Inverse Problems In Imaging Research Articles

Probabilistic geophysical inversion of complex resistivity measurements using the Hamiltonian Monte Carlo method

Summary In this work, we introduce the probabilistic inversion of tomographic complex resistivity (CR) measurements using the Hamiltonian Monte Carlo (HMC) method. The posterior model distribution on which our approach operates accounts for the underlying complex-valued nature of the CR imaging problem accurately by including the individual errors of the measured impedance magnitude and phase, allowing for the application of independent regularization on the inferred subsurface conductivity magnitude and phase, and incorporating the effects of cross-sensitivities. As the tomographic CR inverse problem is non-linear, of high dimension and features strong correlations between model parameters, efficiently sampling from the posterior model distribution is challenging. To meet this challenge we use HMC, a Markov-chain Monte Carlo method that incorporates gradient information to achieve efficient model updates. To maximize the benefit of a given number of forward calculations, we use the No-U-Turn sampler (NUTS) as a variant of HMC. We demonstrate the probabilistic inversion approach on a synthetic CR tomography measurement. The NUTS succeeds in creating a sample of the posterior model distribution that provides us with the ability to analyze correlations between model parameters and to calculate statistical estimators of interest, such as the mean model and the covariance matrix. Our results provide a strong basis for the characterization of the posterior model distribution and uncertainty quantification in the context of the tomographic CR inverse problem.

Diffusion-model-based inverse problem processing for optically-measured sound field

This paper proposes a diffusion-model-based method for addressing inverse problems in optical sound-field imaging. Optical sound-field imaging, known for its high spatial resolution, measures sound by detecting small variations in the refractive index of air caused by sound but often suffers from unavoidable noise contamination. Therefore, we present a diffusion model-based approach for sound-field inverse problems, including denoising, noisy sound-field reconstruction and extrapolation. During inference, sound-field degradation is introduced into the inverse denoising process, with range-null space decomposition used as a solver to handle degradation, iteratively generating degraded sound-field information. Numerical experiments show that our method outperforms other deep-learning-based methods in denoising and reconstruction tasks, and obtains effective results in extrapolation task. The experimental results demonstrate the applicability of our model to the real world.

ISRSL0: compressed sensing MRI with image smoothness regularized-smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} norm

The reconstruction of MR images has always been a challenging inverse problem in medical imaging. Acceleration of MR scanning is of great importance for clinical research and cutting-edge applications. One of the primary efforts to achieve this is using compressed sensing (CS) theory. The CS aims to reconstruct MR images using a small number of sampled data in k-space. The CS-MRI techniques face challenges, including the potential loss of fine structure and increased computational complexity. We introduce a novel framework based on a regularized sparse recovery problem and a sharpening step to improve the CS-MRI approaches regarding fine structure loss under high acceleration factors. This problem is solved via the Half Quadratic Splitting (HQS) approach. The inverse problem for reconstructing MR images is converted into two distinct sub-problems, each of which can be solved separately. One key feature of the proposed approach is the replacement of one sub-problem with a denoiser. This regularization assists the optimization of the Smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} (SL0) norm in escaping local minimums and enhances its precision. The proposed method consists of smoothing, feature modification, and Smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} cost function optimization. The proposed approach improves the SL0 algorithm for MRI reconstruction without complicating it. The convergence of the proposed approach is illustrated analytically. The experimental results show an acceptable performance of the proposed method compared to the network-based approaches.

Space-time reconstruction for lensless imaging using implicit neural representations

Many computational imaging inverse problems are challenged by noise, model mismatch, and other imperfections that decrease reconstruction quality. For data taken sequentially in time, instead of reconstructing each frame independently, space-time algorithms simultaneously reconstruct multiple frames, thereby taking advantage of temporal redundancy through space-time priors. This helps with denoising and provides improved reconstruction quality, but often requires significant computational and memory resources. Designing effective but flexible temporal priors is also challenging. Here, we propose using an implicit neural representation to model dynamics and act as a computationally tractable and flexible space-time prior. We demonstrate this approach on video captured with a lensless imager, DiffuserCam, and show improved reconstruction results and robustness to noise compared to frame-by-frame methods.

