OpenPros: A Large-Scale Dataset for Limited View Prostate Ultrasound Computed Tomography
Authors: Hanchen Wang
Yixuan Wu
Yinan Feng
Peng Jin
Luoyuan Zhang
Shihang Feng
James Wiskin
Baris Turkbey
Peter Pinto
Bradford J Wood
Songting Luo
Yinpeng Chen
Emad Boctor
Youzuo Lin
Venue: ICLR 2026 Poster (2026)
Keywords: Ultrasound Computed Tomography
Prostate Imaging
Benchmark Dataset
Medical Imaging
Primary area: datasets and benchmarks

Abstract: Prostate cancer is one of the most common and lethal cancers among men, making its early detection critically important. Ultrasound computed tomography (USCT) has emerged as an accessible and cost-effective method that reconstructs quantitative tissue parameters, which can serve as potential biomarkers for malignancy. However, current prostate USCT faces considerable barriers: limited-angle acquisitions due to anatomical constraints, tissue heterogeneity, proximity to organs and bony pelvic structures, and lengthy processing times. The lack of large-scale, anatomically precise datasets significantly hampers the development of high-quality, efficient, and generalizable methods. To address this gap, we introduce OpenPros, the first large-scale benchmark dataset for limited-angle prostate USCT, designed to evaluate machine learning algorithms for inverse problems systematically. Our dataset includes over 280,000 paired samples of realistic 2D speed-of-sound (SOS) phantoms and corresponding ultrasound full-waveform data, generated from anatomically accurate 3D digital prostate models derived from 4 real clinical MRI/CT scans and 62 ex vivo prostate specimens with experimental ultrasound measurements, annotated by medical experts. Simulations are conducted under clinically realistic configurations using advanced finite-difference time-domain (FDTD) and Runge-Kutta acoustic wave solvers, both provided as open-source components. Through comprehensive benchmarking, we find that deep learning methods significantly outperform traditional physics-based algorithms in inference efficiency and reconstruction accuracy. However, our results also reveal that current machine learning methods fail to deliver clinically acceptable, high-resolution reconstructions, underscoring critical gaps in generalization, robustness, and uncertainty quantification. By publicly releasing OpenPros, we provide the community with a rigorous benchmark that not only enables fair method comparison but also motivates new advances in physics-informed learning, foundation models for scientific imaging, and uncertainty-aware reconstruction—bridging the gap between academic ML research and real-world clinical deployment. The dataset is publicly accessible at https://open-pros.github.io/.

Published as a conference paper at ICLR 2026
OPENPROS: A LARGE-SCALE DATASET FOR LIMITED VIEW PROSTATE ULTRASOUND COMPUTED TOMOGRA- PHY
Hanchen : Yixuan W Yinan Feng', Peng Jin Luoyuan Zhang', Shihaan Feng', James Wiskin Baris Turkbey", Peter A. Pinto Bradford J. Wood", Songting Luo", Yinpeng Chen'. Emad Boctor", and Youzuo Lin
The University of North Carolina at Chapel Hill, Johnn Hopkins University, The Pennsylvania State University, 'QT Imaging, Inc., 5 National Institutes of Health, "Iowa State University, "Google DeepMind
ABSTRACT
Prostate cancer is one of the most common and lethal cancers among men, making its early detection critically important. Ultrasound computed tomography (USCT) has emerged
accessible and cost-effective method that reconstructs quanti- tative tissue parameters, which can serve as potential biomarkers for malignancy. However, current prostate USCT faces considerable barriers: limited-angle acqui- sitions due to anatomical constraints, tissue heterogeneity, proximity to organs and bony pelvic structures, and lengthy processing times. The lack of large- scale, anatomically precise datasets significantly hampers the development of high-quality, efficient, and generalizable methods. To address this gap, we intro- duce OPENPROS, the first large-scale benchmark dataset for limited-angle prostate USCT, designed to evaluate machine learning algorithms for inverse problems systematically. Our dataset includes over 280,000 paired samples of realistic 2D speed-of-sounds (SOS) phantoms and corresponding ultrasound full-waveform data, generated from anatomically accurate 3D digital prostate models derived from 4 real clinical MRI/CT scans and 62 ex vivo prostate specimens with experimental ultrasound measurements, annotated by medical experts. Simulations con- ducted under clinically realistic configurations using advanced finite-difference time-domain (FDTD) and Runge-Kutta acoustic wave solvers, both provided open-source components. Through comprehensive benchmarking, we find that deep learning methods significantly outperform traditional physics-based algo- rithms in inference efficiency and reconstruction accuracy. However, our results also reveal that current machine learning methods fail deliver clinically accept- able, high-resolution reconstructions, underscoring critical gaps in generalization, robustness, and uncertainty quantification. By publicly releasing OPENPROS, we provide the community with rigorous benchmark that not only enables fair method comparison but also motivates new advances in physics-informer learning, founda- tion models for scientific imaging, and uncertainty- the gap between academic ML research and world clinical deployment. The dataset is publicly accessible at htthh:t:///// httttss://pee-ppeee qithub.
reconstruction bridggg
INTRODUCTION
Prostate cancer is the second most common malignancy in men and is one of the leading causes of cancer-related deaths worldwide. One in eight men suffers from it (Radtke & Hadaschik] 2020 Tosoian et al. 2024). Since the 5-year survival rate for prostate cancer patients significantly drops from nearly 100% to approximately 34% once the disease progresses from localized or regional stages to distant metastases (Institute 2024), early detection of aggressive prostate cancer is of vital
"Equal contribution

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Real Phantom Acquisition Pipeline
[1] MRI-CT (174)) Origial Images
[2] Expert annotation:
[3] Prostata SOS (n=62)
[4] 50 SOB (n x
20 plane extruction
Heanuremarts
Combirutie app
acquaaiion
@isannUtT platfemm
PRT
OpenPros data & Benchmark models
Ground truth (122800000):0000
In g.
Output giossaa
[6] Ultrasound simulation
Ultrasound data
[7] Benchmark
Expariments
1 10p
2
Task Setup
Figure 1: OPENPROS dataset creation and benchmarking pipeline. Top panel: Starting from clinical MRI and CT scans, we employ expert annotations to generate detailed 3D anatomical segmentations. We then incorporate real ultrasound speed-of-sound (SOS) measurements from vivo prostate samples acquired using the QTscan platform. These are integrated into comprehensive 3D abdominal SOS models. Clinically relevant slices are extracted from these models to simulate limited-angle ultrasound tomography scenarios. Bottom panel: The extracted 2D SOS maps form the ground truth for ultrasound simulations governed by the acoustic wave equation. The resulting simulated ultrasound data organized into the OPENPROS dataset. We utilize these data train benchmark physics-based
deep-learning inversion methods, facilitating the evaluation and development of rapid, clinically relevant SOS reconstruction methods under challenging limited-angle conditions.
importance. Medical imaging plays an essential role in this early detection. Among the available imaging modalities, multiparametric MRI (mpMRI) is currently recognized the most advanced and accurate imaging tool for detecting and localizing clinically significant prostate cancer. However, the high cost and limited accessibility of mpMRI restrict its widespread adoption, particularly in rural or low-resource settings (De Rooij et al. 2014 Kasivisvanathan et al. 2018).
In contrast, ultrasound imaging is widely accessible, cost-effective, and capable of real-time imaging. Prostate ultrasound is typically performed transrectally, producing B B-mode (brightness- images. Although transrectal ultrasound (TRUS) is the clinical standard for routine prostate evaluations and biopsy guidance, it has a sensitivity of only 30%-50% for detecting clinically significant tumors and a specificity of 90%% (Beemsterboer et al. 1999 Chen et al., (016). Studies have further shown that tumors located in the anterior apical prostate regions are often undetectable with TRUS due to poor soft-tissue contrast and restricted acoustic windows, and TRUS cannot reliably distinguish malignant lesions from benign conditions such as chronic prostatitis (Maricić et al.) 2010).
Ultrasound computed tomography (USCT) has emerged as a promising alternative, reconstructing quantitative tissue parameters like speed-of-son of-uound (SOS) and acoustic attenuation that serve as potential biomarkers for malignancy (Wul 2024, Williams et al.) 202T). However, the anatomical constraints of prostate imaging inherently limit the acquisition aperture, creating challenging limited-angle condition. Unlike idealized setups where transducers surround the entire imaging domain, prostate imaging is anatomically restricted to transrectal and transabdominal placements, resulting in sparse and angularly limited data. Traditional physics-based methods typically struggle under these conditions, with slow convergence, severe ill-posedness, and significant reconstruction artifacts (Wang et al. 2025 Gilboy et al. 2020). Developing robust USCT algorithms capable of accurately handling -anteed-nglle data thus critically needed for clinical prostate imaging.
