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Transcranial ultrasound imaging presents a significant challenge due to the intricate interplay between ultrasound waves and the heterogeneous human skull. The skull's presence induces distortion, refraction, multiple scattering, and reflection of ultrasound signals, thereby complicating the acquisition of high-quality images. Extracting reflections from the entire waveform is crucial yet exceedingly challenging, as intracranial reflections are often obscured by strong amplitude direct waves and multiple scattering. In this paper, a multiple wave suppression method for ultrasound plane wave imaging is proposed to mitigate the impact of skull interference. Drawing upon prior research, we developed an enhanced high-resolution linear Radon transform using the maximum entropy principle and Bayesian method, facilitating wavefield separation. We detailed the process of wave field separation in the Radon domain through simulation of a model with a high velocity layer. When plane waves emitted at any steering angles, both multiple waves and first arrival waves manifested as distinct energy points. In the brain simulation, we contrasted the characteristic differences between skull reflection and brain-internal signal in Radon domain, and demonstrated that multiples suppression method reduces side and grating lobe levels by approximately 30 dB. Finally, we executed in vitro experiments using a monkey skull to separate weak intracranial reflection signals from strong skull reflections, enhancing the contrast-to-noise ratio by 85 % compared to conventional method using full waveform. This study deeply explores the effect of multiples on effective signal separation, addresses the complexity of wavefield separation, and verifies its efficacy through imaging, thereby significantly advancing ultrasound transcranial imaging techniques.

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Supervised deep learning-based methods have inspired a new wave of image reconstruction methods that implicitly learn effective regularization strategies from a set of training data. While they hold potential for improving image quality, they have also raised concerns regarding their robustness. Instabilities can manifest when learned methods are applied to find approximate solutions to ill-posed image reconstruction problems for which a unique and stable inverse mapping does not exist, which is a typical use case. In this study, we investigate the performance of supervised deep learning-based image reconstruction in an alternate use case in which a stable inverse mapping is known to exist but is not yet analytically available in closed form. For such problems, a deep learning-based method can learn a stable approximation of the unknown inverse mapping that generalizes well to data that differ significantly from the training set. The learned approximation of the inverse mapping eliminates the need to employ an implicit (optimization-based) reconstruction method and can potentially yield insights into the unknown analytic inverse formula. The specific problem addressed is image reconstruction from a particular case of radially truncated circular Radon transform (CRT) data, referred to as 'half-time' measurement data. For the half-time image reconstruction problem, we develop and investigate a learned filtered backprojection method that employs a convolutional neural network to approximate the unknown filtering operation. We demonstrate that this method behaves stably and readily generalizes to data that differ significantly from training data. The developed method may find application to wave-based imaging modalities that include photoacoustic computed tomography.

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UAVs have been widely used in deformation monitoring because of their high availability and flexibility. However, the quality of UAV images is affected by changing attitude and surveying environments, resulting in a low monitoring accuracy. Cross-shaped markers are used to improve the accuracy of UAV monitoring due to their distinct center contrast and absence of eccentricity. However, existing methods cannot rapidly and precisely detect these markers in UAV images. To address these problems, this paper proposes an adaptive Radon-transform-based marker detection and localization method for UAV displacement measurements, focusing on two critical detection parameters, namely, the radius of marker information acquisition and the edge width of the cross-shaped scoring template. The experimental results show that the marker detection rate is 97.2% under different combinations of flight altitudes, radius ratios of marker information acquisition, and marker sizes. Furthermore, the root mean square error of detection and localization is 0.57 pixels, significantly surpassing the performance and accuracy of other methods. We also derive the critical detection radius and appropriate parameter combinations for different heights to further improve the practicality of the method.

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Serial NMR experiments are commonly applied in variable-temperature studies, reaction monitoring, and other tasks. The resonance frequencies often shift linearly over the series, and the shift rates help to characterize the studied system. They can be determined using a classical fitting of peak positions or a more advanced method of Radon transform. However, the optimal procedure for data collection remains to be determined. In this paper, we discuss how to invest experimental time, i.e., whether to measure more scans at the expense of the number of spectra or vice versa. The results indicate that classical fitting provides slightly less error than the Radon transform, although the latter can be the method of choice for a low signal-to-noise ratio. We demonstrate this fact through theoretical consideration, simulations, and an experiment. Finally, we extend our considerations to the linear fitting of peak amplitudes. Interestingly, the optimal setup for measuring peak height changes differs from the one for resonance frequency changes - fewer spectra with more scans provide better results.