Auto-weighted Bayesian Physics-Informed Neural Networks and robust estimations for multitask inverse problems in pore-scale imaging of dissolution

Auto-weighted Bayesian Physics-Informed Neural Networks and robust estimations for multitask inverse problems in pore-scale imaging of dissolution

Imaging light fluence in blood vessels by combining photoacoustic fluctuation imaging and ultrasound power Doppler

Objectives. Numerous optical biomedical imaging or therapeutic modalities suffer from unknown light fluence distribution at depths. Photoacoustic (PA) imaging, which enables imaging blood vessels at the acoustic resolution, probes the product between the fluence and effective optical absorption that depends on the size or density of blood vessels. In the case of unresolved vessels, fluence and absorption can not be decoupled using PA imaging alone without the use of inverse problems. Thus, we propose combining two modalities that are sensitive to blood vessels to directly image fluence maps within vascularized areas, including in unresolved vessels. Approach. To achieve fluence imaging, the combination of photoacoustic fluctuation (PAFI) and Ultrasound Power Doppler (UPD) images is considered. After exposing a new theoretical expression of the UPD image, we establish a fluence imaging method giving quantitative fluence in blood vessels. Fluence imaging involves resolution compensation with a PSF filter that is compared to alternative simpler corrections. Main results. This method universally applies to arbitrary hematocrit and multi-scale vessel imaging. Using a spherical sparse array, we demonstrate 3D fluence imaging within blood vessels in simulation and experiments which is not possible with PAFI alone. Significance. Overall, we show that combining PAFI and UPD has the potential for real-time light dosimetry or could enhance quantitative inverse problems in PA imaging.

Robustness and exploration of variational and machine learning approaches to inverse problems: An overview

AbstractThis paper provides an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations. In this context results of numerical experiments for a one‐dimensional toy problem are provided, showing the robustness of different approaches and empirically verifying theoretical guarantees. Another focus of this review is the exploration of the subspace of data‐consistent solutions through explicit guidance to satisfy specific semantic or textural properties.

Validation of a multilayer perceptron for rapid, direct solution of the electrical impedance tomography inverse problem

Validation of a multilayer perceptron for rapid, direct solution of the electrical impedance tomography inverse problem

ERT image reconstruction using marker region segmentation method

Abstract Inspired by image region segmentation method, a marking region segmentation iterative method is proposed to reconstruct sparse binary images of electrical resistance tomography. The grayscale matrix of the iteration process is mapped to another linear space for segmentation processing, adding the watershed thresholding of marking regions. In the iteration process for estimating conductivity distribution, the target regions are separated to avoid excessive segmentation effects. By applying this method in conjunction with the Landweber iterative model to solve the inverse problem of resistivity tomography imaging, more accurate binary images can be obtained, and the method exhibits superior convergence properties in comparison to the Landweber algorithm. To verify the reconstruction effectiveness of LW-TDIS method, numerical simulations and static experiments are conducted for comparison with three other methods. The results demonstrate that the proposed method effectively reduces reconstruction artifacts, improves reconstruction quality, and achieves better reconstruction performance.

Neural‐network‐based regularization methods for inverse problems in imaging

AbstractThis review provides an introduction to—and overview of—the current state of the art in neural‐network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied mathematics and a basic understanding of neural networks to different concepts of applying neural networks for regularizing inverse problems in imaging. Distinguishing features of this review are, among others, an easily accessible introduction to learned generators and learned priors, in particular diffusion models, for inverse problems, and a section focusing explicitly on existing results in function space analysis of neural‐network‐based approaches in this context.

Research into super-resolution in medical imaging from 2000 to 2023: bibliometric analysis and visualization.

Super-resolution (SR) refers to the use of hardware or software methods to enhance the resolution of low-resolution (LR) images and produce high-resolution (HR) images. SR is applied frequently across a variety of medical imaging contexts, particularly in the enhancement of neuroimaging, with specific techniques including SR microscopy-used for diagnostic biomarkers-and functional magnetic resonance imaging (fMRI)-a neuroimaging method for the measurement and mapping of brain activity. This bibliometric analysis of the literature related to SR in medical imaging was conducted to identify the global trends in this field, and visualization via graphs was completed to offer insights into future research prospects. In order to perform a bibliometric analysis of the SR literature, this study sourced all publications from the Web of Science Core Collection (WoSCC) database published from January 1, 2000, to October 11, 2023. A total of 3,262 articles on SR in medical imaging were evaluated. VOSviewer was used to perform co-occurrence and co-authorship analysis, and network visualization of the literature data, including author, journal, publication year, institution, and keywords, was completed. From 2000 to 2023, the annual publication volume surged from 13 to 366. The top three journals in this field in terms of publication volume were as follows: (I) Scientific Reports (86 publications), (II) IEEE Transactions on Medical Imaging (74 publications), and (III) IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control (56 publications). The most prolific country, institution, and author were the United States (1,017 publications; 31,301 citations), the Chinese Academy of Sciences (124 publications; 2,758 citations), and Dinggang Shen (20 publications; 671 citations), respectively. A cluster analysis of the top 100 keywords was conducted, which revealed the presence of five co-occurrence clusters: (I) SR and artificial intelligence (AI) for medical image enhancement, (II) SR and inverse problem processing concepts for positron emission tomography (PET) image processing, (III) SR ultrasound through microbubbles, (IV) SR microscopy for Alzheimer and Parkinson diseases, and (V) SR in brain fMRI: rapid acquisition and precise imaging. The most recent high-frequency keywords were deep learning (DL), magnetic resonance imaging (MRI), and convolutional neural networks (CNNs). Over the past two decades, the output of publications by countries, institutions, and authors in the field of SR in medical imaging has steadily increased. Based on bibliometric analysis of international trends, the resurgence of SR in medical imaging has been facilitated by advancements in AI. The increasing need for multi-center and multi-modal medical images has further incentivized global collaboration, leading to the diverse research paths in SR medical imaging among prominent scientists.

