arXiv subjects

Umberto Villa

Publications and source records attributed to Umberto Villa.

At least 19 recordsLinked to original sources

arXiv2026

A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling

Diffusion models provide expressive data-driven priors for Bayesian inverse problems, but many diffusion posterior samplers rely on heuristic guidance approximations that can fail for nonlinear operators and multimodal posteriors. In this work, we develop a stabilized path-space framework for diffusion-based posterior sampling. Starting from a base diffusion process whose terminal marginal represents the prior, we define a likelihood-weighted target measure on trajectories and cast posterior sampling as learning a controlled stochastic process whose path measure matches this target. This formulation connects diffusion posterior sampling to stochastic optimal control while preserving the Bayesian structure needed for uncertainty quantification. We introduce a time reparameterization that makes the path-space control problem well posed by removing the bias induced by the unknown initial value function, without auxiliary training. We then learn the control via a trust-region path-space optimization method with log-variance objectives. The path-space perspective also unifies our learned control approach with existing guidance-based samplers, quantifies the sampling error induced by approximate controls, and yields importance sampling corrections for asymptotically exact posterior expectations. We evaluate the proposed framework on a suite of benchmark inverse problems with analytically characterized or high-quality reference posteriors, enabling principled assessment of sampling accuracy and uncertainty quantification. These experiments provide insight into the behavior of diffusion-based posterior samplers and demonstrate improved accuracy and robustness over leading approaches.

cs.LG↗

arXiv2026

Survey of Deep Learning and Physics-Based Approaches in Computational Wave Imaging

Computational wave imaging (CWI) extracts hidden structure and physical properties of a volume of material by analyzing wave signals that traverse that volume. Applications include seismic exploration of the Earth's subsurface, acoustic imaging and non-destructive testing in material science, and ultrasound computed tomography in medicine. Current approaches for solving CWI problems can be divided into two categories: those rooted in traditional physics, and those based on deep learning. Physics-based methods stand out for their ability to provide high-resolution and quantitatively accurate estimates of acoustic properties within the medium. However, they can be computationally intensive and are susceptible to ill-posedness and nonconvexity typical of CWI problems. Machine learning-based computational methods have recently emerged, offering a different perspective to address these challenges. Diverse scientific communities have independently pursued the integration of deep learning in CWI. This review discusses how contemporary scientific machine-learning (ML) techniques, and deep neural networks in particular, have been developed to enhance and integrate with traditional physics-based methods for solving CWI problems. We present a structured framework that consolidates existing research spanning multiple domains, including computational imaging, wave physics, and data science. This study concludes with important lessons learned from existing ML-based methods and identifies technical hurdles and emerging trends through a systematic analysis of the extensive literature on this topic.

cs.LG↗

arXiv2026

A Learning-based Framework for Spatial Impulse Response Compensation in 3D Photoacoustic Computed Tomography

Photoacoustic computed tomography (PACT) is a promising imaging modality that combines the advantages of optical contrast with ultrasound detection. Utilizing ultrasound transducers with larger surface areas can improve detection sensitivity. However, when computationally efficient analytic reconstruction methods that neglect the spatial impulse responses (SIRs) of the transducer are employed, the spatial resolution of the reconstructed images will be compromised. Although optimization-based reconstruction methods can explicitly account for SIR effects, their computational cost is generally high, particularly in three-dimensional (3D) applications. To address the need for accurate but rapid 3D PACT image reconstruction, this study presents a framework for establishing a learned SIR compensation method that operates in the data domain. The learned compensation method maps SIR-corrupted PACT measurement data to compensated data that would have been recorded by idealized point-like transducers. Subsequently, the compensated data can be used with a computationally efficient reconstruction method that neglects SIR effects. Two variants of the learned compensation model are investigated that employ a U-Net model and a specifically designed, physics-inspired model, referred to as Deconv-Net. A fast and analytical training data generation procedure is also a component of the presented framework. The framework is rigorously validated in virtual imaging studies, demonstrating resolution improvement and robustness to noise variations, object complexity, and sound speed heterogeneity. When applied to in-vivo breast imaging data, the learned compensation models revealed fine structures that had been obscured by SIR-induced artifacts. To our knowledge, this is the first demonstration of learned SIR compensation in 3D PACT imaging.

cs.LG↗

arXiv2026

Benchmarking Deep Learning-Based Reconstruction Methods for Photoacoustic Computed Tomography with Clinically Relevant Synthetic Datasets