Furthermore, clinical translation of prostate USCT faces considerable barriers due to the complexity and specialization of current imaging systems. To date, only two USCT systems Vue and QTscan) have received U.S. FDA approval, and both systems focus exclusively on full-angle breast imaging with custom hardware setups unsuited for prostate applications (Sandhu et al. 2015 Malik al. 2018). These existing systems operate at relatively low frequencies, rely patient positioning incompatible with prostate imaging, and require hours for reconstruction. Thus, there is an urgent need for efficient, generalizable, and clinically adaptable prostate-specific USCT platforms. Crucially, this advancement depends on the availability of realistic, anatomically precise digital phantoms and datasets, which are currently lacking in the field (Gilboy et al. 2020 Aalamifar al. 2017).
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Additionally, prostate imaging complexity is increased by high tissue heterogeneity and proximity to multiple adjacent organs and bony pelvic structures, invalidating simplified fluid medium assumptions typically used in breast imaging. These factors severcly compromise USCT image reconstruction quality, further emphasizing the necessity of specialized prostate-specific datasets.
Recent advances in deep learning, particularly convolutional neural networks (CNNs), have shown potential for overcoming these limitations by learning complex mappings directly from ultrasound data to high-resolution SOS maps (Chugh et al.. 2021 Havaei et al. (017). Data-driven approaches bypass computational bottlenecks encountered by iterative solvers and demonstrate the ability to reconstruct detailed tissue properties even under sparse and noisy acquisition conditions. Instead of hours to days of image reconstruction using physics- physics-based methods and the requirement of expert reading as follow-up, the relatively short inference time and the automatic analysis enable faster architectures and easier diagnosis for better patient experience. Furthermore, transformer-basee have recently demonstrated remarkable performance in medical imaging by effectively modeling long-range spatial dependencies, feature particularly beneficial for ultrasound tomography due to the extensive spatial interaction of acoustic waves.
Despite these advancements, progress has been significantly hampered by the lack of large-scale, high-fidelity datasets supporting the development, evaluation. and reproducibility of innovative reconstruction algorithms. Existing USCT datasets typically for breast imaging, which are either synthesized in simulation or derived from real phantoms. Related datasets are listed in Table 1. They exhibit diversity and reflect anatomical realism to good extent, they are not optimal for developing and benchmarking advancing prostate USCT algorithm. There are also anatomical datasets for the male pelvic region but not for USCT purposes. The commercial anatomy softwares such as Zygote Body and Complete Anatomy provide different pricing options for viewing and downloading, but they generally lack anatomical varieties. Moreover, no publicly available dataset adequately addresses the unique challenges posed by limited-view prostate USCT and the existence of bones in the imaging view while simultaneously providing realistic wave propagation modeling and comprehensive full-waveform data.
Table 1: Comparison between our OPENPROS and other existing datasets for the male pelvic region or for medical ultrasound computed tomography. The symbols V X, and NA indicate that the dataset contains, does not contain, or is not applicable to the corresponding feature, respectively.
pasnelts
anataay
beteropencity
Limited uapl:
Public
OPENPHOS (ours)
Lieral
Ruiler of
Kalts
2018
OpenWives
Zonr et
Segars al.
2010
201
The visible lumas project Ackerman 1998
301
701
Zygolc Boaly
Complete Amitomy
301
Motivated by these challenges and the pressing need for prostate USCT, we introduce OPENPROS, the first large-scale dataset specifically designed for limited-angle prostate USCT scenarios. A schematic illustration of the overall pipelines of OPENPROS is shown in Figure 1 Our dataset comprises over 280,000 paired 2D SOS phantoms and ultrasound full-waveform data derived from anatomically realistic 3D prostate models generated from 4 clinical MRI/CT scans and 62 ex vivo prostate specimens with experimentally measured speed-of-soume (SOS), annotated meticulously by clinical experts. OPENPROS serves as a critical benchmark facilitating advances computational efficiency, limited-angle reconstruction accuracy, rapid clinical adaptability, and comprehensive method comparisons across various imaging conditions, including ray-based, single scattering, high-frequenee and limited-angle scenarios.
In summary, our contributions to the community include:
1. Large-scale, anatomically realistic benchmark dataset:
The first comprehensive prostate USCT dataset, derived from clinical MRI/CT scans and detailed expert annotations, designed explicitly to address limited-angle -nngle imaging conditions.
2. High-fidelity, publicly available simulation tools: Advanced finite-difference time-domain (FDTD) and Runge-Kutte Kutta implicit iterative acoustic solvers, openly accessible alongside our dataset to facilitate reproducibility and method development.
3. Comprehensive benchmarking of inversion methods: Thorough evaluation of sayysics-based and deep learning methods under realistic limited-angle conditions, including systematic tests of
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generalization, robustness, and inference efficiency. These baselines establish clear performance
baselines and guide future algorithmic improvements.
The remainder of this paper is structured as follows: In Section 2 we overview the fundamentals of USCT and our task setup. Section details our dataset construction. Section A describes benchmarking experiments. In Section 6 we discuss dataset strengths, limitations, and future research directions. Finally, we conclude in Section by summarizing our key contributions and the broader implications of OPENPROS.
2 ULTRASOUND COMPUTED TOMOGRAPHY AND FORWARD MODELING
In the context of USCT, the forward problem involves simulating acoustic wave propagation through soft tissues, which is governed by the acoustic wave equation. Assuming isotropic medium with constant density, the forward modeling equation is given by:
1 00p
V
c² 012
where 2
2 0y² in 2D, c(2, y) denotes the spatially varying SOS map, p(z, y, t) is the
acoustic pressure field, and s(r, y. f) represents the ultrasound source. In our simulations, the source is prescribed as a controlled ultrasound excitation. Clinically, the primary goal of ultrasound tomography is reconstruct spatially varying SOS maps from recorded pressure fields, enabling accurate tissue characterization and anomaly detection, such as identifying tumors or lesions.
The forward modeling of ultrasound propagation thus entails computing the pressure field from a given SOS distribution c, represented by the highly nonlinear mapping p = f(c). where f(-) encapsulates the complex recorded ultrasound signals form a 4-dimensional tensor p E R S RXTx x where S is the number of sources, R is the number of receivers, T represents the number of time steps, and B denotes the batch dimension. Specifically, in our simulated prostate dataset, we set S = 20, R 322, and T 1000. represented 3-dimensional tensors X
propagation phenomena defined by Equation (T) In practice, the
The output SOS maps to be reconstructed where H and W represent the spatial height and width dimensions. respectively. In our specific configuration, each SOS map has a spatial resolution of 401 161 grid points.
Data-driven USCT leverages neural networks to directly approximate the inverse mapping = (p), as demonstrated in recent studies (Wu Lin 2019). Thus, the specific task addressed this paper is the supervised learning problem, formulated as ming Ep, op,c[[[c. é)), where é = f0- (p). Here, fø represents deep neural network parameterized by 6. trained on pairs of simulated ultrasound signals p and corresponding ground-truth SOS maps The training objective typically incorporates quantitative metrics such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Structural Similarity Index Measure (SSIM) and Pearson Correlation Coefficient (PCC).
OPENPROS DATASET
OPENPROS is the first large-scale benchmark dataset explicitly designed to facilitate research in limited-angle prostate ultrasound computed tomography (USCT). contains anatomically realistic 2D speed-of-soung phantoms, organ segmentation labels, and corresponding simulated ultrasound waveforms derived from detailed 3D digital prostate models. The patient level anatomy ID is named as 3_01, 02, 3_03 and 3_0 44. The prostate level anatomy ID is named as the date of acquisition (in total 62 prostates). Detailed naming strategy can be found in the Appendix A.2 Example data pairs and FDTD simulation code provided in the supplementary materials
In the following subsections, we first show the basic statistics of our dataset and highlight the related domain interests. We then descrihe the design strategies of 3D/2D prostate phantoms which maximize the fidelity. At the end, we discuss the ultrasound data simulation setups.
3.1 DATASET STATISTICS
OPENPROS consists of 280,000 paired examples of 2D SOS phantoms and ultrasound data, systemat- ically derived from realistic 3D digital models. The essential characteristics and data dimensions are summarized in Table
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Table 2: Dataset summary for the OpenPros USCT dataset. SOS maps formatted (sample channel (#physical params, SOS here) x depth (vertical) x width (horizontal)): ultrasound data as (sample channel (#sources) x time x #receivers).
