Cervical length (CL) measurement using transvaginal ultrasound is an effective screening tool to assess the risk of preterm birth. An adequate assessment of CL is crucial, however, manual sonographic CL measurement is highly operator-dependent and cumbersome. Therefore, a reliable and reproducible automatic method for CL measurement is in high demand to reduce inter-rater variability and improve workflow. Despite the increasing use of artificial intelligence techniques in ultrasound, applying deep learning (DL) to analyze ultrasound images of the cervix remains a challenge due to low signal-to-noise ratios and difficulties in capturing the cervical canal, which appears as a thin line and with extremely low contrast against the surrounding tissues. To address these challenges, we have developed CL-Net, a novel DL network that incorporates expert anatomical knowledge to identify the cervix, similar to the approach taken by clinicians. CL-Net captures anatomical features related to CL measurement, facilitating the identification of the cervical canal. It then identifies the cervical canal and automatically provides reproducible and reliable CL measurements. CL-Net achieved a success rate of 95.5% in recognizing the cervical canal, comparable to that of human experts (96.4%). Furthermore, the differences between the CL measurements of CL-Net and ground truth were considerably smaller than those made by non-experts and were comparable to those made by experts (median 1.36 mm, IQR 0.87-2.82 mm, range 0.06-6.95 mm for straight cervix; median 1.31 mm, IQR 0.61-2.65 mm, range 0.01-8.18 mm for curved one).

Accurate and automatic segmentation of three-dimensional (3D) individual teeth from cone-beam computerized tomography (CBCT) images is a challenging problem because of the difficulty in separating an individual tooth from adjacent teeth and its surrounding alveolar bone. Thus, this paper proposes a fully automated method of identifying and segmenting 3D individual teeth from dental CBCT images. The proposed method addresses the aforementioned difficulty by developing a deep learning-based hierarchical multi-step model. First, it automatically generates upper and lower jaws panoramic images to overcome the computational complexity caused by high-dimensional data and the curse of dimensionality associated with limited training dataset. The obtained 2D panoramic images are then used to identify 2D individual teeth and capture loose- and tight- regions of interest (ROIs) of 3D individual teeth. Finally, accurate 3D individual tooth segmentation is achieved using both loose and tight ROIs. Experimental results showed that the proposed method achieved an F1-score of 93.35 percent for tooth identification and a Dice similarity coefficient of 94.79 percent for individual 3D tooth segmentation. The results demonstrate that the proposed method provides an effective clinical and practical framework for digital dentistry.

The estimation of antenatal amniotic fluid (AF) volume (AFV) is important as it offers crucial information about fetal development, fetal well-being, and perinatal prognosis. However, AFV measurement is cumbersome and patient specific. Moreover, it is heavily sonographer-dependent, with measurement accuracy varying greatly depending on the sonographer's experience. Therefore, the development of accurate, robust, and adoptable methods to evaluate AFV is highly desirable. In this regard, automation is expected to reduce user-based variability and workload of sonographers. However, automating AFV measurement is very challenging, because accurate detection of AF pockets is difficult owing to various confusing factors, such as reverberation artifact, AF mimicking region and floating matter. Furthermore, AF pocket exhibits an unspecified variety of shapes and sizes, and ultrasound images often show missing or incomplete structural boundaries. To overcome the abovementioned difficulties, we develop a hierarchical deep-learning-based method, which consider clinicians' anatomical-knowledge-based approaches. The key step is the segmentation of the AF pocket using our proposed deep learning network, AF-net. AF-net is a variation of U-net combined with three complementary concepts - atrous convolution, multi-scale side-input layer, and side-output layer. The experimental results demonstrate that the proposed method provides a measurement of the amniotic fluid index (AFI) that is as robust and precise as the results from clinicians. The proposed method achieved a Dice similarity of 0.877±0.086 for AF segmentation and achieved a mean absolute error of 2.666±2.986 and mean relative error of 0.018±0.023 for AFI value. To the best of our knowledge, our method, for the first time, provides an automated measurement of AFI.

