD	SSIM	0.4904 $ \pm $ 0.0550	0.4411 $ \pm $ 0.0555	0.4146 $ \pm $ 0.0559
AGD	PSNR	25.7508 $ \pm $ 1.9690	24.1128 $ \pm $ 1.9528	22.8848 $ \pm $ 1.9531
PDHG	SSIM	0.5923 $ \pm $ 0.0550	0.5194 $ \pm $ 0.0547	0.4658 $ \pm $ 0.0510
PDHG	PSNR	26.3646 $ \pm $ 1.9443	24.4392 $ \pm $ 1.9321	22.7556 $ \pm $ 1.9428
Post-Processing Methods
FBP+U-Net	SSIM	0.7251 $ \pm $ 0.0519	0.6338 $ \pm $ 0.0659	0.5892 $ \pm $ 0.0678
FBP+U-Net	PSNR	28.7931 $ \pm $ 2.0052	27.3875 $ \pm $ 2.0441	23.8511 $ \pm $ 2.8370
FBP+MSDNet	SSIM	0.7840 $ \pm $ 0.0641	0.7695 $ \pm $ 0.0579	0.7148 $ \pm $ 0.0726
FBP+MSDNet	PSNR	30.7850 $ \pm $ 1.9784	29.0111 $ \pm $ 1.9740	27.4624 $ \pm $ 1.9661
FBP+DnCNN	SSIM	0.5829 $ \pm $ 0.0521	0.5661 $ \pm $ 0.0528	0.5174 $ \pm $ 0.0559
FBP+DnCNN	PSNR	20.4433 $ \pm $ 2.5345	23.4066 $ \pm $ 2.2764	21.2132 $ \pm $ 2.5140
Learned / Unrolled Iterative Methods
LG	SSIM	0.6740 $ \pm $ 0.0652	0.5746 $ \pm $ 0.0655	0.5378 $ \pm $ 0.0706
LG	PSNR	28.1639 $ \pm $ 1.9380	26.3188 $ \pm $ 1.9508	24.7228 $ \pm $ 1.9630
LGTV	SSIM	0.6804 $ \pm $ 0.0647	0.5590 $ \pm $ 0.0639	0.5091 $ \pm $ 0.0643
LGTV	PSNR	28.4131 $ \pm $ 1.9300	26.0867 $ \pm $ 1.9545	25.0225 $ \pm $ 1.9687
LPD	SSIM	0.8296 $ \pm $ 0.0410	0.8049 $ \pm $ 0.0444	0.7724 $ \pm $ 0.0571
LPD	PSNR	31.1723 $ \pm $ 1.9607	29.2534 $ \pm $ 1.9941	28.0734 $ \pm $ 1.9589
Learned Regularizer Methods
AR	SSIM	0.6869 $ \pm $ 0.0505	0.6100 $ \pm $ 0.0543	0.5742 $ \pm $ 0.0620
AR	PSNR	23.8496 $ \pm $ 2.1578	21.1830 $ \pm $ 2.1772	22.2350 $ \pm $ 2.0260
TDV	SSIM	0.5940 $ \pm $ 0.0595	0.5459 $ \pm $ 0.0572	0.5282 $ \pm $ 0.0584
TDV	PSNR	26.3233 $ \pm $ 1.9315	24.8127 $ \pm $ 1.9399	23.3939 $ \pm $ 1.9662
ACR	SSIM	0.7114 $ \pm $ 0.0543	0.6575 $ \pm $ 0.0541	0.5515 $ \pm $ 0.0529
ACR	PSNR	27.1792 $ \pm $ 1.9441	25.3342 $ \pm $ 1.9442	23.4915 $ \pm $ 1.9539
Plug-and-Play Methods
DnCNN-PnP	SSIM	0.7617 $ \pm $ 0.0410	0.6981 $ \pm $ 0.0441	0.6200 $ \pm $ 0.0475
DnCNN-PnP	PSNR	26.9997 $ \pm $ 1.9330	25.0658 $ \pm $ 1.9248	23.4108 $ \pm $ 1.9521
DRUNet-PnP	SSIM	0.7634 $ \pm $ 0.0411	0.7002 $ \pm $ 0.0443	0.6149 $ \pm $ 0.0511
DRUNet-PnP	PSNR	27.0262 $ \pm $ 1.9334	25.0829 $ \pm $ 1.9254	23.4362 $ \pm $ 1.9520
GS-PnP	SSIM	0.6396 $ \pm $ 0.0670	0.5668 $ \pm $ 0.0663	0.4989 $ \pm $ 0.0625
GS-PnP	PSNR	26.3318 $ \pm $ 1.9328	24.5129 $ \pm $ 1.9282	22.8225 $ \pm $ 1.9481

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Table 7. Quantitative analysis of all evaluated methods with respect to PSNR and SSIM on their performance in the CT image reconstruction tasks of Sparse-Angle

