Inverse Image Research Articles

Inverse Problem Algorithm-Based Time-Resolved Imaging of Head and Neck Computed Tomography Angiography Contrast Kinetics with Clinical Testification.

This study mitigated the challenge of head and neck CT angiography by IPA-based time-resolved imaging of contrast kinetics. To this end, 627 cerebral hemorrhage patients with dizziness, brain aneurysm, stroke, or hemorrhagic stroke diagnosis were randomly categorized into three groups, namely, the original dataset (450), verification group (112), and in vivo testified group (65), in the Affiliated BenQ Hospital of Nanjing Medical University. In the first stage, seven risk factors were assigned: age, CTA tube voltage, body surface area, heart rate per minute, cardiac output blood per minute, the actual injected amount of contrast media, and CTA delayed trigger timing. The expectation value of the semi-empirical formula was the CTA number of the patient's left artery (LA). Accordingly, 29 items of the first-order nonlinear equation were calculated via the inverse problem analysis (IPA) technique run in the STATISTICA 7.0 program, yielding a loss function and variance of 3.1837 and 0.8892, respectively. A dimensionless AT was proposed to imply the coincidence, with a lower AT indicating a smaller deviation between theoretical and practical values. The derived formula was confirmed for the verification group of 112 patients, reaching high coincidence, with average ATavg and standard deviation values of 3.57% and 3.06%, respectively. In the second stage, the formula was refined to find the optimal amount of contrast media for the CTA number of LA approaching 400. Finally, the above procedure was applied to head and neck CTA images of the third group of 65 patients, reaching an average CTA number of LA of 407.8 ± 16.2 and finding no significant fluctuations.

Notes on hyperelliptic mapping class groups

AbstractHyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural epimorphisms between mapping class groups of surfaces with marked points. We study these groups in a systematic way. An application of this theory is a counterexample to the genus $2$ case of a conjecture by Putman and Wieland on virtual linear representations of mapping class groups. In the last section, we study profinite completions of hyperelliptic mapping class groups: we extend the congruence subgroup property to the general class of hyperelliptic mapping class groups introduced above and then determine the centralizers of multitwists and of open subgroups in their profinite completions.

Self-Supervised Non-Uniform Low-Light Image Enhancement Combining Image Inversion and Exposure Fusion

Low-light image enhancement is a challenging task in non-uniform low-light conditions, often resulting in local overexposure, noise amplification, and color distortion. To obtain satisfactory enhancement results, most models must resort to carefully selected paired or multi-exposure data sets. In this paper, we propose a self-supervised framework for non-uniform low-light image enhancement to address these issues, only requiring low-light images on their own for training. We first design a robust Retinex model-based image exposure enhancement network (EENet) to obtain global brightness enhancement and noise removal of images by carefully designing the loss function of each decomposition map. Then, to correct overexposed areas in the enhanced image, we incorporate the inverse image of the low-light image for enhancement using EENet. Furthermore, a three-branch asymmetric exposure fusion network (TAFNet) is designed. The two enhanced images and the original image are used as the TAFNet inputs to obtain a globally well-exposed and detail-rich image. Experimental results demonstrate that our framework outperforms some state-of-the-art methods in visual and quantitative comparisons.

Characterizing (∈, ∈∨q)-Anti-Intuitionistic Fuzzy Soft UP (BCC)-Subalgebras of UP (BCC)-Algebras

In this paper, the concepts of (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras and (∈, ∈)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras are introduced and studied. The UP (BCC)-homomorphic image and inverse image are investigated in (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras. Characterizations of (∈, ∈∨q)-anti-intuitionistic fuzzy soft UP (BCC)-subalgebras of UP (BCC)-algebras are discussed.