One of the most challenging issues in computed tomography (CT) is the reduction of beam-hardening artifacts (BHAs). The presence of highly attenuating materials produces BHAs in CT images because of violating the mathematical CT model assumption of the projection data (i.e., that the data is a linear transform of an image). Here, the linear assumption is violated by nonlinear characteristics depending on the polychromatic nature of the X-ray beam combined with the energy-dependent variations in the attenuation coefficients of highly attenuating materials. Very recently, a new BHA-reduction method that uses a beam-hardening filter placed in front of an X-ray beam was developed independently by the first author [ Method for Calibrating Beam-hardening Artifacts of Computed Tomography Image and Computed Tomography Apparatus using Thereof, KR Patent: 10-2018-0023663, 2018] and Butzer et al. [ Dual-energy in industrial CT -- How simple math can reveal structures hidden by artefacts, in Proceedings of the 6th International Conference on Image Formation in X-Ray Computed Tomography, 2020, pp. 94--97]. Experiments reveal that this new method is remarkably effective at reducing BHAs in the presence of high-attenuation materials, and it has already been applied to several industrial CT problems. However, to date, no mathematical basis for its impressive performance has been found. This paper presents this filtered method and, for the first time, provides a theoretical basis for demonstrating the effectiveness of the filter-based methodology.

This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and ill-posed inverse problem. Conventionally, penalty-based regularization methods have been used to deal with the ill-posed problem. However, experiences over the last three decades have shown methodological limitations in utilizing prior knowledge about tracking expected imaging features for medical diagnosis. The proposed method's paradigm is completely different from conventional approaches; the proposed reconstruction uses a variety of training data sets to generate a low dimensional manifold of approximate solutions, which allows conversion of the ill-posed problem to a well-posed one. Variational autoencoder was used to produce a compact and dense representation for lung EIT images with a low dimensional latent space. Then, we learn a robust connection between the EIT data and the low dimensional latent data. Numerical simulations validate the effectiveness and feasibility of the proposed approach.

Ultrasound diagnosis is routinely used in obstetrics and gynecology for fetal biometry, and owing to its time-consuming process, there has been a great demand for automatic estimation. However, the automated analysis of ultrasound images is complicated because they are patient specific, operator dependent, and machine specific. Among various types of fetal biometry, the accurate estimation of abdominal circumference (AC) is especially difficult to perform automatically because the abdomen has low contrast against surroundings, nonuniform contrast, and irregular shape compared to other parameters. We propose a method for the automatic estimation of the fetal AC from two-dimensional ultrasound data through a specially designed convolutional neural network (CNN), which takes account of doctors' decision process, anatomical structure, and the characteristics of the ultrasound image. The proposed method uses CNN to classify ultrasound images (stomach bubble, amniotic fluid, and umbilical vein) and Hough transformation for measuring AC. We test the proposed method using clinical ultrasound data acquired from 56 pregnant women. Experimental results show that, with relatively small training samples, the proposed CNN provides sufficient classification results for AC estimation through the Hough transformation. The proposed method automatically estimates AC from ultrasound images. The method is quantitatively evaluated and shows stable performance in most cases and even for ultrasound images deteriorated by shadowing artifacts. As a result of experiments for our acceptance check, the accuracies are 0.809 and 0.771 with expert 1 and expert 2, respectively, whereas the accuracy between the two experts is 0.905. However, for cases of oversized fetus, when the amniotic fluid is not observed or the abdominal area is distorted, it could not correctly estimate AC.

Electrical impedance tomography (EIT) provides functional images of an electrical conductivity distribution inside the human body. Since the 1980s, many potential clinical applications have arisen using inexpensive portable EIT devices. EIT acquires multiple trans-impedance measurements across the body from an array of surface electrodes around a chosen imaging slice. The conductivity image reconstruction from the measured data is a fundamentally ill-posed inverse problem notoriously vulnerable to measurement noise and artifacts. Most available methods invert the ill-conditioned sensitivity or the Jacobian matrix using a regularized least-squares data-fitting technique. Their performances rely on the regularization parameter, which controls the trade-off between fidelity and robustness. For clinical applications of EIT, it would be desirable to develop a method achieving consistent performance over various uncertain data, regardless of the choice of the regularization parameter. Based on the analysis of the structure of the Jacobian matrix, we propose a fidelity-embedded regularization (FER) method and a motion artifact reduction filter. Incorporating the Jacobian matrix in the regularization process, the new FER method with the motion artifact reduction filter offers stable reconstructions of high-fidelity images from noisy data by taking a very large regularization parameter value. The proposed method showed practical merits in experimental studies of chest EIT imaging.