Dataset
Size
#Train #Validation #Test
Ultrasound Data Shape
SOS Map Shape
OpenPros
6.8 TB
224K / 28K 28K
1140 x 40 x 1000 161
1140 1 401 x 161
OPENPROS supports various critical research topics, including:
Tissue Interfaces: Clearly defined interfaces among prostate, bladder, and surrounding tissues, essential for organ boundary delineation and accurate pathology differentiation. Segmentation labels enhance precision in evaluating inversion algorithms.
Lesion Characterization: Realistically modeled synthetic lesions (c.g., tumors) introduce SOS discontinuities, challenging algorithms in lesion detection and characterization, critical for diagnostic accuracy.
Clinical Variability and Realistic Imaging Conditions: Systematic slicing of high-resolution 3D digital models captures realistic anatomical variability, with advanced finite-difference time-domain (FDTD) simulations reflecting clinical imaging conditions, including limited aperture, acoustic noise, and tissue heterogeneity.
Our sophisticated data generation pipeline, encompassing digital phantom modeling, detailed anatom- ical labeling, and precise acoustic simulations, significantly enhances the clinical relevance and diversity of the dataset.
3.2 3D PROSTATE PHANTOM DESIGN
(a)
(b)
It is important to note that the 3D dig- ital phantoms were derived from hu- man CT/MRI (Nyholm et al., 2018) and USCT scans of ex vivo prostate specimens (Parikh et al., 2024 Wiskin jet al.) 2022; Williams et al. 2202).
Tranireen
Major organs were annotated by perts using T2-weighted MRI, fat was segmented from -e-weihteed MRI, bones were segmented from X-ray CT, and the speed of sound and at- tenuation of ex vivo prostate samples were measured using a QT scanner (QT Imaging Inc., Novato, California, USA). Speed of sound of other organs acquired from ITIS foundation tissue database (Baumgariner et al. 2024). To best mimic the tissue heterogeneity, we employed Gaussian distributions with given mean values and standard devia- tions from the tissue database assign speed of sound in different tissue types. These derivations from human data reduces the reliance on synthetic simulation and maximizes the fidelity of the dataset, especially in the prostate area. Additional details phantom construction, applications, and open access availability can be found in (Wu et al. 2024). The 3D abdominal anatomical structure and the ultrasound probe placement sketch can be found in Figure 2 a) and the illustration of 3D phantom can be found in Figure ().
Figure 2: (a) Anatomical structure and probe placement. Two prohes-abdommnnal (on the body surface) and transrectal (in the rectum)-are used in our simulation. Image courtesy of Complete Anatomy. (b) 3D digital SOS phantom. SOS distribution in the anatomically realistic prostate model.
3.3 2D PROSTATE PHANTOM EXTRACTION
We generate 2D speed-of-sound phantoms by slicing our anatomically realistic 3D prostate volumes under clinically realistic probe configurations. For each phantom, we place one transrectal probe in the rectum and one abdominal probe on the body surface, then sample cross-sections across a range of rotations (++45) and small random perturbations. This process yields 280 K paired 2D SOS maps and corresponding ultrasound waveforms that faithfully capture patient-specifer anatomy and limited-angle acquisition variability.
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More detailed 2D phantom extraction strategy can be found in Appendix A.1
3.4 ULTRASOUND DATA SIMULATION
We simulate ultrasound wave propagation using finiteddifference time-domain (FDTD) solver based on the 2D acoustic wave equation discussed above. The numerical scheme adopts fourth-order accuracy in space and second-orde -oddrr accuracy in time, offering reliable trade-off between numerical precision and computational efficiency. This configuration particularly well-suited for capturing fine-grained wave interactions in heterogeneous prostate tissue environments.
Each simulation conducted under two acquisition configurations, placing sources and receivers along the top and bottom boundaries of the computational grid. A total of 20 sources (10 at the top and 10 the bottom, shown as yellow stars in Figure 3 are uniformly distributed along each boundary. For every source, 322 receivers (shown red dots in Figure 3) are placed across the entire lateral extent of the domain, enabling comprehensive capture of the scattered wavefield. A Ricker wavelet with MHz peak frequency serves as the excitation pulse, consistent with clinical transducer characteristics. The wavefield is recorded over 1,000 time steps at a sampling interval of Al = 1 x 10-7 seconds, covering total duration of 100 jus. To suppress artificial reflections, 120 grid points absorbing boundary condition (ABC) are applied to each boundary. Two examples of our simulations and the corresponding SOS maps are shown in Figure]
Reflection Surface source
Reflection
Transmission Rectum source
Transmission
SOS map
Rectum source
Surface source
Without Bone
sources
receeierrs
A: Direct Wave
Weak Reflection Organs
C: Strong Reflection of Bone
D: Transmission through Bone
With Bone
Multi-scatterings
Bone
Figure 3: Examples of simulated ultrasound data and phantoms: without (lop) and with (bottom) bone in the phantoms. We show two example channels reflections and transmissions with sources (yellow stars) and receivers (red dots) on the two probes. Our PDE solvers can simulate complex and realistic ultrasound wave phenomena, including transmissions, reflections, direct waves, and multi scatterings.
The spatial discretization of the domain uses grid spacing of 0.375 mm, resulting in a field of view of approximately 60 mm in width and 150 mm in depth. Each SOS map has a spatial resolution of 401 161 grid points, corresponding to a physical field of view of 60 mm (lateral) by 150 mm (axial), with uniform grid spacing of 0.375 mm in the lateral and axial directions. These physical dimensions and spacings are kept constant across all examples in the dataset. This configuration mirrors the anatomical scale of the prostate and its surrounding structures. A summary of the physical simulation parameters and the physical meaning of the dimension shown in Table
Importantly, the simulated ultrasound data for each sample contains 40 distinct channels, organized to reflect practical probe configurations: Channels (0-9) source on body surface, receiver on body surface; (10-19) source body surface, receiver in rectum; (20-29) source in rectum, receiver in

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Table 3: Physical Meaning of the Prostate USCT Dataset
Grid
SOS Map
Source
Source Line
Receiver
Receiver Line
Time
Recorded
Dataset
Spacing
Spatial Size
Spucing
Length
Spacing
Length
Spacing
Time
OpenPros
0.375 mm
60 mm 150 mm
3.75 mm
60 mm
0.375 mm
60 mm
1 10
100 js
rectum;; and (30-39) source in rectum, receiver body surface. This setup emulates both conven- tional transabdominal and transrectal imaging pathways, enabling detailed studies of transmission and reflection across diverse acoustic paths.
4 OPENPROS BENCHMARKS
OPENPROS enables systematic investigation of three core questions in limited-angle prostate USCT: (1) inference efficiency, (2) reconstruction accuracy, and (3) out-of-distribution (OOD) general- ization. We compare two physics-based baselines, Delay-and-Sum beamforming and multi-stage USCT inversion, against two data-driven models: CNN-based InversionNet (Wu & Lin 2019) and Vision Transformer (ViT)-based variant (Dosovitskiy al. 2020), referred here as Vit-Inversion.
Performance is evaluated using four metrics: mean absolute error (MAF) and root-mean-squee error (RMSE) for numerical fidelity, and structural similarity index (SSIM) and Pearson correlation coefficient (PCC) for perceptual and structural alignment. All models are trained and evaluated under identical settings on NVIDIA H100 GPUs.
4.1 BENCHMARK METHOSS FOR PROSTATE USCT
Beamforming, classical ultrasound imaging method, reconstructs images by aligning and summing received ul- trasound echoes according to assumed sound speeds and propagation paths. In this baseline, beamforming serves as fast, adooted approach for generating initial ultrasound images, highlighting the inherent limitations under restricted-view conditions.
Beamforming
USCT
VIT-Inversion
Large Bone
Physics- based USCT is performed in three-stage multi-frequency frame-
Small Bone
work. Starting from a smoothed ini- tial SOS model, we first invert low- frequency data, then mid-frequency data, and finally full-band data. At each stage, synthetic waveforms are generated via forward operator and compared to observed data; the SOS model is updated by minimizing the waveform misfit.
No Bone
InversionNet (Wu & Lin 2019) pro-
posed a dally-convolutions. network model the seismic inversion pro- cess. With the encoder and the de- coder, the network was trained in su- pervised scheme by taking 2D (time x # of receivers) seismic data from multiple sources as the input and pre- dicting 2D (depth x length) velocity maps the output.