A rapid 3D magnetotelluric forward approach for arbitrary anisotropic conductivities in the Fourier domain

Previous studies have shown that anisotropy generally exists in geological bodies such as sedimentary rocks and fault zones, and more and more attention has been paid to the arbitrary conductivity media in surveys with the magnetotelluric sounding method. With the breakthrough development of computer hardware technology, large-scale 3D magnetotelluric modeling in anisotropic media has gradually become possible. At present, there are 3D magnetotelluric field simulation algorithms based on finite differences or finite elements for arbitrary anisotropic conductivity. In order to solve the common computational efficiency problems of the existing algorithms, we proposed a rapid 3D magnetotelluric forward approach for arbitrary anisotropic conductivity in the Fourier domain. Through the 2D Fourier transform, the governing equation can be converted from the space domain to the Fourier domain, thereby greatly reducing the calculation amount of the numerical simulation and improving the calculation efficiency. Then, the classical 1D anisotropy model is used to verify the correctness and the computational efficiency. Finally, the 3D anisotropic models of land and ocean are calculated, and the influence characteristics of the anisotropic medium on the magnetotelluric response are analyzed. The proposed algorithm will be used in the inverse imaging technique for large-scale 3D anisotropic data in future studies.

Regularising Inverse Problems with Generative Machine Learning Models

Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this survey paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The considered regularisers penalise images that are far from the range of a generative model that has learned to produce images similar to a training dataset. We name this family generative regularisers. The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess generative models and guide future research. In our numerical experiments, we evaluate three common generative models, autoencoders, variational autoencoders and generative adversarial networks, against our desired criteria. We also test three different generative regularisers on the inverse problems of deblurring, deconvolution, and tomography. We show that restricting solutions of the inverse problem to lie exactly in the range of a generative model can give good results but that allowing small deviations from the range of the generator produces more consistent results. Finally, we discuss future directions and open problems in the field.

TEM Strata Inversion Imaging with IP Effect Based on Enhanced GCN by Extracting Long-Dependency Features

Utilizing neural network models to inverse time-domain electromagnetic signals enables rapid acquisition of electrical structures, a non-intrusive method widely applied in geological and environmental surveys. However, traditional multi-layer perceptron (MLP) feature extraction is limited, struggling with cases involving complex electrical media with induced polarization effects, thereby limiting the inversion model’s predictive capacity. A graph-topology-based neural network model for strata electrical structure imaging with long-dependency feature extraction was proposed. We employ graph convolutional networks (GCN) for capturing non-Euclidean features like resistivity-thickness coupling and Long Short-Term Memory (LSTM) to capture long-dependency features. The LSTM compensates for GCN’s constraints in capturing distant node relationships. Using case studies with 5-strata and 9-strata resistivity models containing induced polarization effects, compared to traditional MLP networks, the proposed model utilizing time-domain features and graph-topology-based electrical structure extraction significantly improves performance. The mean absolute error in inversion misfit is reduced from 10–20% to around 2–3%.

Sequential method conformal mappings

The well-known, very important Schwarz–Christoffel integral does not yet completely solve the problem of mapping a half-plane onto a predetermined polygon. This integral includes parameters (inverse images of the polygon), the relationship of which with the lengths of the edges of the polygon is not known in advance. The main difficulty in using the Schwarz–Christoffel formula lies in determining these parameters. If this difficulty can be overcome in some effective way, then the Schwarz–Christoffel formula expands the range of conformally mapped regions so much that it can be considered “universal”, given that the curvilinear boundary of the mapped region can be approximated by a broken line. Thus, together with the Schwarz–Christoffel formula, a new direction in the theory of functions arises - numerical methods of conformal mapping. However, these approximate numerical methods were developed independently of the Schwarz–Christoffel formula.

Reconstruction of target scattering centres based on characteristics analysis of inverse synthetic aperture radar images

AbstractDue to the aircraft targets’ uncooperative character, acquiring the complete scattering characteristics of enemy aircraft is challenging. An effective reconstruction method of target scattering centres based on characteristics analysis of inverse synthetic aperture radar (ISAR) images is proposed in this letter. First, a positive definite manifold characterizing ISAR images of different attitudes is constructed. Then, Kullback–Leibler divergence is used as a measure of the variability between ISAR images. Finally, an ISAR image interpolation method based on the characteristics analysis of ISAR images is proposed to obtain the scattering characteristics with more attitudes. Furthermore, simulation results confirm that the proposed method is effective.