This paper presents a static electrical impedance tomography (EIT) technique that evaluates abdominal obesity by estimating the thickness of subcutaneous fat. EIT has a fundamental drawback for absolute admittivity imaging because of its lack of reference data for handling the forward modeling errors. To reduce the effect of boundary geometry errors in imaging abdominal fat, we develop a depth-based reconstruction method that uses a specially chosen current pattern to construct reference-like data, which are then used to identify the border between subcutaneous fat and muscle. The performance of the proposed method is demonstrated by numerical simulations using 32-channel EIT system and a humanlike domain.

This paper describes the mathematical grounds for a highly undersampled magnetic resonance electrical impedance tomography (MREIT) method, with the aim of visualizing the dynamic changes in electrical tissue properties that occur in response to physiological activity. MREIT with fully sampled magnetic resonance (MR) data (satisfying the Nyquist criterion) has been shown to be capable of high-resolution conductivity imaging in numerical simulations and in animal experiments. However, when the data are undersampled (violating the Nyquist criterion for reducing data acquisition time), it is difficult to extract the component of magnetic flux density that is induced by boundary injection currents, and it is the data from this component that are used in performing the standard MREIT algorithm. Here, we show that it is possible to localize small conductivity perturbations using highly undersampled MR data. We perform various numerical simulations to support our theoretical results.

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency dependence, as is often seen in biological tissues. We discuss reconstruction methods for both fully known and partially known spectral profiles and demonstrate in the latter case the successful employment of difference imaging. We also study the reconstruction with an imperfectly known boundary and show that the multifrequency approach can eliminate modeling errors and recover almost all inclusions. In addition, we develop an efficient group sparse recovery algorithm for the robust solution of related linear inverse problems. Several numerical simulations are presented to illustrate and validate the approach.

This paper proposes a new method to correct beam hardening artifacts caused by the presence of metal in polychromatic X-ray computed tomography (CT) without degrading the intact anatomical images. Metal artifacts due to beam-hardening, which are a consequence of X-ray beam polychromaticity, are becoming an increasingly important issue affecting CT scanning as medical implants become more common in a generally aging population. The associated higher-order beam-hardening factors can be corrected via analysis of the mismatch between measured sinogram data and the ideal forward projectors in CT reconstruction by considering the known geometry of high-attenuation objects. Without prior knowledge of the spectrum parameters or energy-dependent attenuation coefficients, the proposed correction allows the background CT image (i.e., the image before its corruption by metal artifacts) to be extracted from the uncorrected CT image. Computer simulations and phantom experiments demonstrate the effectiveness of the proposed method to alleviate beam hardening artifacts.

Quantitative susceptibility mapping (QSM) is a new medical imaging technique that can visualize magnetic susceptibility, changes of which in tissue indicate various disease processes involving iron transport. The inverse problem of QSM is to recover the susceptibility distribution of the human body from the measured local field that is expressed by the convolution of the susceptibility distribution with the magnetic field generated by a unit dipole. The inverse problem is ill-posed due to the presence of zeros at a cone in the Fourier representation of the unit dipole kernel. Reconstruction methods have been greatly improved to give better recovery of tissue susceptibility data for QSM, and various clinical applications have been pursued. However, rigorous mathematical analyses for the inverse problem, such as demonstrations of the existence and uniqueness of solutions and error characterizations, have not yet been presented. This paper provides for the first time not only a theoretical ground for QSM but also the underlying cause of streaking artifacts.

Magnetic resonance electrical property tomography (MREPT) is a new imaging modality to visualize a distribution of admittivity γ = σ+iωε inside the human body where σ and ε denote electrical conductivity and permittivity, respectively. Using B1 maps acquired by an magnetic resonance imaging scanner, it produces cross-sectional images of σ and ε at the Larmor frequency. Since current MREPT methods rely on an assumption of a locally homogeneous admittivity, there occurs a reconstruction error where this assumption fails. Rigorously analyzing the reconstruction error in MREPT, we showed that the error is fundamental and may cause technical difficulties in interpreting MREPT images of a general inhomogeneous object. We performed numerical simulations and phantom experiments to quantitatively support the error analysis. We compared the MREPT image reconstruction problem with that of magnetic resonance electrical impedance tomography (MREIT) to highlight distinct features of both methods to probe the same object in terms of its high- and low-frequency conductivity distributions, respectively. MREPT images showed large errors along boundaries where admittivity values changed whereas MREIT images showed no such boundary effects. Noting that MREIT makes use of the term neglected in MREPT, a novel MREPT admittivity image reconstruction method is proposed to deal with the boundary effects, which requires further investigation on the complex directional derivative in the real Euclidian space [Formula: see text].

