Imaging Problems Research Articles

High precision 3D optical detection technology based on shear interferometry with arbitrarily shear amounts

Differential interferometry is an effective method that has high contrast and can effectively overcome the “duplicate image” problem caused by shear interferometry. However, differential interferometry is limited by the addition of additional optical elements, such as grating, Nomarski, or Wollaston prisms, to realize shear interference, and the shear amount is difficult to adjust. A 3D shape reconstruction algorithm based on shear interference is proposed in this paper, which is appropriate for arbitrary shear amounts and directions. This algorithm overcomes the problem of duplicate images through an iterative phase addition approach, and simulated 3D morphology results of surface irregular defects are successfully reconstructed under arbitrary shear directions and shear amounts such that the maximum reconstruction error is only 10−11 m. Furthermore, the morphologies of defects with large gradients can be obtained by adjusting the shear amount and applying an image interpolation approach, which can overcome the problem of phase ambiguity in monochromatic interferometry. Based on this algorithm, an optical testing system is designed that uses a mirror to adjust the shear amount and direction without adding additional optical elements to effectively simplify the experimental device and reduce the cost. Experiments are completed to confirm the feasibility of the proposed method, which can successfully obtain 3D morphology data of optical defects.

Pneumonia Disease Detection Using Chest X-Rays and Machine Learning

Pneumonia is a deadly disease affecting millions worldwide, caused by microorganisms and environmental factors. It leads to lung fluid build-up, making breathing difficult, and is a leading cause of death. Early detection and treatment are crucial for preventing severe outcomes. Chest X-rays are commonly used for diagnoses due to their accessibility and low costs; however, detecting pneumonia through X-rays is challenging. Automated methods are needed, and machine learning can solve complex computer vision problems in medical imaging. This research develops a robust machine learning model for the early detection of pneumonia using chest X-rays, leveraging advanced image processing techniques and deep learning algorithms that accurately identify pneumonia patterns, enabling prompt diagnosis and treatment. The research develops a CNN model from the ground up and a ResNet-50 pretrained model This study uses the RSNA pneumonia detection challenge original dataset comprising 26,684 chest array images collected from unique patients (56% male, 44% females) to build a machine learning model for the early detection of pneumonia. The data are made up of pneumonia (31.6%) and non-pneumonia (68.8%), providing an effective foundation for the model training and evaluation. A reduced size of the dataset was used to examine the impact of data size and both versions were tested with and without the use of augmentation. The models were compared with existing works, the model’s effectiveness in detecting pneumonia was compared with one another, and the impact of augmentation and the dataset size on the performance of the models was examined. The overall best accuracy achieved was that of the CNN model from scratch, with no augmentation, an accuracy of 0.79, a precision of 0.76, a recall of 0.73, and an F1 score of 0.74. However, the pretrained model, with lower overall accuracy, was found to be more generalizable.

Volumetric reconstruction of soot volume fraction through 3-D masked Tikhonov regularization

The ill-posed nature of the tomographic inverse problem for soot volume fraction reconstruction often creates artifacts and provides lower reconstruction accuracy, particularly when viewing angles are limited. In this study, a volumetric masked-based 3-D Tikhonov regularization method is proposed to reconstruct soot volume fraction in a purely absorbing flame. The 3-D Tikhonov regularization method addresses the ill-posedness by penalizing unrealistic variations in the soot volume fraction, thus enhancing the robustness of the reconstruction. Additionally, volumetric masking derived from light field ray-tracing refines the reconstruction by accurately defining the flame's boundaries and improving the soot volume fraction inversion accuracy. Numerical simulations were conducted on a bimodal asymmetric flame to analyze the effects of varying viewing angles and volumetric masking strategies. Experimental studies were also performed to reconstruct soot volume fraction under different combustion operating conditions. Both numerical simulations and experimental studies demonstrate that the proposed method not only works on a limited number of viewing angles but also mitigates the reconstruction artifacts and decreases the computational costs.