Finite element modeling of the electrical impedance tomography technique driven by machine learning

To create a human-like skin for a robotic application, current touch sensor technologies have a few drawbacks. Electrical Impedance Tomography (EIT) is a candidate for this application due to its applicability over complex geometries; nevertheless, it has accuracy concerns. This study employs artificial neural networks (ANNs) to investigate the accuracy and capability of EIT-based touch sensors. A finite element (FE) model is utilized to solve the forward EIT problem while simultaneously determining the system’s comprehensive mechanical response. The FE model is comprised of a polyurethane (PU) foam domain, a conductive spray layer and a set of sixteen electrodes. To replicate the process of touching the sensor body, a punch of varying diameters and touch forces is utilized. The mechanical response of the sensor body is modeled using the hyperfoam material model calibrated through experimental uniaxial and shear test data, while the electric conductivity of the sprayed skin surface is obtained experimentally as function of applied strain. The viscoelastic behavior of the PU foam material is also obtained experimentally. These experimental data were implemented in the FE model through user subroutines to model the mechanical and electrical properties of the sensor in the EIT forward problem. The traditional EIT inverse problem image reconstruction was replaced utilizing ANNs as an alternative to extract mechanics based parameters. The ANNs were created to predict the spatial coordinates of the touch point, and they were proven to be extremely accurate. Using the EIT voltage readings as input, the ANNs were utilized to forecast the system’s mechanical behavior such as contact pressure, contact area, indentation depth, and touching force.

A stronger form of locally closed set and its homeomorphic image

Through this paper, via the operators $(\cdot)^{\star}$ and $\Psi$, we presented notion of $\star$-Locally set in an ideal topological space $\zeta_{\mathbb{I}}$ as a new stronger form of locally closed set, and considered relations with various existing weak form of locally closed set. Preservations of direct images as well as inverse images of $(\cdot)^{\star}$, $\Psi$, $\star$-perfect and various weak forms of locally closed set including $\star$-Locally closed set are important investigating part. Besides, we pointed out that consideration of `bijectivity' in Lemma 3.1 of [24] is sufficient, and the Lemma 3.3 of [24] is wrong. We demonstrated two modifications of the last one.

Approximating properties of metric and generalized metric projections in uniformly convex and uniformly smooth Banach spaces

This note conducts a comparative study of some approximating properties of the metric projection, generalized projection, and generalized metric projection in uniformly convex and uniformly smooth Banach spaces. We prove that the inverse images of the metric projections are closed and convex cones, but they are not necessarily convex. In contrast, inverse images of the generalized projection are closed and convex cones. Furthermore, the inverse images of the generalized metric projection are neither a convex set nor a cone. We also prove that the distance from a point to its projection on a convex set is a weakly lower semicontinuous function for all three notions of projections. We provide illustrating examples to highlight the different behavior of the three projections in Banach spaces.

Adaptive motion error compensation method based on bat algorithm for maneuvering targets in inverse synthetic aperture LiDAR imaging

Adaptive motion error compensation method based on bat algorithm for maneuvering targets in inverse synthetic aperture LiDAR imaging

Homomorphisms and inverse homomorphisms on graph-walking automata

Graph-walking automata analyze an input graph by moving between its nodes, following the edges. This paper investigates the effect of node-replacement graph homomorphisms and inverse homomorphisms on recognizability by these automata. For deterministic graph-walking automata, it is shown that the family of graph languages they recognize is closed under inverse homomorphisms: for an n-state automaton, the inverse homomorphic images of the graphs it accepts can be recognized by an automaton with at most kn+1 states, where k is the number of labels of edge end-points in the pre-image graphs. At the same time, it is proved that in the worst case these inverse homomorphic images require a deterministic graph-walking automaton with at least kn states. The upper bound kn+1 also holds for nondeterministic graph-walking automata. The second result is that already for tree-walking automata, both deterministic and nondeterministic, the families they recognize are not closed under injective homomorphisms. Here the proof is based on a new homomorphic characterization of regular tree languages: every regular tree language is representable as h−1(g(all trees)), for some injective node-replacement homomorphisms g and h.