Most video surveillance systems require to manually set a motion detection sensitivity level to generate motion alarms. The performance of motion detection algorithms, embedded in closed circuit television (CCTV) camera and digital video recorder (DVR), usually depends upon the preselected motion sensitivity level, which is expected to work in all environmental conditions. Due to the preselected sensitivity level, false alarms and detection failures usually exist in video surveillance systems. The proposed motion detection model based upon variational energy provides a robust detection method at various illumination changes and noise levels of image sequences without tuning any parameter manually. We analyze the structure mathematically and demonstrate the effectiveness of the proposed model with numerous experiments in various environmental conditions. Due to the compact structure and efficiency of the proposed model, it could be implemented in a small embedded system.

Time-difference electrical impedance tomography (tdEIT) requires two data sets measured at two different times. The difference between them is utilized to produce images of time-dependent changes in a complex conductivity distribution inside the human body. Frequency-difference EIT (fdEIT) was proposed to image frequency-dependent changes of a complex conductivity distribution. It has potential applications in tumor and stroke imaging since it can visualize an anomaly without requiring any time-reference data obtained in the absence of an anomaly. In this paper, we provide a rigorous analysis for the detectability of an anomaly based on a constructive and quantitative physical correlation between a measured fdEIT data set and an anomaly. From this, we propose a new noniterative frequency-difference anomaly detection method called the factorization method (FM) and elaborate its physical justification. To demonstrate its practical applicability, we performed fdEIT phantom imaging experiments using a multifrequency EIT system. Applying the FM to measured frequency-difference boundary voltage data sets, we could quantitatively evaluate indicator functions inside the imaging domain, of which values at each position reveal presence or absence of an anomaly. We found that the FM successfully localizes anomalies inside an imaging domain with a frequency-dependent complex conductivity distribution. We propose the new FM as an anomaly detection algorithm in fdEIT for potential applications in tumor and stroke imaging.

We present the first in vivo cross-sectional conductivity image of the human leg with 1.7 mm pixel size using the magnetic resonance electrical impedance tomography (MREIT) technique. After a review of its experimental protocol by an Institutional Review Board (IRB), we performed MREIT imaging experiments of four human subjects using a 3 T MRI scanner. Adopting thin and flexible carbon-hydrogel electrodes with a large surface area and good contact, we could inject as much as 9 mA current in a form of 15 ms pulse into the leg without producing a painful sensation and motion artifact. Sequentially injecting two imaging currents in two different directions, we collected induced magnetic flux density data inside the leg. Scaled conductivity images reconstructed by using the single-step harmonic B(z) algorithm well distinguished different parts of the subcutaneous adipose tissue, muscle, crural fascia, intermuscular septum and bone inside the leg. We could observe spurious noise spikes in the outer layer of the bone primarily due to the MR signal void phenomenon there. Around the fat, the chemical shift of about two pixels occurred obscuring the boundary of the fat region. Future work should include a fat correction method incorporated in the MREIT pulse sequence and improvements in radio-frequency coils and image reconstruction algorithms. Further human imaging experiments are planned and being conducted to produce conductivity images from different parts of the human body.

Magnetic resonance elastography (MRE) is an imaging modality capable of visualizing the elastic properties of an object using magnetic resonance imaging (MRI) measurements of transverse acoustic strain waves induced in the object by a harmonically oscillating mechanical vibration. Various algorithms have been designed to determine the mechanical properties of the object under the assumptions of linear elasticity, isotropic and local homogeneity. One of the challenging problems in MRE is to reduce the noise effects and to maintain contrast in the reconstructed shear modulus images. In this paper, we propose a new algorithm designed to reduce the degree of noise amplification in the reconstructed shear modulus images without the assumption of local homogeneity. Investigating the relation between the measured displacement data and the stress wave vector, the proposed algorithm uses an iterative reconstruction formula based on a decomposition of the stress wave vector. Numerical simulation experiments and real experiments with agarose gel phantoms and human liver data demonstrate that the proposed algorithm is more robust to noise compared to standard inversion algorithms and stably determines the shear modulus.