Figure 4: Benchmark results for limited-angle prostate USCT. Each column shows different inversion method the same phan- (col 1) ground-truth SOS map: (col Delay-and-Sum beam- forming; (col 3) physics-based based USCT: (col 4) InversionNet: (col 5) ViT-Inversion. Rows correspond to three representative prostate slices illustrating challenging (top), moderate (middle), and simple (bottom) anatomical scenarios. Zoom-in figures of the prostate region (orange squares) are shown Figure
ViT-Inversion: A Vision Trans- former (Dosovisskiy al. 2020 that
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partitions the 3D waveform tensor [S, R] into spatio-temporal patches, embeds them into to- kens, and applies multi-hes head self-attention to capture long-range wave interactions. A lightweight upsampling CNN refines the patch-wise outputs into full-resolution SOS maps.
The train/test splits for the in-distribution (ID) experiments in the section: we randomly partition all available 2D samples the slice level into training, and test sets (90% / 10%), without enforeing patient exclusivity. As a result, slices from the same 3D anatomy can appear in both train and test sets; this protocol intentionally designed measure interpolation performance within the set of anatomies seen during training.
Training configurations and hyperparameters are provided in App. A.4
4.2
RESULT ANALYSIS
Table 4: Quantitative in-distribution results (mean + std over all test slices).
Method
MAEL
RMSEL
SSIM
PCC1
InversionNet
0.0074 + 0.0037
0.0247
0.0166
0.9955
0.0037
0.9851 1 0.0262
ViT-Inversion
0.0067 = 0.0057
0.0205 0.0172
0.9967 0.0035
0.9893 = 0. 0.0219
Quantitative Results Table reports MAE, RMSE, SSIM, and PCC for our two learned baselines. Traditional physics-based USCT (not shown) achieves RMSE s 0.16 and SSIM ~ 0.90. leaving substantial room for improvement. In contrast, the learned models reduce RMSE to 0.0297 (Inver- sionNet) and 0.0268 (ViT-Inversion) about 5-6x lower than the physics-based baseline- and reach near-perte near-perfect structural fidelity (SSIM 0. 0.9877/0.9908) (9008...... Inversinno is best across all four metries, followed closely by InversionNet. We also report both the mean and standard deviation of each metric over all test samples. Concretely, for each test slice we compute MAE, MSE, RMSE, PCC, and SSIM between the reconstructed and ground-truth SOS maps, and then aggregate these values across the entire ID test set. Table 4 summarizes these statistics for InversionNet and InT-Inversin.
Ground Truth
Beamforming
USCT
InversionNet
VIT-Imeersion
Qualitative Observations FigureApreeent three rep- resentative prostate slices under challenging (top), moderate (middle). and simple (bottom) anatomical
Large Bone
Small Bone
conditions. Delay-and- Sum beamforming yields noisy, low-contrast images incapable of resolving detailed prostate structures. Physics-basse based
No Bone
USCT
significantly reduces these artifacts and better recovers the general gland shape but produces overly blurred images lacking fine anatom- ical details. Machine learning-basse based methods, including InversionNet and ViT-Inversion, markedly outperform physics-basee USCT in reconstructing the global anatomical structure and boundaries. However, the zoom-in prostate images shown in Figure illustrate that despite better overall shape reconstruction, these learned methods still cannot accurately resolve fine structures within the prostate. The internal prostate structures remain smoothed, and small lesions or detailed boundaries are not distinctly reconstructed, indicating significant room for improvement imaging resolution and accuracy.
Figure 5: Zoom-in comparison of prostate regions. Enlarged views (orange squares in Figure showing detailed reconstruction quality within the prostate region across baseline methods: (col 1) Ground truth; (col 2) Delay-and-Sin beamforming: (col physics-based USCT: (col 4) InversionNet: (col 5) ViT- Inversion. Each row corresponds the same anatomical scenario as in Figure Note that although the learned methods recover general anatomical shapes more clearly, the fine internal structures and boundaries remain poorly resolved.
Inference Efficiency Comparison addition to superior accuracy, data-driven methods offer remarkable computational efficiency suitable for real-time imaging applications, as summarized in
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Table 7 (see appendix). Traditional physics-basee inversions, such as beamforming and multi-starn stage USCT, incur significant computational overheads, requiring approximately 4 hours and 24 hours per sample, respectively. In sharp contrast, the data-driven approaches achieve pear-instantancous reconstructions: InversionNet requires only 4.9 milliseconds per sample, while ViT-Inversion com- pletes inference in roughly 8.9 milliseconds due to its transformer architecture. This stark difference highlights the practical feasibility and potential clinical value of learned models in enabling rapid, real-time prostate imaging.
5 ABLATION STUDY
Generalization Tests To assess how well our models generalize to truly unseen anatomies, we conducted three distribbiitt tests using data splits that reflect realistic clinical scenarios: (1) Patient-Levv Generalization: Train patients 3 3_01, 3_02, 3303, test on an entirely unseen patient 3_04. (2) Seave-One-Prostate. Out: Train on 60 prostates from all four patients except two held-out prostates (i.e., 2022-09 - 6
09); test on those withheld prostates. (3) Combined Generalization: Train on 60 prostates drawn only from patients 3_01-3_0000 03; test on both remaining prostates of patient 3_04.
T summarizes MAE, RMSE, SSIM, and PCC for InversionNet and ViT-Inversion under each scenario. In the natient-level split, performance drops relative to in no-distribution (ID) training, with errors increasing by roughly 3-5x. ViT-Inversion consistently outperforms InversionNet, yielding lower MAF/RMSE and higher SSIM/PCC, which indicates improved generalization ability when encountering anatomies from unseen patients. These results highlight the difficulty of patient-level generalization in limited-angle prostate USCT.
Table 5: Generalization Test Results. Evaluation of inversion methods (mean t std) the InversionNet results and mean for the ViT- Inversion results.
prostate anatomics. We show
Scenario
Method
MAEI
RMSET
SSIM
PCC1
InversionNet
0.0322 = 0.0100
0.1010 0.0460
0.9399 0.0195
0.8271 # 0.2027
Patient-level
ViT-Inversion
0.0276
0.0890
0.9496
0.8689
InversionNet
0.0069 = 0.0064
0.0273 0.0157
0,9899 = 0.0067
0,9894 + 0.0174
Prostate-level
ViT-Inversion
0.0061
0.0210
0.9934
0.9937
InversionNet
0.0323 0.0099
0.1017
0.0462
0.9408
0.0195
0.8251 + 0.2017
Combined
ViT-Inversion
0,0280
0,0916
0,9482
0.8663
By contrast, the leave-one-prostate-ouu split shows minimal and, in some cases, negligible degradation compared ID. ViT-Inversion achieves slight improvements over InversionNet across all metrics. These results show that intra-patient anatomical variability poses little difficulty for the models, thus generalization across unseen prostates comparatively straightforward.
The combined OOD split mirrors the patient-level challenge: both models exhibit substantial error increases, with ViT-Inversion consistently outperforming InversionNet across metrics. Overall, while intra-patient generalization is well handled, robust patient-agnost reconstruction under limited-angle conditions remains significant open challenge.
Robustness to Input Noise We also assess robustness to measurement corruption by adding zero- mean Gaussian noise to the test waveforms while keeping all models trained on clean data only; see for full protocol and tables. We sweep a E {0.01, 0.02, 0.05) (roughly 26/23/ 119 dB PSNR). Performance decreases monotonically with noise, and VIT Inverrion is consistently more resilient (SSIM 0.987 - 0.935) than InversionNet (SSIM 0.944 - 0.825). Details and additional metrics (MAE/MSJJRMSE/PCC are reported in App. A.6
Extra Ablation Studies We performed extra ablation studies in the appendix. including view- dependent difficulty study A.7 robustness tests of probe placement errors A.8 dataset scaling study A.9 and structure-aware boundary metrics A.10

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6 DISCUSSION
Our OPENPROS dataset offers an unprecedented resource for developing limited- -angle prostate USCT algorithms. With over 280,000 paired SOS phantoms and ultrasound simulations derived from clinical data, it realistically captures tissue heterogeneity and anatomical constraints of prostate imaging. Our open-source FDTD and Runge-Kutta solvers ensure transparent benchmarking and reproducibility.
However, the dataset currently includes limited number of patient anatomies, potentially underrep- resenting certain anatomical variations. Additionally, we simulate only SOS distributions, omitting other critical acoustic parameters like attenuation and density. Our 2D simulations do not account for three-dimensional propagation and out-of-plane scattering, simplifying some real-world conditions. This 2D, SOS-only setting is a clear simplification compared to a full 3D clinical USCT system, but it preserves the key ill- ill-posedness of limited-angle prostate USCT while remaining computation- ally tractable. It enables us to generate approximately 280k paired waveform-SOS samples and to systematieally compare reconstruction methods at scale. We therefore position OPENPROT fast-prototyping benchmark for waveform-to-SOS reconstruction, with the expectation that successful ideas will later be re-evaluated in more complete 3D, mulai-peramettr models.