A rapid detection method of towed array seismic surface wave for leakage passage of dyke-dam

Rapid detection of leakage passage in dykes has become a committed step in flood prevention work. The seismic surface wave method can be given the S-wave velocity information of the near-surface (≤ 20 m), and qualitatively evaluate the transverse position, depth range, and direction of the leakage passage. The low acquisition efficiency of the cone geophone in the conventional point measurement mode does not meet the requirements of rapid detection. A single survey line has a small coverage area and lacks comparison with neighboring survey lines, so it is not possible to obtain the direction of extension of the leakage passage. In this paper, we propose a rapid detection method of the towed array seismic surface wave for leakage passage of a dyke-dam. Forty-eight gravity geophones are arranged in three columns, 16 in each column, to form the array geometry. Surface wave imaging methods are inversion and fast imaging. The main shortcomings of inversion calculation are (1) lacking shallow information, (2) low vertical resolution, and (3) multiple solutions. To overcome the above issues, the imaging calculation of the surface wave dispersion curve is implemented using fast imaging method. The proposed array geometry is used to collect seismic data. The simulated data and measured data show that fast imaging has the following advantages: (1) It can make full use of the dispersion curve of broadband seismic data, does not lose shallow information, and has high imaging accuracy. (2) It uses the dispersion curve directly for imaging, does not lose any details of velocity changes, and has a high vertical resolution. (3) The imaging results are unique. In contrast to the inversion results, the fast imaging results clearly distinguish the location of the leakage passage and highlight the lateral variability of the leakage passage. The results of the model data and measured data demonstrate the efficiency and high resolution of the towed array seismic geometry and the fast imaging method for leakage passage detection.

Multiplicative noise removal using complementary total generalized variation and nonlocal low rank regularization

The problem of multiplicative image denoising is a typical ill-posed inverse problem which has been extensively studied in the past few decades and is still an open problem. Exploiting appropriate image priors is critical to solve ill-posed inverse image restoration problem. The existing total generalized variation (TGV) based approaches have achieved significant performance in removing the multiplicative noise. However, these TGV regularized approaches only consider the local smoothness prior of the potential clean image, which limits their ability for image restoration. Other than the local smoothness property, the nonlocal self-similarity prior of images can also be exploited to offer helpful remedy for better image reconstruction. In this paper, to simultaneously make use of both the local smoothness prior and nonlocal self-similarity prior, we integrate the TGV regularizer with the nonlocal low rank regularizer to propose a novel variational model for multiplicative image denoising. Specifically, in the objective function, the nonlocal low rank regularization is expressed by the celebrated weighted nuclear norm minimization (WNNM) which has recently been applied to image denoising and presents state-of-art result. Then, we apply the split Bregman algorithm to efficiently solve the resulting model. Numerical experiments demonstrate that the proposed method achieve superior performance over the competing methods, including the state-of-the-art SAR-BM3D method.

Dynamic Electromagnetic Scattering Simulation of Tilt-Rotor Aircraft in Multiple Modes.

To study the electromagnetic scattering of tilt-rotor aircraft during multi-mode continuous flight, a dynamic simulation approach is presented. A time-varying mesh method is established to characterize the dynamic rotation and tilting of tilt-rotor aircraft. Shooting and bouncing rays and the uniform theory of diffraction are used to calculate the multi-mode radar cross-section (RCS). And the scattering mechanisms of tilt-rotor aircraft are investigated by extracting the micro-Doppler and inverse synthetic aperture radar images. The results show that the dynamic RCS of tilt-rotor aircraft in helicopter and airplane mode exhibits obvious periodicity, and the transition mode leads to a strong specular reflection on the rotor's upper surface, which increases the RCS with a maximum increase of about 36 dB. The maximum micro-Doppler shift has functional relationships with flight time, tilt speed, and wave incident direction. By analyzing the change patterns of maximum shift, the real-time flight state and mode can be identified. There are some significant scattering sources on the body of tilt-rotor aircraft that are distributed in a planar or point-like manner, and the importance of different scattering sources varies in different flight modes. The pre-studies on the key scattering areas can provide effective help for the stealth design of the target.