Deep learning (DL)-based image reconstruction methods for photoacoustic computed tomography (PACT) have developed rapidly in recent years. However, most existing methods have not employed standardized datasets, and their evaluations rely on traditional image quality (IQ) metrics that may lack clinical relevance. The absence of a standardized framework for clinically meaningful IQ assessment hinders fair comparison and raises concerns about the reproducibility and reliability of reported advancements in PACT. A benchmarking framework is proposed that provides open-source, anatomically plausible synthetic datasets and evaluation strategies for DL-based acoustic inversion methods in PACT. The datasets each include over 11,000 two-dimensional (2D) stochastic breast objects with clinically relevant lesions and paired measurements at varying modeling complexity. The evaluation strategies incorporate both traditional and task-based IQ measures to assess fidelity and clinical utility. A preliminary benchmarking study is conducted to demonstrate the framework's utility by comparing DL-based and physics-based reconstruction methods. The benchmarking study demonstrated that the proposed framework enabled comprehensive, quantitative comparisons of reconstruction performance and revealed important limitations in certain DL-based methods. Although they performed well according to traditional IQ measures, they often failed to accurately recover lesions. This highlights the inadequacy of traditional metrics and motivates the need for task-based assessments. The proposed benchmarking framework enables systematic comparisons of DL-based acoustic inversion methods for 2D PACT. By integrating clinically relevant synthetic datasets with rigorous evaluation protocols, it enables reproducible, objective assessments and facilitates method development and system optimization in PACT.

physics.med-ph↗

arXiv2026

A Convergent Generalized Krylov Subspace Method for Compressed Sensing MRI Reconstruction with Gradient-Driven Denoisers

Model-based reconstruction plays a key role in compressed sensing (CS) MRI, as it incorporates effective image regularizers to improve the quality of reconstruction. The Plug-and-Play and Regularization-by-Denoising frameworks leverage advanced denoisers (e.g., convolutional neural network (CNN)-based denoisers) and have demonstrated strong empirical performance. However, their theoretical guarantees remain limited, as practical CNNs often violate key assumptions. In contrast, gradient-driven denoisers achieve competitive performance, and the required assumptions for theoretical analysis are easily satisfied. However, solving the associated optimization problem remains computationally demanding. To address this challenge, we propose a generalized Krylov subspace method (GKSM) to solve the optimization problem efficiently. Moreover, we also establish rigorous convergence guarantees for GKSM in nonconvex settings. Numerical experiments on CS MRI reconstruction with spiral and radial acquisitions validate both the computational efficiency of GKSM and the accuracy of the theoretical predictions. The proposed optimization method is applicable to any linear inverse problem.

eess.IV↗

arXiv2025

Taylor Approximation Variance Reduction for Approximation Errors in PDE-constrained Bayesian Inverse Problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors (between the accurate parameter-to-observable mapping and the surrogate). The statistics of these errors are in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

math.OC↗

arXiv2025

Stochastic numerical head phantoms to enable virtual imaging studies of transcranial photoacoustic computed tomography

Transcranial photoacoustic computed tomography (PACT) is an emerging neuroimaging modality, but skull-induced aberrations can result in severe image artifacts if not compensated for during image reconstruction. The development of advanced image reconstruction methods for transcranial PACT is hindered by the lack of well-characterized, clinically relevant evaluation frameworks. Virtual imaging studies offer a solution, but require realistic numerical phantoms. To address this need, this study introduces a framework for generating ensembles of realistic 3D numerical head phantoms for virtual imaging studies. The framework uses adjunct CT data to create anatomical phantoms, which are then enhanced with stochastically synthesized vasculature and assigned realistic optical and acoustic-elastic properties. The utility of the framework is demonstrated through a case study on the impact of skull modeling errors on transcranial PACT image quality. By allowing researchers to assess and refine reconstruction methods meaningfully, the presented framework is expected to accelerate the development of transcranial PACT.

physics.med-ph↗

arXiv2025

Application of a Virtual Imaging Framework for Investigating a Deep Learning-Based Reconstruction Method for 3D Quantitative Photoacoustic Computed Tomography

Quantitative photoacoustic computed tomography (qPACT) is a promising imaging modality for estimating physiological parameters such as blood oxygen saturation. However, developing robust qPACT reconstruction methods remains challenging due to computational demands, modeling difficulties, and experimental uncertainties. Learning-based methods have been proposed to address these issues but remain largely unvalidated. Virtual imaging (VI) studies are essential for validating such methods early in development, before proceeding to less-controlled phantom or in vivo studies. Effective VI studies must employ ensembles of stochastically generated numerical phantoms that accurately reflect relevant anatomy and physiology. Yet, most prior VI studies for qPACT relied on overly simplified phantoms. In this work, a realistic VI testbed is employed for the first time to assess a representative 3D learning-based qPACT reconstruction method for breast imaging. The method is evaluated across subject variability and physical factors such as measurement noise and acoustic aberrations, offering insights into its strengths and limitations.