Magnetic resonance electrical impedance tomography (MREIT) attempts to provide conductivity images of an electrically conducting object with a high spatial resolution. When we inject current into the object, it produces internal distributions of current density and magnetic flux density. By using a magnetic resonance imaging (MRI) scanner, we can measure B(z) data where z is the direction of the main magnetic field of the scanner. Conductivity images are reconstructed based on the relation between the injection current and B(z) data. The harmonic B(z) algorithm was the first constructive MREIT imaging method and it has been quite successful in previous numerical and experimental studies. Its performance is, however, degraded when the imaging object contains low-conductivity regions such as bones and lungs. To overcome this difficulty, we carefully analyzed the structure of a current density distribution near such problematic regions and proposed a new technique, called the local harmonic B(z) algorithm. We first reconstruct conductivity values in local regions with a low conductivity contrast, separated from those problematic regions. Then, the method of characteristics is employed to find conductivity values in the problematic regions. One of the most interesting observations of the new algorithm is that it can provide a scaled conductivity image in a local region without knowing conductivity values outside the region. We present the performance of the new algorithm by using computer simulation methods.

In this paper, we propose a new level set-based partial differential equation (PDE) for the purpose of bimodal segmentation. The PDE is derived from an energy functional which is a modified version of the fitting term of the Chan-Vese model. The energy functional is designed to obtain a stationary global minimum, i.e., the level set function which evolves by the Euler-Lagrange equation of the energy functional has a unique convergence state. The existence of a global minimum makes the algorithm invariant to the initialization of the level set function, whereas the existence of a convergence state makes it possible to set a termination criterion on the algorithm. Furthermore, since the level set function converges to one of the two fixed values which are determined by the amount of the shifting of the Heaviside functions, an initialization of the level set function close to those values can result in a fast convergence.

Magnetic resonance electrical impedance tomography (MREIT) is designed to produce high resolution conductivity images of an electrically conducting subject by injecting current and measuring the longitudinal component, Bz, of the induced magnetic flux density B = (Bx, By, Bz). In MREIT, accurate measurements of Bz are essential in producing correct conductivity images. However, the measured Bz data may contain fundamental defects in local regions where MR magnitude image data are small. These defective Bz data result in completely wrong conductivity values there and also affect the overall accuracy of reconstructed conductivity images. Hence, these defects should be appropriately recovered in order to carry out any MREIT image reconstruction algorithm. This paper proposes a new method of recovering Bz data in defective regions based on its physical properties and neighboring information of Bz. The technique will be indispensable for conductivity imaging in MREIT from animal or human subjects including defective regions such as lungs, bones, and any gas-filled internal organs.

In this paper, we propose the use of the Gauss curvature in a Gauss curvature-driven diffusion equation for noise removal. The proposed scheme uses the Gauss curvature as the conductance term and controls the amount of diffusion. The main advantage of the scheme is that it preserves important structures, such as straight edges, curvy edges, ramps, corners, small-scaled features, etc.

In magnetic resonance electrical impedance tomography (MREIT), we try to visualize cross-sectional conductivity (or resistivity) images of a subject. We inject electrical currents into the subject through surface electrodes and measure the z component Bz of the induced internal magnetic flux density using an MRI scanner. Here, z is the direction of the main magnetic field of the MRI scanner. We formulate the conductivity image reconstruction problem in MREIT from a careful analysis of the relationship between the injection current and the induced magnetic flux density Bz. Based on the novel mathematical formulation, we propose the gradient Bz decomposition algorithm to reconstruct conductivity images. This new algorithm needs to differentiate Bz only once in contrast to the previously developed harmonic Bz algorithm where the numerical computation of (inverted delta)2Bz is required. The new algorithm, therefore, has the important advantage of much improved noise tolerance. Numerical simulations with added random noise of realistic amounts show the feasibility of the algorithm in practical applications and also its robustness against measurement noise.

Recently, a new static resistivity image reconstruction algorithm is proposed utilizing internal current density data obtained by magnetic resonance current density imaging technique. This new imaging method is called magnetic resonance electrical impedance tomography (MREIT). The derivation and performance of J-substitution algorithm in MREIT have been reported as a new accurate and high-resolution static impedance imaging technique via computer simulation methods. In this paper, we present experimental procedures, denoising techniques, and image reconstructions using a 0.3-tesla (T) experimental MREIT system and saline phantoms. MREIT using J-substitution algorithm effectively utilizes the internal current density information resolving the problem inherent in a conventional EIT, that is, the low sensitivity of boundary measurements to any changes of internal tissue resistivity values. Resistivity images of saline phantoms show an accuracy of 6.8%-47.2% and spatial resolution of 64 x 64. Both of them can be significantly improved by using an MRI system with a better signal-to-noise ratio.