Adaptive local density estimation in tomography

We study the non-parametric estimation of a multidimensional unknown density f in a tomography problem based on independent and identically distributed observations, whose common density is proportional to the Radon transform of f. We identify the underlying statistical inverse problem and use a spectral cut-off regularization to deduce an estimator. A fully data-driven choice of the cut-off parameter m ∈ R + is proposed and studied. To discuss the bias-variance trade off, we consider Sobolev spaces and show the minimax-optimality of the spectral cut-off density estimator. In a simulation study, we illustrate a reasonable behaviour of the studied fully data-driven estimator.

The regularity of solutions to the L p Gauss image problem

Abstract The L p {L}_{p} Gauss image problem amounts to solving a class of Monge-Ampère type equations on the sphere. In this article, we discuss the regularity of solutions to the L p {L}_{p} Gauss image problem.

Stroke Detection and Monitoring by Means of a Multifrequency Microwave Inversion Approach

In the area of biomedical diagnostics, microwave imaging techniques have been recently proposed for performing brain stroke detection and monitoring. Indeed, theoretically, these techniques make it possible to meet the timeliness requirements of such a diagnosis with portable systems. Moreover, relying on the use of microwaves, they are noninvasive and allow continuous monitoring of critical patients. In this paper, the microwave imaging problem is solved by exploiting multifrequency data by an inexact-Newton method formulated in the framework of non-constant exponent Lebesgue spaces. First, the method is numerically validated with three-dimensional head models affected by anatomically-realistic strokes. Then, a further assessment through experimental data obtained with a cylindrical phantom is conducted. A quite accurate reconstruction of the variations of dielectric properties inside the patient’s head due to the insurgence of stroke is obtained in both numerical and experimental cases, showing the potentiality of the proposed approach.

BayesBay: A Versatile Bayesian Inversion Framework Written in Python

Abstract The lack of versatile tools for Bayesian inference presents a significant challenge to researchers in geophysics, who often resort to developing bespoke codes to address specific classes of inverse problems. In this study, we present BayesBay, a Python package for generalized transdimensional and hierarchical Markov chain Monte Carlo sampling. Leveraging object-oriented programming principles, BayesBay facilitates the definition of Bayesian sampling problems across a range of applications. This includes joint inversions of multiple data sets with different forward functions and unknown noise properties, as well as complex parameterizations involving multiple parameters with unknown dimensionality and/or spatially varying priors. We illustrate BayesBay from both a technical and a practical perspective. The first two applications are common in geophysics: a 2D tomographic problem and a joint inversion for the 1D subsurface structure. The third involves partition modeling and requires a sophisticated parameterization with two nested levels of transdimensionality. In all cases, BayesBay recovers known solutions, highlighting its potential to address a broad range of inverse problems.

The AIRI plug-and-play algorithm for image reconstruction in radio-interferometry: variations and robustness

Abstract Plug-and-Play (PnP) algorithms are appealing alternatives to proximal algorithms when solving inverse imaging problems. By learning a Deep Neural Network (DNN) denoiser behaving as a proximal operator, one waives the computational complexity of optimisation algorithms induced by sophisticated image priors, and the sub-optimality of handcrafted priors compared to DNNs. Such features are highly desirable in radio-interferometric (RI) imaging, where precision and scalability of the image reconstruction process are key. In previous work, we introduced AIRI, PnP counterpart to the unconstrained variant of the SARA optimisation algorithm, relying on a forward-backward algorithmic backbone. Here, we introduce variations of AIRI towards a more general and robust PnP paradigm in RI imaging. Firstly, we show that the AIRI denoisers can be used without any alteration to instantiate a PnP counterpart to the constrained SARA optimisation algorithm itself, relying on a primal-dual forward-backward algorithmic backbone, thus extending the remit of the AIRI paradigm. Secondly, we show that AIRI algorithms are robust to strong variations in the nature of the training dataset, with denoisers trained on medical images yielding similar reconstruction quality to those trained on astronomical images. Thirdly, we develop a functionality to quantify the model uncertainty introduced by the randomness in the training process. We validate the image reconstruction and uncertainty quantification functionality of AIRI algorithms against the SARA family and CLEAN, both in simulation and on real data of the ESO 137-006 galaxy acquired with the MeerKAT telescope. AIRI code is available in the BASPLib code library† on GitHub.