Anisotropic tomography of eastern Tibet and its uncertainty from hypocentral errors

SUMMARY The mechanism responsible for the lateral expansion and uplift of the eastern Tibetan Plateau remains a topic of ongoing debate, partly due to discrepancies in the results of seismic velocity and anisotropy. In local earthquake tomography, hypocentral uncertainties can cause significant errors in the tomographic model. However, this issue has received limited attention in previous studies. In this work, we employ the weighted least-squares (WLS) method to solve the tomographic inversion problem. A power exponent coefficient, which is called weighting level, is introduced into the weighting matrix to control the relative contribution of the data with different hypocentral errors to the final tomographic result. Our data set contains high-quality Pg, Pn and Sg arrival times of local earthquakes recorded by the dense Chinese seismic network in eastern Tibet during 2008–2022. We comprehensively analyse the inversion results derived from the WLS inversions with different weighting levels to evaluate the robustness of isotropic velocity anomalies and azimuthal anisotropy. The most robust feature of our results is a striking low-velocity (low-Vp) zone surrounded by high-velocity (high-Vp) anomalies and fault parallel fast-velocity directions (FVDs) of azimuthal anisotropy in the lower crust beneath the western side of the Longmenshan fault zone. Taking into account many previous results of the region, we deem that the low-Vp zone reflects hot and wet upwelling flow from the deep asthenosphere, which ascends to the lower crust along the fault zone. At the NE margin of the Tibetan Plateau, significant low-Vp anomalies exist in the lower crust and the FVDs are consistent with the motion direction of the Tibetan block revealed by GPS (Global Positioning System) observations. We think that lower crustal flow exists beneath NE Tibet, which controls the plateau expansion toward the northeast. A low-Vp anomaly appears at 30 km depth beneath the Sichuan Basin. However, as the weighting level increases, the amplitude of this low-Vp anomaly decreases by more than 6 per cent, suggesting that this low-Vp anomaly has a lower accuracy than the other features.

Image reconstruction based on TV-L1 model for planar array capacitance defect detection

Planar array capacitive imaging is an emerging nondestructive testing (NDT) technology with broad application prospects. The severe ill-posed inverse problem of planar array capacitive imaging reduces quality of reconstructed images. In this paper, a total variation regularization model with an L1-norm (TV-L1 model) of 3 × 4 planar array capacitance imaging is established for imaging the defects detected in the inner layers of multi-layer composite components. Considering the solution instability caused by the non-differentiability of the TV-L1 model, a variable splitting self-adaptive augmented Lagrange alternating direction algorithm (VS-SALAD) is proposed. An augmented Lagrange method enhances model splitability, and a series of subproblems are obtained by variable splitting operation. The subproblems are solved iteratively using alternating minimization method with self-adaptive penalty parameter. Experimental results demonstrate that TV-L1 model effectively alleviates the ill-posed problem, and the proposed algorithm significantly improves both the quality of reconstructed images and solving speed of the TV-L1 model.

Simultaneous Activity and Attenuation Estimation in TOF-PET With TV-Constrained Nonconvex Optimization.

An alternating direction method of multipliers (ADMM) framework is developed for nonsmooth biconvex optimization for inverse problems in imaging. In particular, the simultaneous estimation of activity and attenuation (SAA) problem in time-of-flight positron emission tomography (TOF-PET) has such a structure when maximum likelihood estimation (MLE) is employed. The ADMM framework is applied to MLE for SAA in TOF-PET, resulting in the ADMM-SAA algorithm. This algorithm is extended by imposing total variation (TV) constraints on both the activity and attenuation map, resulting in the ADMM-TVSAA algorithm. The performance of this algorithm is illustrated using the penalized maximum likelihood activity and attenuation estimation (P-MLAA) algorithm as a reference.