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Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful tools in analytical chemistry. An important step in the analysis of NMR data is the assignment of resonance frequencies to the corresponding atoms in the molecule being investigated. The traditional approach considers the spectrum's characteristic parameters: chemical shift values, internuclear couplings, and peak intensities. In this paper, we show how to support the process of assigning a series of spectra of similar organic compounds by using temperature coefficients, that is, the rates of change in chemical shift values associated with given changes in temperature.

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In this article, we present a new method called point spread function (PSF)-Radon transform algorithm. This algorithm consists on recovering the instrument PSF from the Radon transform (in the line direction axis) of the line spread function (i.e., the image of a line). We present the method and tested with synthetic images, and real images from macro lens camera and microscopy. A stand-alone program along with a tutorial is available, for any interested user, in Martinez (PSF-Radon transform algorithm, standalone program). RESEARCH HIGHLIGHTS: Determining the instrument PSF is a key issue. Precise PSF determinations are mandatory if image improvement is performed numerically by deconvolution. Much less exposure time to achieve the same performance than a measurement of the PSF from a very small bead. Does not require having to adjust the PSF by an analytical function to overcome the noise uncertainties.

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Objective. This paper addresses performing inverse radon transform (IRT) with artificial neural network (ANN) or deep learning, simultaneously with cardiac motion correction (MC). The suggested application domain is cardiac image reconstruction in emission or transmission tomography where IRT is relevant. Our main contribution is in proposing an ANN architecture that is particularly suitable for this purpose.Approach. We validate our approach with two types of datasets. First, we use an abstract object that looks like a heart to simulate motion-blurred radon transform. With the known ground truth in hand, we then train our proposed ANN architecture and validate its effectiveness in MC. Second, we used human cardiac gated datasets for training and validation of our approach. The gating mechanism bins data over time using the electro-cardiogram (ECG) signals for cardiac motion correction.Main results. We have shown that trained ANNs can perform motion-corrected image reconstruction directly from a motion-corrupted sinogram. We have compared our model against two other known ANN-based approaches.Significance. Our method paves the way for eliminating any need for hardware gating in medical imaging.

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Aims: Analysis of colonoscopy images is an important diagnostic procedure in the identification of colorectal cancer. It has been observed that owing to advancements in technology, numerous machine-learning models now excel in the analysis of colorectal polyps classification. This work focused on developing a framework that can classify polyps using images during colonoscopy. Materials and Methods: First, the images were corrected by removing their spectral reflection. Second, feature pools were obtained by applying Radon transform (θ=45, 90, 135, and 180). From the Radon transform, fractal dimension was calculated as a feature vector combined with Zernike moment obtained from the Zernike features. Finally, Extreme Gradient Boosting (XGBoost) algorithm was applied for the classification and to compare it with state-of-the-art methods. Results: The experimental results obtained with the proposed framework have been reported, cross-validated, and discussed. The proposed method gives a classification accuracy of 93% for light XGBoost and 92% for XGBoost. Conclusion: This study shows that by applying scale invariant features over a small dataset, XGBoost outperforms state-of-the-art methods when it comes to polyp classification.

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In this work, two methods are proposed for solving the problem of one-dimensional barcode segmentation in images, with an emphasis on augmented reality (AR) applications. These methods take the partial discrete Radon transform as a building block. The first proposed method uses overlapping tiles for obtaining good angle precision while maintaining good spatial precision. The second one uses an encoder-decoder structure inspired by state-of-the-art convolutional neural networks for segmentation while maintaining a classical processing framework, thus not requiring training. It is shown that the second method's processing time is lower than the video acquisition time with a 1024 × 1024 input on a CPU, which had not been previously achieved. The accuracy it obtained on datasets widely used by the scientific community was almost on par with that obtained using the most-recent state-of-the-art methods using deep learning. Beyond the challenges of those datasets, the method proposed is particularly well suited to image sequences taken with short exposure and exhibiting motion blur and lens blur, which are expected in a real-world AR scenario. Two implementations of the proposed methods are made available to the scientific community: one for easy prototyping and one optimised for parallel implementation, which can be run on desktop and mobile phone CPUs.