Transformer models for quantum gate set tomography

Quantum computation represents a promising frontier in the domain of high-performance computing, blending quantum information theory with practical applications to overcome the limitations of classical computation. This study investigates the challenges of manufacturing high-fidelity and scalable quantum processors. Quantum gate set tomography (QGST) is a critical method for characterizing quantum processors and understanding their operational capabilities and limitations. This paper introduces Ml4Qgst as a novel approach to QGST by integrating machine learning techniques, specifically utilizing a transformer neural network model. Adapting the transformer model for QGST addresses the computational complexity of modeling quantum systems. Advanced training strategies, including data grouping and curriculum learning, are employed to enhance model performance, demonstrating significant congruence with ground-truth values. We benchmark this training pipeline on the constructed learning model, to successfully perform QGST for 2 and 3 gates on single-qubit and two-qubit systems, with over-rotation error and depolarizing noise estimation with comparable accuracy to pyGSTi. This research marks a pioneering step in applying deep neural networks to the complex problem of quantum gate set tomography, showcasing the potential of machine learning to tackle nonlinear tomography challenges in quantum computing.

Grounding Grid Electrical Impedance Imaging Method Based on an Improved Conditional Generative Adversarial Network

The grounding grid is an important piece of equipment to ensure the safety of a power system, and thus research detecting on its corrosion status is of great significance. Electrical impedance tomography (EIT) is an effective method for grounding grid corrosion imaging. However, the inverse process of image reconstruction has pathological solutions, which lead to unstable imaging results. This paper proposes a grounding grid electrical impedance imaging method based on an improved conditional generative adversarial network (CGAN), aiming to improve imaging precision and accuracy. Its generator combines a preprocessing module and a U-Net model with a convolutional block attention module (CBAM). The discriminator adopts a PatchGAN structure. First, a grounding grid forward problem model was built to calculate the boundary voltage. Then, the image was initialized through the preprocessing module, and the important features of ground grid corrosion were extracted again through the encoder module, decoder module and attention module. Finally, the generator and discriminator continuously optimized the objective function and conducted adversarial training to achieve ground grid electrical impedance imaging. Imaging was performed on grounding grids with different corrosion conditions. The results showed a final average peak signal-to-noise ratio of 20.04. The average structural similarity was 0.901. The accuracy of corrosion position judgment was 94.3%. The error of corrosion degree judgment was 9.8%. This method effectively improves the pathological problem of grounding grid imaging and improves the precision and accuracy, with certain noise resistance and universality.

Pedagogical study of the image of a magnetic dipole in front of a superconducting sphere

Abstract The method of images to solve certain electrostatic boundary-value problems is taught worldwide in undergraduate-level physics courses. Though it is also possible to employ this technique for solving magnetostatic boundary value problems, examples of this usage are rarely found in textbooks or physics pedagogy literature. In particular, the problem of finding the field due to a magnetic dipole kept in front of a superconducting sphere is an interesting one, because (i) it helps the students to compare with the grounded conducting sphere image problem in electrostatics, and (ii) offers a greater degree of difficulty since the source is a dipole (vector), rather than an electric charge (scalar). The present work demonstrates an intuitive way of solving the problem. The case in which the source dipole is oriented radially with respect to the sphere is solved with a single dipole image. In the case of the transverse orientation of the source dipole, we model the dipole as a current loop. Then, we find the image of the radial and transverse current elements that satisfy the boundary conditions. Then, we show that this method can be used to deduce the form of the image dipoles when the dipole is oriented in the transverse direction. This method is very much intuitive and accessible for undergraduate-level students.

A class of Landweber-type iterative methods based on the Radon transform for incomplete view tomography

Background We study the reconstruction problem for incomplete view tomography, including sparse view tomography and limited angle tomography, by the Landweber iteration and its accelerated version. Traditional implementations of these Landweber-type iterative methods necessitate multiple large-scale matrix-vector multiplications, which in turn require substantial time and storage resources. Objective This paper aims to develop and test a novel and efficient discretization approach for a class of Landweber-type methods that minimizes storage requirements by incorporating the specific structure of the incomplete view Radon transform. Methods We prove that the normal operator of incomplete view Radon transform in these methods is a compact convolution operator, and derive the explicit representation of its convolution kernel. Discretized by the pixel basis, these Landweber-type iterative methods can be implemented quickly and accurately by introducing a discretized convolution operation between two small-scale matrices with minimal storage requirements. Results For the simulated complete and limited angle data, the reconstruction results using various Landweber-type methods with our proposed discretization scheme achieve a 1-5dB improvement in PSNR and require one-third of computation time compared to the traditional approach. For the simulated sparse view data, our discretization scheme yields a valid image with the highest PSNR. Conclusions The Landweber-type iterative methods, when combined with our proposed discretization approach based on the Radon transform, are effective for addressing the incomplete view tomography problem.