Beyond the baseline CNN and ViT models evaluated in this paper, OPENPROS is designed to serve as testbed for a broader family of reconstruction approaches, including UNet-like encoder-decoder architectures, diffusion and other generative models, and neural operator methods that directly learn PDE solution operators (e.g.. (Dai et al. 2023)). The large number of paired waveform SOS examples and the availability of both ID and OOD evaluation protocols make it possible to systematically study how these different model classes trade off reconstruction fidelity, generalization across anatomies, and computational cost in realistic limited-angle USCT settings.
Future work will expand the patient dataset, introduce multiparametric acoustic maps, and extend simulations to three dimensions. Incorporating clinically relevant pathologies and carefully designed nut-of-distribuus scenarios will further enhance the robustness and clinical applicability of future USCT solutions.
7 CONCLUSION
In this work, we have introduced OPENPROS, the first comprehensive, large-scale benchmark dataset specifically designed for limited-angle prostate ultrasound computed tomography. With over 280,000 expertly annotated 2D speed-of-sound phantoms paired with high-fidelity simulated ultrasound data, OPENPROS facilitates efficient benchmarking of both poysics-based and advanced deep learning re- construction algorithms. Our baseline experiments clearly demonstrate that deep learning approaches significantly outperform conventional physics-based methods in terms of inference speed and image quality. However, critical challenges remain, notably in resolving fine anatomical details within the prostate and achieving robust generalization across unseen anatomies. By making OPENPROS publicly available, we encourage the research community to leverage and expand this foundational resource, ultimately advancing toward clinically viable, high-resolution prostate imaging solutions.
ACKNOWLEDGEMENT
This work was supported by the University of North Carolina at Chapel Hill School of Data Science and Society through a faculty start-up grant, and by the U.S. National Science Foundation under Award No. 2504439. This work was also supported in part by the NIH Center for Interventional Oncology and the Intramural Research Program of the National Institutes of Health, including the National Cancer Institute and the National Institute of Biomedical Imaging and Bicengineering. through intramural NIH Grants ZAA CL.040015 and 1ZIDBC01 1242, as well as support from the NIBIB Center for Biomedical Engineering Technology Acceleration (BETA Center). Yixuan Wu was supported by the Graduate Partnerships Program, the Fellows Award for Research Excellence, and the Prostate Cancer Research Program Early Investigator Research Award, Congressionally Directed Medical Research Program, U.S. Department of Defense (HT94252410648),
Computational resources were provided by the University of North Carolina at Chapel Hill Informa- tion Technology Services Research Computing, the NSF ACCESS program, and the National Center for Supercomputing Applications.
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A
APPENDIX
Supplementary materials arrangement:
Section describes the detailed steps of how 2D phantoms are sliced from the 3D speed-of- sound volumes.
Section
presents the naming strategy of the OPENPROS dataset.
Section
details the benchmark evaluation metrics of OPENPROS.
Section
A
specifies the baseline models' training configurations and eyper-parameters..
Section
A.5
compares the conventional k- kawave simulation method with the open-sourced OPEN-
PRos simu
a pipeline.
Section
A.6
analyzes robustness under additive measurement noise.
Section
A.
investigates view-dependent reconstruction difficulty (bone vs. no-bone propagation
paths).
Section
A.S
evaluates robustness to probe placement errors.
Section
A.9
studies dataset scale ablation for learning-basee baaned reconstruction.
Section A.10
introduces structure-awart boundary metrics and gland-level segmentation evalua-
tion.
Section
describes the usage of large language models our work.
A.1
DETAILS OF 2D PHANTOM EXTRACTION
Bladder
Prostate
2D slicing planes
Figure 6: Schematic of our 2D phantom extraction. The green plane indicates the area between transrectal and abdominal probes.
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Starting from our 3D prostate volumes (SOS maps and organ masks), apply the following pipeline to produce each 2D phantom:
1. Volume loading and isotropic resampling. We load the segmentation masks and SOS volumes from each patient scan, resample anisotropic voxels onto uniform 0.375 mm grid, and pad exterior regions with baseline SOS of 1,500 m/s to emulate coupling gel.
Initial probe placement. A pair of valid points separated by cm within the segmented rectum defines the transrectal transducer line. The abdominal transducer is then positioned 15 anterior along the same axis.
3. Systematic rotation and translation. To emulate clinical acquisition angles, rotate both probe lines jointly from -45 to +450 in 5 increments and translate them within +1 mm each Cartesian direction.
4. Slice extraction. At each probe configuration, we extract the 2D plane containing both transducer lines. The resulting slice preserves the anatomical interfaces, tissue heterogeneity, and relative probe geometry.
Random perturbations, We add a small jitter of #1 each rotation angle and #1 mm each transducer coordinate to enrich variability.
Altogether, this procedure produces 280,000 unique 2D SOS phantoms with matching ultrasound data under limited-angle conditions. An illustration of the slicing geometry is shown in Figure 6
A.2 NAMING OF OPENPROS
The data files follow a structured naming convention: __0{i]___ (Date) (Category)
[ .py. where (i) represents patient IDs (1-4), (Date) denotes unique prostate sample identifiers, and [Category) ) specifies data types, including ultrasound data (data) and SOS maps (sos). For example, 3 02 2022 06 1000060000000006 06_sos___.___ss_0 npy refers SOS data for patient 3_02 and prostate sample 2022 06-06.
A.3 EVALUATION METRICS
To evaluate the performance of the proposed CNN-based reconstruction methods, we employ four quantitative metrics that comprehensively assess numerical accuracy and perceptual similarity be- tween the reconstructed and true SOS images. Here, we denote the true SOS image as 8, the predicted image 8, and N the total number of pixels in each image.
Mean Squared Error (MSE) measures the pixel-wise squared differences:
N MSE
Σ ss 8,)2
(2)
N
where 8; and & denote the and predicted SOS values at pixel i.
Mean Absolute Error (MAE) calculates the average absolute difference, providing robustness against outliers:
MAE
8; Sz)-
Structural Similarity Index Measure (SSIM) assesses the perceptual quality, accounting for luminance, contrast, and structural similarities:
SSIM 8) (2pa + (2) - C2)
(4)
(12 2 Ci)(o + of C2)
where Hs: M4 denote the means, a., dg the variances, and ass the covariance between true and predicted images. Constants C1 and C2 stabilize division by weak denominators.
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Pearson Correlation Coefficient (PCC) quantifies the linear correlation between true and predicted images, measuring structural consistency:
Ex 5)(8: -)
PCC
(5)
N V. (s: 5)² Ei= (8. 3)2
N
where and & denote the mean pixel values of the and predicted SOS images, respectively.
A.4 TRAINING PROCEDURE
All baseline models (InversionNet and ViT- ViT-Inversion) were trained using supervised learning approach on the proposed large-scale OPENPROS dataset. The dataset comprises a total of 280,080 samples, with 255,360 used for training and 27,360 for validation/testing.
For fair comparison, we kept the training settings identical across all methods. We employed the Adam optimizer with initial learning rate of 10-1, batch size of 512, and trained each model for up to 120 epochs. Early stopping was implemented based on validation set performance to prevent overfitting. Table 6 summarizes these training parameters.
Table 6: Training parameters consistently used all baseline methods.
Total Epochs
Training Samples
Test Samples
Batch Size
Optimizer
Learning Rate
240
255,360
27,360
512
Adam
10-4
The model sizes and training times for each baseline method are listed in Table 7 conducted on NVIDIA H100 GPUs.
All experiments
Table 7: Computational cost and model comparison for baseline methods on the OPENPROS prostate USCT dataset.
Method
Training Cost (GPC hour)
Inference Cost (GPU second/sample)
Model Size
Beamforming
N/A
14400
N/A
USCT
N/A
86400
N/A
InversionNet
240
0.0049
20.45M
ViT-Inversion
128
0.0089
28.33M
A.5 CONVENTIONAL K- WAVE VS. OUR ULTRASOUND SIMULATION ALGORITHMS
Ultrasound imaging methods can be broadly categorized by their simulation paradigms. Conventional TRUS simulations, commonly used for B-mode imaging, rely on signal processing pipelines such delay-and-sum (DAS) beamforming applied to simulated echoes. These simulations often implemented using toolboxes like MATLAB k-Wave (Treeby & Cox 2010). which model acoustic wave propagation using pseudospectral methods and reconstruct images from envelope-detected signals. While fast and widely adopted in the clinical ultrasound community, this approach simplifies underlying physics and often introduces artifacts due assumptions like homogeneous backgrounds, limited diffraction modeling, or approximate transducer responses.