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The characterization of suspended dust near the Martian surface is extremely relevant to understand the climate of Mars. In this frame, a Dust Sensor instrument, an infrared device designed to obtain the effective parameters of Martian dust using the scattering properties of the dust particles, was developed. The purpose of this article is to present a novel methodology to calculate, from experimental data, an instrumental function of the Dust Sensor that allows solving the direct problem and providing the signal that this instrument would provide given a distribution of particles. The experimental method is based on recording the signal measured when a Lambertian reflector is gradually introduced into the interaction volume at different distances from the detector and source and applying tomography techniques (inverse Radon transform) to obtain the image of a section of the interaction volume. This method provides a complete mapping of the interaction volume experimentally, which determines the Wf function. The method was applied to solve a specific case study. Among the advantages of this method, it should be noted that it avoids assumptions and idealizations of the dimensions of the volume of interaction and reduces the time required to carry out simulations.

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Cerebrovascular segmentation based on phase-contrast magnetic resonance angiography (PC-MRA) provides patient-specific intracranial vascular structures for neurosurgery planning. However, the vascular complex topology and spatial sparsity make the task challenging. Inspired by the computed tomography reconstruction, this paper proposes a Radon Projection Composition Network (RPC-Net) for cerebrovascular segmentation in PC-MRA, aiming to enhance distribution probability of vessels and fully obtain the vascular topological information. Multi-directional Radon projections of the images are introduced and a two-stream network is used to learn the features of the 3D images and projections. The projection domain features are remapped to the 3D image domain by filtered back-projection transform to obtain the image-projection joint features for predicting vessel voxels. A four-fold cross-validation experiment was performed on a local dataset containing 128 PC-MRA scans. The average Dice similarity coefficient, precision and recall of the RPC-Net achieved 86.12%, 85.91% and 86.50%, respectively, while the average completeness and validity of the vessel structure were 85.50% and 92.38%, respectively. The proposed method outperformed the existing methods, especially with significant improvement on the extraction of small and low-intensity vessels. Moreover, the applicability of the segmentation for electrode trajectory planning was also validated. The results demonstrate that the RPC-Net realizes an accurate and complete cerebrovascular segmentation and has potential applications in assisting neurosurgery preoperative planning.

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This study examined methods for estimating the innervation zone (IZ) of a muscle using recorded monopolar high density M waves. Two IZ estimation methods based on principal component analysis (PCA) and Radon transform (RT) were examined. Experimental M waves, acquired from the biceps brachii muscles of nine healthy subjects were used as testing data sets. The performance of the two methods was evaluated by comparing their IZ estimations with manual IZ detection by experienced human operators. Compared with manual detection, the agreement rate of the estimated IZs was 83% and 63% for PCA and RT based methods, respectively, both using monopolar high density M waves. In contrast, the agreement rate was 56% for cross correlation analysis using bipolar high density M waves. The mean difference in estimated IZ location between manual detection and the tested method was 0.12 ± 0.28 inter-electrode-distance (IED) for PCA, 0.33 ± 0.41 IED for RT and 0.39 ± 0.74 IED for cross correlation-based methods. The results indicate that the PCA based method was able to automatically detect muscle IZs from monopolar M waves. Thus, PCA provides an alternative approach to estimate IZ location of voluntary or electrically-evoked muscle contractions, and may have particular value for IZ detection in patients with impaired voluntary muscle activation.

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The derivation of a crystal structure and its phase-specific parameters from a single wide-angle backscattered Kikuchi diffraction pattern requires reliable extraction of the Bragg angles. By means of the first derivative of the lattice profile, an attempt is made to determine fully automatically and reproducibly the band widths in simulated Kikuchi patterns. Even under such ideal conditions (projection centre, wavelength and lattice plane traces are perfectly known), this leads to a lattice parameter distribution whose mean shows a linear offset that correlates with the mean atomic number Z of the pattern-forming phase. The consideration of as many Kikuchi bands as possible reduces the errors that typically occur if only a single band is analysed. On the other hand, the width of the resulting distribution is such that higher image resolution of diffraction patterns, employing longer wavelengths to produce wider bands or the use of higher interference orders is less advantageous than commonly assumed.