physics.med-ph↗

arXiv2025

A Virtual Imaging Framework for Three-Dimensional Quantitative Optoacoustic Tomography Using Stochastic Numerical Breast Phantoms

Optoacoustic tomography (OAT) is a promising modality for breast cancer diagnosis because tumor angiogenesis and, potentially, hypoxia can be visualized using quantitative OAT (qOAT) techniques. Clinically meaningful inference generally requires accurate image reconstruction, which depends on measurement quality and the imager design. Virtual imaging offers a cost-effective alternative to experimental prototyping for system design evaluation and supports computational method development. This work presents a comprehensive virtual imaging framework for breast qOAT, extending a stochastic numerical breast phantom (NBP) generator by incorporating skin tone variation and both benign and malignant lesions. It enables end-to-end simulation, modeling transducer spatial and acousto-electric impulse responses. Its utility is demonstrated through a case study comparing two system designs. A total of 1,020 NBPs and associated measurement data have been made publicly available to accelerate research in optoacoustic and optical imaging. The framework provides a versatile platform for advancing computational methods and guiding system design optimization.

physics.med-ph↗

arXiv2025

Benchmarking Diffusion Annealing-Based Bayesian Inverse Problem Solvers

In recent years, the ascendance of diffusion modeling as a state-of-the-art generative modeling approach has spurred significant interest in their use as priors in Bayesian inverse problems. However, it is unclear how to optimally integrate a diffusion model trained on the prior distribution with a given likelihood function to obtain posterior samples. While algorithms developed for this purpose can produce high-quality, diverse point estimates of the unknown parameters of interest, they are often tested on problems where the prior distribution is analytically unknown, making it difficult to assess their performance in providing rigorous uncertainty quantification. Motivated by this challenge, this work introduces three benchmark problems for evaluating the performance of diffusion model based samplers. The benchmark problems, which are inspired by problems in image inpainting, x-ray tomography, and phase retrieval, have a posterior density that is analytically known. In this setting, approximate ground-truth posterior samples can be obtained, enabling principled evaluation of the performance of posterior sampling algorithms. This work also introduces a general framework for diffusion model based posterior sampling, Bayesian Inverse Problem Solvers through Diffusion Annealing (BIPSDA). This framework unifies several recently proposed diffusion-model-based posterior sampling algorithms and contains novel algorithms that can be realized through flexible combinations of design choices. We tested the performance of a set of BIPSDA algorithms, including previously proposed state-of-the-art approaches, on the proposed benchmark problems. The results provide insight into the strengths and limitations of existing diffusion-model based posterior samplers, while the benchmark problems provide a testing ground for future algorithmic developments.

math.OC↗

arXiv2025

Predictive Digital Twins with Quantified Uncertainty for Patient-Specific Decision Making in Oncology

Quantifying the uncertainty in predictive models is critical for establishing trust and enabling risk-informed decision making for personalized medicine. In contrast to one-size-fits-all approaches that seek to mitigate risk at the population level, digital twins enable personalized modeling thereby potentially improving individual patient outcomes. Realizing digital twins in biomedicine requires scalable and efficient methods to integrate patient data with mechanistic models of disease progression. This study develops an end-to-end data-to-decisions methodology that combines longitudinal non-invasive imaging data with mechanistic models to estimate and predict spatiotemporal tumor progression accounting for patient-specific anatomy. Through the solution of a statistical inverse problem, imaging data inform the spatially varying parameters of a reaction-diffusion model of tumor progression. An efficient parallel implementation of the forward model coupled with a scalable approximation of the Bayesian posterior distribution enables rigorous, but tractable, quantification of uncertainty due to the sparse, noisy measurements. The methodology is verified on a virtual patient with synthetic data to control for model inadequacy, noise level, and the frequency of data collection. The application to decision-making is illustrated by evaluating the importance of imaging frequency and formulating an optimal experimental design question. The clinical relevance is demonstrated through a model validation study on a cohort of patients with publicly available longitudinal imaging data.

cs.CE↗

arXiv2025

Learned Correction Methods for Ultrasound Computed Tomography Imaging Using Simplified Physics Models