Efficient Bayesian Physics Informed Neural Networks for Surface Tomography via Ensemble Kalman Inversion

Surface travel-time tomography is a widely-used method to characterize the structure of the underground. However, conventional seismic tomography techniques often require a high-fidelity numerical forward model, which leads to significant computational burden and time consumption. Additionally, the inverse problem in travel-time tomography is prone to ill-posedness and lacks uncertainty quantification for the inferred results.

On the Solution of Linearized Inverse Scattering Problems in Near-Field Microwave Imaging by Operator Inversion and Matched Filtering

On the Solution of Linearized Inverse Scattering Problems in Near-Field Microwave Imaging by Operator Inversion and Matched Filtering

Problems of magnetic resonance diagnosis for gastric-type mucin-positive cervical lesions of the uterus and its solutions using artificial intelligence.

To reveal problems of magnetic resonance imaging (MRI) for diagnosing gastric-type mucin-positive (GMPLs) and gastric-type mucin-negative (GMNLs) cervical lesions. We selected 172 patients suspected to have lobular endocervical glandular hyperplasia; their pelvic MR images were categorised into the training (n = 132) and validation (n = 40) groups. The images of the validation group were read twice by three pairs of six readers to reveal the accuracy, area under the curve (AUC), and intraclass correlation coefficient (ICC). The readers evaluated three images (sagittal T2-weighted image [T2WI], axial T2WI, and axial T1-weighted image [T1WI]) in every patient. The pre-trained convolutional neural network (pCNN) was used to differentiate between GMPLs and GMNLs and perform four-fold cross-validation using cases in the training group. The accuracy and AUC were obtained using the MR images in the validation group. For each case, three images (sagittal T2WI and axial T2WI/T1WI) were entered into the CNN. Calculations were performed twice independently. ICC (2,1) between first- and second-time CNN was evaluated, and these results were compared with those of readers. The highest accuracy of readers was 77.50%. The highest ICC (1,1) between a pair of readers was 0.750. All ICC (2,1) values were <0.7, indicating poor agreement; the highest accuracy of CNN was 82.50%. The AUC did not differ significantly between the CNN and readers. The ICC (2,1) of CNN was 0.965. Variation in the inter-reader or intra-reader accuracy in MRI diagnosis limits differentiation between GMPL and GMNL. CNN is nearly as accurate as readers but improves the reproducibility of diagnosis.

Electronic Health Records (EHR) Extraction Using Various NLP Models

Information recorded in electronic medical health records, clinical reports, and summaries has the possibility of revolutionizing health-related research and its corresponding industry. EMR data can be used for epidemiological studies, disease registries, data banks, drug safety surveillance, clinical trials, and healthcare audits. With the rapid adoption of electronic health records (EHRs), it is desirable to harvest information and knowledge from EHRs to support automated systems and to enable secondary use of EHRs for clinical and translational research; thereby increasing efficiency. One critical component which is predominantly used to facilitate the secondary use of EHR data is information extraction (IE) task, which automatically extracts and encodes clinical information from a given text. Now, a natural language processing model (NLP) focuses on “developing computational models for understanding the interaction between data science and language”. In the clinical domain, researchers have often used NLP systems to identify clinical syndromes and common biomedical concepts from imaging data, radiology reports, discharge summaries, problem lists, nursing documentation, drug reviews, and medical education documents. These data can help doctors determine patients' health condition(s) including diagnostic information, procedures and tests performed, treatment results, drugs administered, and more. Therefore, we hope to gain some insights and develop strategies to improve the utilization of these NLP systems in the clinical domain. We hope to provide a vision for addressing the existing data challenge(s) in this domain. For this, we would look at the various models that have been used/published over the years and test them for their attributes including effectiveness, accuracy, precision, etc. We believe that adding a probabilistic graphical model framework for structured output prediction would further improve the performance of our system. This experiment remains our future work.