In contrast, our dataset adopts physically grounded modeling framework based on the 2D acoustic wave equation. We employ a finite-difference solver with fourth-order spatial and second-order temporal accuracy to simulate full-wave propagation through heterogeneous tissue. This method captures wavefront curvature, multi-path scattering, and fine-grained variations in the SOS map, offering a far more realistic approximation of ultrasound interactions in complex anatomical regions such the prostate. This fidelity is especially critical under limited-angl acquisition constraints common in prostate imaging, where traditional methods often fail to reconstruct accurate quantitative maps.
Unlike baseb methods, our simulation does not rely on beamforming post- processro.,,,ng allowing it serve foundation for quantitative imaging tasks like USCT. While k-Wave simulations
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computationally efficient for B B-mode image formation, FDTD method remains tractable at scale and better suited for generating ground truth waveforms for learning-basee inverse solvers.
Moreover, provide two forward modeling solvers part of our open-source release: finite- difference solver with fourth-order spatial and second-order temporal accuracy, and an alternative Runge-Kutta implicit iterative solver. The former prioritizes accuracy and efficiency in time-domain modeling, while the latter offers enhanced numerical stability and can serve as basis for future 3D extensions. Both solvers are publicly available with our dataset, supporting reproducibility and extensibility for ultrasound tomography and machine learning research. Additionally, the solvers support execution on both GPU and CPU platforms.
A.6 NOISE ROBUSTNESS UNDER ADDITIVE MEASUREMENT PERTURBATIONS
Setup To assess robustness to measurement corruption, perturb the test waveforms with zero- mean i.i.d. Gaussian noise and evaluate the pretrained models without any fine-tuning (all models were trained only clean data):
p N~ o²1).
Noise is applied to the input tensor after the same normalization used during training. We sweep {0, 0.01, 0.02, 0.05]; for reference, these levels correspond to input PSNRs of approximately 26 dB, dB, and 19 dB, respectively. Reconstructions are compared to the clean ground-truth SOS using MAE, MSE, RMSE, SSIM, and PCC.
Results Tables l summarize performance for ViT-Inversion and InversionNet. Both models degrade monotonically noise increases, but ViT-Inversion is substantially more resilient across all metrics. At a 0.01 (Rs 26 dB), ViT-Inversion maintains SSIM & 0.987 and PCC s 0.982, while InversionNet drops SSIM 0.944 and PCC 0.837. At the highest noise level = 19 dB), ViT-Inversion still preserves moderate structural fidelity (SSIM 0.935, PCC 0.796), whereas InversionNet falls SSIM 0.825 and PCC 0.388. These trends suggest that attention- based models better suppress high-frequency perturbations by leveraging longer-range context in the wavefield.
0.05,
Table 8: Noise robustness of ViT-Inversion. Gaussian noise (0, o²) added to test inputs; models trained on clean data only.
ViT-Inversion
0
0.01
0.02
0.05
PSNR (dB)
26
23
19
MAE
0.0067
0.0084
0.0137
0.0366
RMSE
0.0268
0.0330
0.0521
0.1149
PCC
0.9893
0.9824
0.9507
0.7965
SSIM
0.9909
0.9872
0.9759
0.9347
Table Noise robustness of InversionNet. Same protocol Table
InversionNet
0.01
0.02
0.05
PSNR (dB)
26
23
19
MAB
0.0074
0.0287
0.0573
0.1228
RMSE
0.0297
0.0964
0.1700
0,3155
PCC
0,9851
0.8372
0.6604
0.3881
SSIM
0.9877
0.9437
0.8998
0.8252
Takeaways and implications (1) Robustness without noise exposure during training is lim- ited especcillyl for convolution-only models models--highighhin the importance of noise-aware data augmentation and/or denoising endst- (2) Attention mechanisms appear to confer greater sta- bility measurement noise in this task. (3) Practical deployment will likely benefit from simple
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Table 10: View-dependent performance of ViT-Invvesiion in-distribution test slices, stratified by bone involvement along the propagation paths. Metrics are reported as means over slices in each group. Lower better for MAE/MSE/RMSE; higher is better for PCC/SSIM.
Metric
No bones (7063 samples)
Small bones (6694 samples)
Big bones (13603 samples)
MAE 900
0.0046
0.0059
0.0082
MSE
4.52x10-+
1.17x10
RMSE
0.0098
0.0213
0.0342
PCC
0.9740
0,9884
0.9976
SSIM 0.9921
0.9908
0.9902
defenses such as SNR- ENR-matched augmentation, temporal filtering of waveforms, and uncertainty-aware inference; we include these as future baselines in subsequent releases.
A.7 VIEW-DEPENDENT DIFFICULTY: BONE VS. NO-BONE PATHS
To better understand which acquisition configurations are easier harder to reconstruct, we stratify the test slices according to whether the dominant ultrasound propagation paths intersect the pelvic bone. Specifically, we group slices into three categories: no bones, where rays from the probe to the prostate region do not intersect bone; (ii) small bones, where bone intersections occur but occupy a relatively small angular extent; and (iii) big bones, where prostate region largely shadowed by bone, corresponding to more severe limited-angle geometries.
Table T0 reports the performance of the ViT-Inversion baseline on these three categories in the in-distribution setting. We observe that MAE and RMSE increase as the amount of bone along the propagation paths increases: the no bones group yields the lowest errors, the small bones group shows intermediate errors, and the big bones group exhibits the highest errors. This trend confirms that views with strong bone interference are substantially harder to reconstruct, while bone-free views are comparatively easier. SSIM remains high in all three categories, indicating good overall structural similarity, but amplitude-wis wise errors are clearly more pronounced in the presence of bone.
A.8 ROBUSTNESS TO PROBE PLACEMENT ERRORS
In this section, we use experiments to analyze the baseline model's robustness to probe placement emoos. To directly address this concern, we regenerated waveform data by perturbing only the abdom- inal probe position in the forward simulator while keeping the rectal probe fixed, All perturbations 2-pixel mismatch on the SOS grid (approximately 0.75 mm the FDTD grid). We study three cases:
Depth error: The abdominal sources and receivers are shifted deeper by pixels, with no change applied the rectal probe.
Horizontal mismatch: The SOS map is padded by 2 pixels on the right for the simulation, and the abdominal probe is shifted laterally by 2 pixels; the rectal probe remains unchanged.
Angular mismatch: The abdominal probe is slightly tilted by lowering its right endpoint by pixels and re- re-interpolating all element positions along the tilted line; again, the rectal probe is not modified.
We then apply the trained ViT' model without any retraining or adaptation, thereby isolating its robustness to geometry mismatch. The quantitative results are shown Table
Table 11: Robustness Probe Placement Perturbations.
Mismatch Type
MAEJ
MSEJ
RMSE
PCCT
SSIM
Baseline
0.007374
0.000885
0.029743
0.98509
0.98767
Angle
0.009829
0.001807
0.042510
0.976239
0.981784
Depth
0.013245
0.003513
0.059269
0.959708
0.972126
Horizontal
0.010061
0.001608
0.040098
0.972594
0.981417
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Across all perturbation types, the model maintains high structural similarity and correlation (SSIM > 0.97 and PCC > 0.96), with depth mismatch producing the largest degradation and horizontal/angle mismatches leading more moderate changes relative to the baseline. These results indicate that the learned model is reasonably robust to small, controlled errors in probe placement.
Finally, note that "SOS background shifts" in the sense of perturbing fixed homogeneous background parameter are not directly applicable our setting: our USCT inversion directly estimates the full SOS field and does not assume optimize around separate homogeneous background model.
A.9 DATASET SCALE ABLATION
We conduct subset training experiments where InversionNet and the ViT-based model are trained using 10%, 25%, and 50% the original training set. For both architectures, increasing dataset size consistently improves reconstruction performance: MAE and RMSE decrease, while PCC and SSIM increase.
For example, InversionNet achieves an RMSE reduction from approximately 0.0488 (10%) to 0.0360 (50%), while the VIT model reduces RMSE from approximately 0.0456 (10%) to 0.0258 (50%). These results highlight the importance of large-scale data for learning- braneng-basedd based USCT reconstruction.
Detailed quantitative results (mean + standard deviation) are reported in Tables 12 and
Table 12: Subset Training Results for InversionNet (mean + std).