Void fraction measurement of gas–liquid two-phase flow based on compressed sensing theory and capacitively coupled electrical resistance tomography system

Capacitively coupled electrical resistance tomography (CCERT) is an innovative technique for electrical resistance tomography based on capacitively coupled contactless conductivity detection (C4D). Despite its potential, there are only a few studies on image reconstruction algorithms for CCERT. To address this, a CCERT measurement system is developed, and the compressed sensing (CS) theory is applied to the inverse problem imaging of CCERT to improve the image reconstruction quality and speed. Firstly, a mathematical CCERT image reconstruction model is constructed under CS theory and three algorithms under CS theory are employed to solve the convex optimization problem of the reconstruction model. Then a thresholding operation is applied to obtain the post-processed image and compared it with the classical linear back projection and Landweber algorithms. The simulation results demonstrate that the Barzilai–Borwein gradient projection for sparse reconstruction (GPSR-BB) algorithm yields more satisfactory imaging results than the other four algorithms. Additionally, three sensitivity matrix optimization methods for GPSR-BB algorithm are compared and find that the new method of screening the rows of the sensitivity matrix to zero is more effective than the other two common optimization methods in terms of reconstructed image quality. Finally, the static experiments of void fraction measurement are conducted using the developed CCERT system. The results indicated that the absolute error of void fraction measurement by GPSR-BB algorithm was less than 6.59% in the range of void fraction from 0.90% to 66.29%.

A novel seismic full waveform inversion approach for assessing the internal structure of a medieval sea dike

AbstractCoastal protection in the form of dike constructions has a long history at the German North Frisian coast dating back to the High Middle Ages. As the vast majority of the dikes built prior to the devastating storm surges of the Middle Ages have been irretrievably destroyed, mostly sparse remains and only a few well preserved of these medieval dikes are found along the German North Frisian coast and within the Wadden Sea. Not all details of their construction and dimensions are yet understood. In the present case study, we investigate the historical Schardeich on the island of Pellworm in the German North Sea in a noninvasive way using shear waves (SH‐waves). For the data interpretation, we applied a combination of seismic full waveform inversion and classical seismic reflection imaging to determine the interior structure of the dike and its underlying layers at the highest possible resolution. The results obtained on land are compared with dike remains found in the tidal flats. These remains show up in marine seismic sections as characteristic reflections, which probably represent a compaction layer caused by the load of the former dike. For ground truthing, we compare the seismic results with internal dike structures found in nearby excavations. The comparison highlights that FWI is a reliable tool for near‐surface archaeological prospecting. We find that SH‐wave FWI provides decimetre‐scale velocity and density models that allow, together with the seismic reflection section, to determine distinct construction phases of the dike. The investigated dike further shows a depression at base level of about 0.75 m, which is of the same order as observed for the dike base reflections in the tidal flats. Transferring these findings to the dike remains mapped in the tidal flats, we derive a height of the former dike from 2.2 to 4.4 m.

The effects of topological features on convolutional neural networks—an explanatory analysis via Grad-CAM

Topological data analysis (TDA) characterizes the global structure of data based on topological invariants such as persistent homology, whereas convolutional neural networks (CNNs) are capable of characterizing local features in the global structure of the data. In contrast, a combined model of TDA and CNN, a family of multimodal networks, simultaneously takes the image and the corresponding topological features as the input to the network for classification, thereby significantly improving the performance of a single CNN. This innovative approach has been recently successful in various applications. However, there is a lack of explanation regarding how and why topological signatures, when combined with a CNN, improve discriminative power. In this paper, we use persistent homology to compute topological features and subsequently demonstrate both qualitatively and quantitatively the effects of topological signatures on a CNN model, for which the Grad-CAM analysis of multimodal networks and topological inverse image map are proposed and appropriately utilized. For experimental validation, we utilize two famous datasets: the transient versus bogus image dataset and the HAM10000 dataset. Using Grad-CAM analysis of multimodal networks, we demonstrate that topological features enforce the image network of a CNN to focus more on significant and meaningful regions across images rather than task-irrelevant artifacts such as background noise and texture.