Ultrasound computed tomography (USCT) is an emerging modality for breast imaging. Image reconstruction methods that incorporate accurate wave physics produce high resolution quantitative images of acoustic properties but are computationally expensive. The use of a simplified linear model in reconstruction reduces computational expense at the cost of reduced accuracy. This work aims to systematically compare different learning approaches for USCT reconstruction utilizing simplified linear models. This work considered various learning approaches to compensate for errors stemming from a linearized wave propagation model: correction in the data and image domains. The resulting image reconstruction methods are systematically assessed, alongside data-driven and model-based methods, in four virtual imaging studies utilizing anatomically realistic numerical phantoms. Image quality was assessed utilizing relative root mean square error (RRMSE), structural similarity index measure (SSIM), and a task-based assessment for tumor detection. Correction in the measurement domain resulted in images with minor visual artifacts and highly accurate task performance. Correction in the image domain demonstrated a heavy bias on training data, resulting in hallucinations, but greater robustness to measurement noise. Combining both forms of correction performed best in terms of RRMSE and SSIM, at the cost of task performance. This work systematically assessed learned reconstruction methods incorporating an approximated physical model for USCT imaging. Results demonstrated the importance of incorporating physics, compared to data-driven methods. Learning a correction in the data domain led to better task performance and robust out-of-distribution generalization compared to correction in the image domain.

eess.IV↗

arXiv2024

Learning a Filtered Backprojection Reconstruction Method for Photoacoustic Computed Tomography with Hemispherical Measurement Geometries

In certain three-dimensional (3D) applications of photoacoustic computed tomography (PACT), including \textit{in vivo} breast imaging, hemispherical measurement apertures that enclose the object within their convex hull are employed for data acquisition. Data acquired with such measurement geometries are referred to as \textit{half-scan} data, as only half of a complete spherical measurement aperture is employed. Although previous studies have demonstrated that half-scan data can uniquely and stably reconstruct the sought-after object, no closed-form reconstruction formula for use with half-scan data has been reported. To address this, a semi-analytic reconstruction method in the form of filtered backprojection (FBP), referred to as the half-scan FBP method, is developed in this work. Because the explicit form of the filtering operation in the half-scan FBP method is not currently known, a learning-based method is proposed to approximate it. The proposed method is systematically investigated by use of virtual imaging studies of 3D breast PACT that employ ensembles of numerical breast phantoms and a physics-based model of the data acquisition process. The method is subsequently applied to experimental data acquired in an \textit{in vivo} breast PACT study. The results confirm that the half-scan FBP method can accurately reconstruct 3D images from half-scan data. Importantly, because the sought-after inverse mapping is well-posed, the reconstruction method remains accurate even when applied to data that differ considerably from those employed to learn the filtering operation.

physics.med-ph↗

arXiv2024

Investigating the Use of Traveltime and Reflection Tomography for Deep Learning-Based Sound-Speed Estimation in Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) quantifies acoustic tissue properties such as the speed-of-sound (SOS). Although full-waveform inversion (FWI) is an effective method for accurate SOS reconstruction, it can be computationally challenging for large-scale problems. Deep learning-based image-to-image learned reconstruction (IILR) methods can offer computationally efficient alternatives. This study investigates the impact of the chosen input modalities on IILR methods for high-resolution SOS reconstruction in USCT. The selected modalities are traveltime tomography (TT) and reflection tomography (RT), which produce a low-resolution SOS map and a reflectivity map, respectively. These modalities have been chosen for their lower computational cost relative to FWI and their capacity to provide complementary information: TT offers a direct SOS measure, while RT reveals tissue boundary information. Systematic analyses were facilitated by employing a virtual USCT imaging system with anatomically realistic numerical breast phantoms. Within this testbed, a supervised convolutional neural network (CNN) was trained to map dual-channel (TT and RT images) to a high-resolution SOS map. Single-input CNNs were trained separately using inputs from each modality alone (TT or RT) for comparison. The accuracy of the methods was systematically assessed using normalized root mean squared error (NRMSE), structural similarity index measure (SSIM), and peak signal-to-noise ratio (PSNR). For tumor detection performance, receiver operating characteristic analysis was employed. The dual-channel IILR method was also tested on clinical human breast data. Ensemble average of the NRMSE, SSIM, and PSNR evaluated on this clinical dataset were 0.2355, 0.8845, and 28.33 dB, respectively.

eess.IV↗

arXiv2024

Optimizing Quantitative Photoacoustic Imaging Systems: The Bayesian Cramér-Rao Bound Approach