Metric
10%
25 %
50%
MAE
0.014151 1 0.006491
0.013643 1 0.018162
0.010478 1. 0.013810
MSE
0.003107 1 0.003620
0.003867 1 0.022751
0.002462 1 0.016337
RMSE
0,048756 + 0.027011
0.045856 + 0.041998
0.035999 + 0.034152
PCC
0,957021 = 0.058652
0.959368 + 0.066839
0,973800 = 0.047682
SSIM
0.971254 + 0.012155
0.975261 + 0.019335
0.981490 + 0.015850
Table 13: Subset Training Results for ViT-Inversion (mean + std).
Metric
10%
25%
50%
MAE
0.013624 + 0.006603
0.011839 + 0.007811
0.008236 + 0.005039
MSE
0.002955 + 0.004330
0.002255 + 0.007821
0.000986 + 0.004823
RMSE
0.045610 + 0.029575
0.039792 + 0.025909
0.025761 + 0.017956
PCC
0,960069 + 0.060274
0.968068 + 0.053930
0.984177 + 0.027592
SSIM
0,974953 1 0.013378
0.978290 1 0.01
0.987186 1 0.008936
A. STRUCTURE-AWARE BOUNDARY METRICS
To complement global image-level metries, we introduce structure-aware evaluations focused on prostate gland boundaries.
Boundary-Band Error Metries For each test slice, we extract the prostate boundary from the ground boound-truth mask and define a narrow band of width pixels centered around this boundary. Within this boundary band, compute MAE, MSE, and RMSE to assess reconstruction accuracy in anatomically critical regions.
For InversionNet, the boundary- RMSE is 0.0131 = 0.0137, indicating accurate recovery of gland contours. This boundary-focused evaluation provides a clinically meaningful complement to global averages, it directly measures reconstruction fidelity in regions relevant for gland delineation and downstream diagnostic tasks.
Gland-Level Segmentation Evaluation In addition to boundary-band errors, we perform a segmentation-base evaluation reconstructed SOS maps.
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Published as a conference paper at ICLR 2026
Table 14: Structure-Aware Boundary Metrics (InversionNet) computed within 5-pixel prostate boundary band.
Metric
Mean
Std
MAE
0.005534
0.004368
MSE
0,000359
0.000986
RMSE
0.013097
0.013678
We follow MedSAM (a al. 2024) and use its public implementation (attps://qithu3
com/ wwwp://wonnngoooooo lab/ MedSAM) as proxy for strong prostate segmenter. For each test slice in selected subset, we manually draw bounding box around the prostate and:
Apply MedSAM to the ground-truth SOS map and compute the Dice score against the ground-truth prostate mask.
2. Apply MedSAM to the predicted SOS map and compute the Dice score against the same ground- truth mask.
Because MedSAM is applied identically in both cases, this comparison isolates the degree to which gland-level structural information is preserved in the reconstructed SOS maps.
Table 15: Gland-Level Segmentation Evaluation Using MedSAM. Dice scores computed against ground-truth prostate masks.
Input to MedSAM
Reference Mask
Dice Score
Ground-Truth SOS
GT Prostate Mask
0,831982
Predicted SOS
Prostate Mask
0.8313445
The absolute Dice difference between ground-truth and reconstructed SOS inputs less than 7x 10-4, indicating negligible degradation in gland-level segmentation performance. This result demonstrates that the reconstrueted SOS maps preserve prostate boundary information at a level comparable to ground truth for downstream gland-level tasks.
We emphasize that OPENPROS is designed primarily for quantitative reconstruction accuracy assessment. Accordingly, pixel- wise metrics (MAE, RMSE) and structural similarity metries (SSIM, PCC) remain essential for comprehensive benchmarking, while the structure-awant aware metrics reported here provide complementary clinical relevance.
A.11 USAGE OF LARGE LANGUAGE MODELS (LLMS)
During the preparation of this manuscript, we used a large language model (LLM) to assist with language polishing, structural refinement, and presentation clarity. The LLM provided feedback on phrasing, grammar, and flow, suggested alternatives to reduce redundancy, and generated LTTEX formatting tables and equations. All scientific ideas, experiments, analyses, and conclusions were conceived, designed, and carried out entirely by the authors.
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Reviews:
[{"review_id": "zRHZcTwzJZ", "reviewer": "Reviewer_kNhg", "summary": "The authors build 3D digital phantoms of the male pelvis by combining four MRI/CT patient anatomies with 62 ex-vivo prostate SOS maps, resulting in 248 model variants. They then simulate two-dimensional acoustic wave propagation using a finite-difference time-domain solver, producing paired input–output samples: ultrasound waveforms and their corresponding ground-truth SOS maps. By slicing and rotating these models, they generate about 280K 2D examples meant to reflect the geometric and acoustic variability encountered in trans-rectal and trans-abdominal USCT setups.\n\nThey also use the dataset to compare some baselines:\n1) classical beamforming,\n2) iterative physics-based USCT inversion,\nand 3,4) two learned models: InversionNet (cnn) and a ViTvariant.\n\nThe learned models achieve lower pixelwise errors and run orders of magnitude faster than physics-based inversion, though their outputs remain too smooth to resolve fine prostate boundaries or lesions. Unfortunately out-of-distribution tests, where one patient anatomy is held out, reveal major performance degradation. This i s evidence of poor generalization beyond the limited training anatomies.", "questions": "1) The dataset is generated from four patient anatomies and 62 ex-vivo prostate samples. This needs to become more transparent in the paper -- from the very start.\n2) How were the four patient anatomies selected? Are they representative? Please provide some info about where they come from: healthy, diseased, varied in size, age, pathology?\n3) The paper slices 3D anatomies into many 2D samples. how do you ensure that (almost) identical slices or planes are not split across train/validation/test sets?\n4) The large difference between ID and OOD results suggests overfitting to specific anatomies. This worries me a lot. Maybe the authors can also report confidence intervals across anatomies and make the OOD evaluation a central table in the main paper?\n5) How is the performance affected by sensor or probe minor placement errors or SOS background shifts? A robustness study would help. \n6) It is not clear to me what will be finally released by the authors. waveforms, SOS maps, code, and 3D phantoms? What about the original MRI/CT data?\n7) in terms of related work, a more SOTA approach would be to use neural operator learning -- something like this https://arxiv.org/abs/2304.03297 . I suggest you discuss this in the conclusions?\n8-9) A couple of more technical questions: \nthe forward model only focuses on SOS. Out-of-plane scattering, attenuation, and density variations are ignored. Have you tried to validate the simulator against 3D k-Wave simulations? How big are the errors when ignoring such things? \nAnd how does ex-vivo SOS differ from in-vivo values at body temperature?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. Addresses a clinically important and computationally demanding imaging problem\n2. Provides an open and standardized resource that can make it easier for other people to design and evaluate their own models\n3. The selected benchmarks are reasonable and cover both physics-based and learned approaches\n4. The paper is technically good and the simulation details are sufficient, I think, if someone wants to reproduce the results", "weaknesses": "My main concern: the dataset is based on only four patient anatomies and this is mentioned only deep in the methods and appendix (I think it should be mentioned in the abstract or, worst-case, introduction). The anatomical diversity is therefore extremely limited!\n\n- All simulations are 2D and reconstruct only SOS, ignoring attenuation and density. \n- The machine-learning component is incremental (standard CNN and ViT baselines) without any more recent architectures or hybrid physics-learning integration. But this is not a major issue because I recognize that the main contribution of the paper is teh dataset.\n- Evaluation focuses on image-level metrics rather than clinically more meaningful goals such as gland boundary accuracy or lesion detection\n- The ex-vivo data used for SOS ground truth may differ from in-vivo conditions. This is not something the paper discusses or tries to quantify.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KGWHSO4b7Y", "reviewer": "Reviewer_PsHV", "summary": "The authors present a dataset (OpenPros) for ultrasound computed tomography (USCT) of the prostate that is generated from 4 anatomical MRI+CT images, expert annotations of different anatomical areas, speed-of-sound measurment, and ultrasound simulation using a wave equation. The authors compare OpenPros to other available USCT datasets and include benchmarks for physics-based and data-driven methods that measure (1) inference efficiency, (2) reconstruction accuracy, (3) and out-of-distribution generalization. Overall the paper is well written, most of the methods are explained clearly, and the paper is reasonably well-justified as a dataset contribution to field. However, there is not much clarity around whether whether the simulated dataset is sufficient to serve as a comprehensive machine learning benchmark for image reconstruction e.g. are 280K examples are derived from just 4 patients, which limits the effectiveness of the presented benchmarks.", "questions": "- I am actually unsure about the suitability of this paper for ICLR. Why do the authors think this is important for the ICLR community (typically focused on neural network representations or similar)? To be clear, I think this paper is valuable for the broader machine learning community, but seems better suited for IEEE TCI, APL Bioengineering, or even CVPR or WACV.\n- The paper begins with a discussion of prostate cancer. Is there any evidence that the generated dataset would help in detection of prostate cancer, given that the reconstruction quality (e.g. Fig 5) is so poor?