The development of RBL-STEM learning materials to improve students' metaliteracy in solving watermarking image problems using rainbow antimagic coloring

The rapid development of information in this era emphasizes the importance of improving students' metaliteracy skills. One of the models and approaches that can be applied is Research Based Learning (RBL) integrated with Science, Technology, Engineering and Mathematics (STEM). The purpose of this study is to identify RBL-STEM activities, explain the steps and results of creating RBL-STEM learning materials, and examine data on the results of creating learning resources to increase students' metaliteracy level. Research and development (R&amp;D) was the methodology used. The products of this research are the results of the development of learning tools in the form of students’ assignment designs, students’ worksheets, and learning outcome tests. The learning tool development process yielded data that met a validity requirement of 95.5%. The trial involved 40 students’, and the use of the RBL-STEM learning resources was found to be effective with a 96.77% effectiveness criterion and practical with a 97.71% practicality criterion. In addition, students’ responded positively to the learning experience and were highly engaged. Students’ metaliteracy increased as they solved rainbow antimagic coloring problems, according to the pretest and posttest study. This study also identified three levels of metaliteracy proficiency: high, medium, and low. The research findings were validated using statistical analysis, phase image, N-Vivo, and word cloud, which also demonstrated an improvement in students’ metaliteracy skills. Thus, RBL-STEM has the potential to improve students' metaliteracy in real-world contexts, such as the application of watermarking image.

Orbital angular momentum multiplexing holography based on multi-plane light conversion.

Orbital angular momentum (OAM), with its unique orthogonality, is widely applied in optical holographic encryption and information storage. Theoretically, the topological charge of OAM holography is infinite. However, in practice, it is restricted by the Nyquist-Shannon sampling theorem and experimental equipment, resulting in a relatively small number of practically usable channels. We propose an OAM holography technique based on multi-plane light conversion (MPLC) to increase the number of multiplexed channels in OAM holography. In contrast to conventional OAM holographic designs, the present design employs a limited number of phase planes to achieve multi-channel coaxial OAM multiplexing holograms. In the experiment, we using four MPLC phase planes to reconstruct six coaxial OAM holograms, the peak signal-to-noise ratio (PSNR) value of the reconstructed holograms exceeds 20 dB, and the crosstalk between multiple modes is less than -19 dB. This mitigates the crosstalk problem of multiple images and provides what we believe to be a new way to realize large-capacity and high-quality optical holography encryption and information storage.

Entropy-Regularized Iterative Weighted Shrinkage-Thresholding Algorithm (ERIWSTA) for inverse problems in imaging.

The iterative shrinkage-thresholding algorithm (ISTA) is a classic optimization algorithm for solving ill-posed linear inverse problems. Recently, this algorithm has continued to improve, and the iterative weighted shrinkage-thresholding algorithm (IWSTA) is one of the improved versions with a more evident advantage over the ISTA. It processes features with different weights, making different features have different contributions. However, the weights of the existing IWSTA do not conform to the usual definition of weights: their sum is not 1, and they are distributed over an extensive range. These problems may make it challenging to interpret and analyze the weights, leading to inaccurate solution results. Therefore, this paper proposes a new IWSTA, namely, the entropy-regularized IWSTA (ERIWSTA), with weights that are easy to calculate and interpret. The weights automatically fall within the range of [0, 1] and are guaranteed to sum to 1. At this point, considering the weights as the probabilities of the contributions of different attributes to the model can enhance the interpretation ability of the algorithm. Specifically, we add an entropy regularization term to the objective function of the problem model and then use the Lagrange multiplier method to solve the weights. Experimental results of a computed tomography (CT) image reconstruction task show that the ERIWSTA outperforms the existing methods in terms of convergence speed and recovery accuracy.

On the solution of the interpretation tomography problem within the framework of the linear integral representation method and discrete gravity and magnetic potential theories

A new of principle approach to solving inverse problems of geophysics on the background of the linear integral representation method and discrete gravity and magnetic potential theories is proposed. This approach makes it possible to restore the continuously distributed masses with relatively high accuracy from the heterogeneous data in some network points.