Method	Metric	CT Image Reconstruction Task
Method	Metric	Sparse-Angle 360	Sparse-Angle 120	Sparse-Angle 60
Classical Methods
FBP	SSIM	0.2947 $ \pm $ 0.0453	0.1231 $ \pm $ 0.0225	0.0611 $ \pm $ 0.0112
FBP	PSNR	24.9674 $ \pm $ 2.0415	19.8769 $ \pm $ 2.0124	16.6451 $ \pm $ 1.9972
AGD	SSIM	0.3867 $ \pm $ 0.0563	0.4142 $ \pm $ 0.0630	0.4333 $ \pm $ 0.0664
AGD	PSNR	26.9629 $ \pm $ 2.0444	27.5127 $ \pm $ 1.9948	27.2796 $ \pm $ 1.9553
PDHG	SSIM	0.6998 $ \pm $ 0.0685	0.6712 $ \pm $ 0.0718	0.5952 $ \pm $ 0.0728
PDHG	PSNR	32.9158 $ \pm $ 1.9739	31.7980 $ \pm $ 1.9798	29.8020 $ \pm $ 1.9326
Post-Processing Methods
FBP+U-Net	SSIM	0.7449 $ \pm $ 0.0801	0.7518 $ \pm $ 0.0657	0.7728 $ \pm $ 0.0592
FBP+U-Net	PSNR	30.4766 $ \pm $ 3.4844	26.0785 $ \pm $ 6.3779	19.5421 $ \pm $ 9.9613
FBP+MSDNet	SSIM	0.8392 $ \pm $ 0.0473	0.7993 $ \pm $ 0.0650	0.7626 $ \pm $ 0.0789
FBP+MSDNet	PSNR	33.1188 $ \pm $ 1.9820	32.2993 $ \pm $ 1.9928	30.9931 $ \pm $ 1.9875
FBP+DnCNN	SSIM	0.7864 $ \pm $ 0.0618	0.6701 $ \pm $ 0.0864	0.6180 $ \pm $ 0.0796
FBP+DnCNN	PSNR	31.7575 $ \pm $ 2.0213	29.1817 $ \pm $ 2.3053	28.6079 $ \pm $ 2.3389
Learned / Unrolled Iterative Methods
LG	SSIM	0.7846 $ \pm $ 0.0628	0.6795 $ \pm $ 0.0790	0.6428 $ \pm $ 0.0777
LG	PSNR	32.5946 $ \pm $ 1.9764	31.1950 $ \pm $ 1.9658	29.9360 $ \pm $ 1.9603
LGTV	SSIM	0.7811 $ \pm $ 0.0659	0.7100 $ \pm $ 0.0745	0.7081 $ \pm $ 0.0689
LGTV	PSNR	32.9404 $ \pm $ 1.9666	31.4072 $ \pm $ 1.9647	29.9021 $ \pm $ 1.9357
LPD	SSIM	0.8433 $ \pm $ 0.0479	0.8300 $ \pm $ 0.0500	0.8206 $ \pm $ 0.0508
LPD	PSNR	33.3809 $ \pm $ 1.9513	32.7032 $ \pm $ 1.9685	32.0583 $ \pm $ 1.9789
Learned Regularizer Methods
AR	SSIM	0.8309 $ \pm $ 0.0447	0.8117 $ \pm $ 0.0553	0.7949 $ \pm $ 0.0595
AR	PSNR	32.8067 $ \pm $ 1.9714	32.1030 $ \pm $ 1.9577	30.8378 $ \pm $ 1.9532
TDV	SSIM	0.6815 $ \pm $ 0.0736	0.6235 $ \pm $ 0.0741	0.5725 $ \pm $ 0.0728
TDV	PSNR	32.2673 $ \pm $ 1.9641	30.6585 $ \pm $ 1.9357	28.9451 $ \pm $ 1.8995
ACR	SSIM	0.8271 $ \pm $ 0.0494	0.8074 $ \pm $ 0.0539	0.7849 $ \pm $ 0.0524
ACR	PSNR	33.1537 $ \pm $ 1.9632	31.9181 $ \pm $ 1.9666	30.5147$ \pm $1.9338
Plug-and-Play Methods
DnCNN-PnP	SSIM	0.8405 $ \pm $ 0.0432	0.8021 $ \pm $ 0.0465	0.7637 $ \pm $ 0.0484
DnCNN-PnP	PSNR	32.4627 $ \pm $ 1.9309	31.3847 $ \pm $ 1.9271	29.9350 $ \pm $ 1.8980
DRUNet-PnP	SSIM	0.8398 $ \pm $ 0.0433	0.8000 $ \pm $ 0.0465	0.7658 $ \pm $ 0.0498
DRUNet-PnP	PSNR	32.5065 $ \pm $ 1.9324	31.3949 $ \pm $ 1.9266	29.9518 $ \pm $ 1.9085
GS-PnP	SSIM	0.7622 $ \pm $ 0.0628	0.7588 $ \pm $ 0.0684	0.6937 $ \pm $ 0.0701
GS-PnP	PSNR	32.1977 $ \pm $ 1.9353	31.2728 $ \pm $ 1.9370	29.5791 $ \pm $ 1.8960

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