Quantitative photoacoustic computed tomography (qPACT) is an emerging medical imaging modality that carries the promise of high-contrast, fine-resolution imaging of clinically relevant quantities like hemoglobin concentration and blood-oxygen saturation. However, qPACT image reconstruction is governed by a multiphysics, partial differential equation (PDE) based inverse problem that is highly non-linear and severely ill-posed. Compounding the difficulty of the problem is the lack of established design standards for qPACT imaging systems, as there is currently a proliferation of qPACT system designs for various applications and it is unknown which ones are optimal or how to best modify the systems under various design constraints. This work introduces a novel computational approach for the optimal experimental design (OED) of qPACT imaging systems based on the Bayesian Cramér-Rao bound (CRB). Our approach incorporates several techniques to address challenges associated with forming the bound in the infinite-dimensional function space setting of qPACT, including priors with trace-class covariance operators and the use of the variational adjoint method to compute derivatives of the log-likelihood function needed in the bound computation. The resulting Bayesian CRB based design metric is computationally efficient and independent of the choice of estimator used to solve the inverse problem. The efficacy of the bound in guiding experimental design was demonstrated in a numerical study of qPACT design schemes under a stylized two-dimensional imaging geometry. To the best of our knowledge, this is the first work to propose Bayesian CRB based design for systems governed by PDEs.

physics.med-ph↗

arXiv2024

ProxNF: Neural Field Proximal Training for High-Resolution 4D Dynamic Image Reconstruction

Accurate spatiotemporal image reconstruction methods are needed for a wide range of biomedical research areas but face challenges due to data incompleteness and computational burden. Data incompleteness arises from the undersampling often required to increase frame rates, while computational burden emerges due to the memory footprint of high-resolution images with three spatial dimensions and extended time horizons. Neural fields (NFs), an emerging class of neural networks that act as continuous representations of spatiotemporal objects, have previously been introduced to solve these dynamic imaging problems by reframing image reconstruction as a problem of estimating network parameters. Neural fields can address the twin challenges of data incompleteness and computational burden by exploiting underlying redundancies in these spatiotemporal objects. This work proposes ProxNF, a novel neural field training approach for spatiotemporal image reconstruction leveraging proximal splitting methods to separate computations involving the imaging operator from updates of the network parameters. Specifically, ProxNF evaluates the (subsampled) gradient of the data-fidelity term in the image domain and uses a fully supervised learning approach to update the neural field parameters. This method is demonstrated in two numerical phantom studies and an in-vivo application to tumor perfusion imaging in small animal models using dynamic contrast-enhanced photoacoustic computed tomography (DCE PACT).

eess.IV↗

arXiv2024

Revisiting the joint estimation of initial pressure and speed-of-sound distributions in photoacoustic computed tomography with consideration of canonical object constraints

In photoacoustic computed tomography (PACT) the accurate estimation of the initial pressure (IP) distribution generally requires knowledge of the object's heterogeneous speed-of-sound (SOS) distribution. Although hybrid imagers that combine ultrasound tomography with PACT have been proposed, in many current applications of PACT the SOS distribution remains unknown. Joint reconstruction (JR) of the IP and SOS distributions from PACT measurement data alone can address this issue. However, this joint estimation problem is ill-posed and corresponds to a non-convex optimization problem. While certain regularization strategies have been deployed, stabilizing the JR problem to yield accurate estimates of the IP and SOS distributions has remained an open challenge. To address this, the presented numerical studies explore the effectiveness of easy to implement canonical object constraints for stabilizing the JR problem. The considered constraints include support, bound, and total variation constraints, which are incorporated into an optimization-based method for JR. Computer-simulation studies that employ anatomically realistic numerical breast phantoms are conducted to evaluate the impact of these object constraints on JR accuracy. Additionally, the impact of certain data inconsistencies, such as caused by measurement noise and physics modeling mismatches, on the effectiveness of the object constraints is investigated. The results demonstrate, for the first time, that the incorporation of canonical object constraints in an optimization-based image reconstruction method holds significant potential for mitigating the ill-posed nature of the PACT JR problem.

physics.med-ph↗

arXiv2024

Democratizing Uncertainty Quantification

Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling Bridge), a high-level abstraction and software protocol that facilitates universal interoperability of UQ software with simulation codes. It breaks down the technical complexity of advanced UQ applications and enables separation of concerns between experts. UM-Bridge democratizes UQ by allowing effective interdisciplinary collaboration, accelerating the development of advanced UQ methods, and making it easy to perform UQ analyses from prototype to High Performance Computing (HPC) scale. In addition, we present a library of ready-to-run UQ benchmark problems, all easily accessible through UM-Bridge. These benchmarks support UQ methodology research, enabling reproducible performance comparisons. We demonstrate UM-Bridge with several scientific applications, harnessing HPC resources even using UQ codes not designed with HPC support.

cs.MS↗