Parametric investigation of flow and heat transfer on the reflooding quenching of a cylinder rod in forced convection

A reflooding quenching boiling experiment in forced convection was conducted to investigate the flow and heat transfer performance of a FeCrAl cylindrical rod under various subcooling degrees and flow rates. Employing image processing and inverse heat conduction problem (IHCP) methods, the research provides insights into vapor film thickness, quenching front propagation, wall temperature cooling rate and minimum film boiling temperature. Key observations include the presence of numerous extremely small bubbles dispersing around the rod and a third quenching front appears in the middle of the rod under higher subcooling condition at 25 °C, attributed to a thinner vapor film, smaller bubbles resulting from film rupture and the inertia of fluid flow. Within the experimental range, the impact of the subcooling degree on the fluid flow and heat transfer performance during the quenching boiling process is more pronounced than that of the coolant flow rate. The evolution of the vapor film indicates a substantial reduction of 78.76 % in film thickness and a significant increase of 185.71 % in propagation velocity with an increase in subcooling degree, while an elevation in flow rate lead to a 29.84 % decrease in film thickness and a 45 % increase in propagation velocity. Heat transfer performance benefits from increased subcooling degrees throughout the entire quenching boiling process, whereas flow rate impacts the heat transfer performance of film boiling alone. Furthermore, by incorporating the impact of flow velocity, a predictive formula for Tmin is established with an error margin within ±5 %.

A Loss Landscape Perspective and Simulations for Imaging Inverse Problems Based on AI and Neuron Network Training Method

A Loss Landscape Perspective and Simulations for Imaging Inverse Problems Based on AI and Neuron Network Training Method

Seismic Tomography 2024

ABSTRACT Seismic tomography is the most abundant source of information about the internal structure of the Earth at scales ranging from a few meters to thousands of kilometers. It constrains the properties of active volcanoes, earthquake fault zones, deep reservoirs and storage sites, glaciers and ice sheets, or the entire globe. It contributes to outstanding societal problems related to natural hazards, resource exploration, underground storage, and many more. The recent advances in seismic tomography are being translated to nondestructive testing, medical ultrasound, and helioseismology. Nearly 50 yr after its first successful applications, this article offers a snapshot of modern seismic tomography. Focused on major challenges and particularly promising research directions, it is intended to guide both Earth science professionals and early-career scientists. The individual contributions by the coauthors provide diverse perspectives on topics that may at first seem disconnected but are closely tied together by a few coherent threads: multiparameter inversion for properties related to dynamic processes, data quality, and geographic coverage, uncertainty quantification that is useful for geologic interpretation, new formulations of tomographic inverse problems that address concrete geologic questions more directly, and the presentation and quantitative comparison of tomographic models. It remains to be seen which of these problems will be considered solved, solved to some extent, or practically unsolvable over the next decade.

Principal Uncertainty Quantification With Spatial Correlation for Image Restoration Problems.

Uncertainty quantification for inverse problems in imaging has drawn much attention lately. Existing approaches towards this task define uncertainty regions based on probable values per pixel, while ignoring spatial correlations within the image, resulting in an exaggerated volume of uncertainty. In this paper, we propose PUQ (Principal Uncertainty Quantification) - a novel definition and corresponding analysis of uncertainty regions that takes into account spatial relationships within the image, thus providing reduced volume regions. Using recent advancements in generative models, we derive uncertainty intervals around principal components of the empirical posterior distribution, forming an ambiguity region that guarantees the inclusion of true unseen values with a user-defined confidence probability. To improve computational efficiency and interpretability, we also guarantee the recovery of true unseen values using only a few principal directions, resulting in more informative uncertainty regions. Our approach is verified through experiments on image colorization, super-resolution, and inpainting; its effectiveness is shown through comparison to baseline methods, demonstrating significantly tighter uncertainty regions.

Bayesian imaging inverse problem with SA-Roundtrip prior via HMC-pCN sampler

Bayesian inference with deep generative prior has received considerable interest for solving imaging inverse problems in many scientific and engineering fields. The selection of the prior distribution is learned from, and therefore an important representation learning of, available prior measurements. The SA-Roundtrip, a novel deep generative prior, is introduced to enable controlled sampling generation and identify the data's intrinsic dimension. This prior incorporates a self-attention structure within a bidirectional generative adversarial network. Subsequently, Bayesian inference is applied to the posterior distribution in the low-dimensional latent space using the Hamiltonian Monte Carlo with preconditioned Crank-Nicolson (HMC-pCN) algorithm, which is proven to be ergodic under specific conditions. Experiments conducted on computed tomography (CT) reconstruction with the MNIST and TomoPhantom datasets reveal that the proposed method outperforms state-of-the-art comparisons, consistently yielding a robust and superior point estimator along with precise uncertainty quantification.

NF-ULA: Normalizing Flow-Based Unadjusted Langevin Algorithm for Imaging Inverse Problems

NF-ULA: Normalizing Flow-Based Unadjusted Langevin Algorithm for Imaging Inverse Problems