\n- What problem specifically would training on the generated dataset solve?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 2, "strengths": "- The paper is very well written and justified\n- The paper does a good job of designing tasks for the dataset that could potentially determine its efficacy. The areas of (1) inference efficiency, (2) reconstruction accuracy, (3) and out-of-distribution generalization are all interesting and important.\n- The paper does a good job of comparing to the USCT literature, including deep learning methods for image reconstruction.", "weaknesses": "- The dataset size is a severe limitation in my opinion. It is not at all clear why 280K number of samples are needed for machine learning training. Ablation experiments controlling the number of generated samples could help here in showing the increased benefit from more samples, justifying the approach.\n- The metrics in Table 5 are not given enough context. Figure 5 offers some insight into potential benefits of data-driven methods, but this could be better quantified using the annotations. \n- Additional analysis of the types of representations learned or exploited by models mapping the prostate tissue seems to be important for the community, but not included in the paper. Even an assessment of which views are easily reconstructed, and which fail, would make a significant difference in the quality of the paper and contribution for the ICLR community.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "QYVf2luzyz", "reviewer": "Reviewer_ow6B", "summary": "This paper introduces OPENPROS, a new large-scale (280,000 samples) benchmark dataset for limited-angle prostate Ultrasound Computed Tomography (USCT) . The authors identify a critical gap in prostate cancer imaging: while USCT can reconstruct quantitative tissue biomarkers like Speed-of-Sound (SOS), it is hampered by anatomical constraints (e.g., the pelvic bone) that create a severe limited-angle acquisition problem . The lack of realistic data has hindered the development of robust reconstruction algorithms.\n\nThe primary contribution is the dataset itself, which features a high-fidelity data generation pipeline: 3D anatomical models are derived from real clinical MRI/CT scans (from 4 patients), and these are combined with real ex vivo ultrasound SOS measurements (from 62 prostate samples) . This anatomical ground truth is then used with advanced, open-sourced FDTD and Runge-Kutta wave solvers to generate paired SOS maps and full-waveform ultrasound data \n\nThe paper also provides a comprehensive benchmark, comparing traditional physics-based methods against deep learning models (InversionNet, ViT-Inversion) . The key findings are: 1) DL methods are faster and more accurate at general reconstruction than physics-based methods . 2) Critically, current DL models fail to resolve fine internal prostate structures and exhibit poor generalization to unseen patient anatomies", "questions": "1. The motivation is cancer detection and the dataset claims to have lesions. Why is there no benchmark, metric, or qualitative result related to lesion detection or reconstruction in Section 4?\n\n2. Given the N=4 patient limitation, how can the community be confident that models trained on this data are learning generalizable features of prostate USCT, rather than just overfitting to the 4 specific pelvic bone structures in the dataset?\n\n3. Can you please clarify the actual aperture size used for the 322 receivers? Is it 60mm (Table 3) or 150mm (Section 3.4)? How does this compare to the real-world probes in Figure 2a you aim to model?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. This is the first public, large-scale dataset specifically for limited-angle prostate USCT.\n\n2. The method of creating phantoms by combining real MRI/CT anatomical structures with ex vivo SOS measurements is a key strength, ensuring high anatomical realism \n\n3. Providing the FDTD and Runge-Kutta solvers is a valuable contribution that enhances reproducibility and enables future work.\n\n4. The authors are transparent about the failures of current DL methods, particularly in resolving fine details and in OOD generalization , which correctly frames this as a challenging open problem.", "weaknesses": "1. The most significant weakness is that the 280,000 samples are derived from the anatomical structures of only 4 patients. This homogeneity means models may simply overfit to these 4 anatomical configurations, and the \"patient-level\" OOD test (train on 3, test on 1) is statistically insufficient to make strong claims about generalization.\n\n2. The paper is heavily motivated by cancer detection and claims the dataset includes \"synthetic lesions\". However, the entire benchmark and results section focuses only on reconstructing general anatomy . The clinical-facing motivation is completely disconnected from the actual technical evaluation.\n\n3. The use of 2D simulation is a major simplification. It ignores real-world 3D propagation and out-of-plane scattering effects, meaning models trained on this data may not be at all applicable to real 3D clinical systems.\n\n4. There is a contradiction in the text regarding the simulation aperture. The text implies a wide aperture (\"entire lateral extent\" of 150mm), while Table 3 suggests a 60mm length. Both 60mm and 150mm seem much larger than the clinical probes shown in Figure 2a. This suggests the simulation may be providing more data than a real probe, making the problem artificially easier.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "2IVKXZYc1c", "reviewer": "Reviewer_KYSw", "summary": "The authors introduced OPENPROS, the first large-scale benchmark dataset for limited-angle prostate Ultrasound computed tomography, designed to evaluate machine learning algorithms for inverse problems. Baseline comparisons proposed based on physics-based approaches and DL-based approaches. Dataset is open source, and seems like quite clinically meaningful in the specific use case. However, several limitations exists. For example but not limited to, it is hard for me to evaluate if it is truly clinically meaningful because I’m lacking the specific domain knowledge, etc.", "questions": "1. “Our dataset comprises over 280,000 paired 2D SOS phantoms and ultrasound full-waveform data derived from anatomically realistic 3D prostate models generated from clinical MRI/CT scans and ex vivo ultrasound measurements, annotated meticulously by clinical experts.” Have all these patients underwent RP to take the whole prostate out so that you can do the ex vivo measurement? Or it is just ex vivo phantoms measurements?\n2. “In our specific configuration, each SOS map has a spatial resolution of 401 × 161 grid points.” Is the physical resolution the same across different SOS maps?\n3. Is the simulated ultrasound meaningful enough in your use case in comparison to real patients’ ultrasound?\n4. “To best mimic the tissue heterogeneity, we employed Gaussian distributions with given mean values and standard deviations from the tissue database to assign speed of sound in different tissue types.” Do you have any references saying this approach could be reasonable?\n5. When the authors introduced the samples, rather than only mention 280,000 slides, it would be better to also mention how many patients got involved in the study and the dataset, since generally you would like to split the train/test set by patients, not by slides to guarantee the independence.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The proposed dataset size is large.\n2. The authors stated that this dataset is the first one in their specific use case, could be meaningful.\t \n3. The manuscript is well-written.", "weaknesses": "1. More detailed explanation of the relationships in between USTC, 2D SOS phantoms and ultrasound is needed. I cannot understand the clinical problem behind. Many reviewers have expertise in medical imaging, many also have expertise in prostate imaging, but I guess very limit readers and reviewers understand the relationship among them. For example, although I’m familiar with abdominal imaging and related applications, when I looked at the statement “Our dataset comprises over 280,000 paired 2D SOS phantoms and ultrasound full-waveform data derived from anatomically realistic 3D prostate models generated from clinical MRI/CT scans and ex vivo ultrasound measurements, annotated meticulously by clinical experts.”, I don’t know what does it really mean. 280,000 is a very large number in general, but what about in the context of USTC, 2D SOS phantoms, etc. ? What should I focus? I think this part needs to be emphasized since you are proposing a dataset, and it should impress the readers about the quantity of the data, quality of the data and the clinical meaningfulness about the proposal. Now I don’t feel them. Or, maybe it is purely my lack of expertise. If other reviewers have the similar problem or questions, I would like to suggest you to seek for conferences like MICCAI, or journals like IEEE TMI, MIA etc. I do believe that you put lots of effort into the dataset, but it’s hard for me to really measure it. \n2. “It contains anatomically realistic 2D speed-of-sound phantoms, organ segmentation labels, and corresponding simulated ultrasound waveforms derived from detailed 3D digital prostate models.” It seems like the data are generated from phantoms not patients, and the ultrasound waveforms were simulated. Therefore, how the study really means in clinical applications might be questionable.\n3. “two data-driven models: CNN-based InversionNet Wu & Lin (2019) and a Vision Transformer (ViT)-based variant Dosovitskiy et al. (2020), referred to here as ViT-Inversion.” No image reconstruction methods related to inverse problems like UNet-like or Diffusion-based models (could be other generative models) introduced.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)