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Three-dimensional scanning technology has been traditionally used in the medical and engineering industries, but these scanners can be expensive or limited in their capabilities. This research aimed to develop low-cost 3D scanning using rotation and immersion in a water-based fluid. This technique uses a reconstruction approach similar to CT scanners but with significantly less instrumentation and cost than traditional CT scanners or other optical scanning techniques. The setup consisted of a container filled with a mixture of water and Xanthan gum. The object to be scanned was submerged at various rotation angles. A stepper motor slide with a needle was used to measure the fluid level increment as the object being scanned was submerged into the container. The results showed that the 3D scanning using immersion in a water-based fluid was feasible and could be adapted to a wide range of object sizes. The technique produced reconstructed images of objects with gaps or irregularly shaped openings in a low-cost fashion. A 3D printed model with a width of 30.7200 ± 0.2388 mm and height of 31.6800 ± 0.3445 mm was compared to its scan to evaluate the precision of the technique. Its width/height ratio (0.9697 ± 0.0084) overlaps the margin of error of the width/height ratio of the reconstructed image (0.9649 ± 0.0191), showing statistical similarities. The signal-to-noise ratio was calculated at around 6 dB. Suggestions for future work are made to improve the parameters of this promising, low-cost technique.

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Purpose: The purpose of the study is to propose an algorithm to implement and visualize radiation attenuation-integrated Radon transform based on Beer-Lambert law during emission computed tomography simulation using a deterministic model and also to perform image analysis on resulting images. Methods: Two types of phantoms are designed: plain-disk phantom and patterned-disk phantom. The large disk is filled with an activity of 5 units and the smaller disks have 10 units of activity of 99mTc isotope as an emission map. Three transmission maps for patterned-disk phantom are created with uniform linear attenuation coefficient. Phantoms are scanned with 360° and 180° acquisition arcs. Then, using the algorithm designed, the exponential Radon transform is implemented. After that, the projections are back-projected and filtered to generate tomographic slices. Finally, all slices are analyzed using profile plotting and curve fitting. Moreover, an attenuation Hadamard matrix is provided to facilitate attenuation modeling. Results: The uniform intensity of activity in the phantoms is converted to a disk with progressively decreasing intensity from the periphery to the center in the tomographic slices. Similarly, the circles positioned more centrally appear less intense than those positioned in the periphery, despite all circles having equal activity. When the phantom is scanned in 180° arc, the circles closest to the camera are visualized more intensely. The profile curves of the slices generated by exponential Radon transformation are depicted as U-shaped in profile plotting and are fitted to a bi-exponential function with a near-perfect precision. Conclusions: The incorporation of radiation attenuation results in the development of more realistic models for quantification purposes.

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In this paper we characterize the set of functions that can be represented by infinite width neural networks with RePU activation function max(0,x)p, when the network coefficients are regularized by an ℓ2/p (quasi)norm. Compared to the more well-known ReLU activation function (which corresponds to p=1), the RePU activation functions exhibit a greater degree of smoothness which makes them preferable in several applications. Our main result shows that such representations are possible for a given function if and only if the function is κ-order Lipschitz and its R-norm is finite. This extends earlier work on this topic that has been restricted to the case of the ReLU activation function and coefficient bounds with respect to the ℓ2 norm. Since for q<2, ℓq regularizations are known to promote sparsity, our results also shed light on the ability to obtain sparse neural network representations.

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This work presents a new approach suitable for mapping reciprocal space in three dimensions with standard laboratory equipment and a typical X-ray diffraction setup. The method is based on symmetric and coplanar high-resolution X-ray diffraction, ideally realized using 2D X-ray pixel detectors. The processing of experimental data exploits the Radon transform commonly used in medical and materials science. It is shown that this technique can also be used for diffraction mapping in reciprocal space even if a highly collimated beam is not available. The application of the method is demonstrated for various types of epitaxial microcrystals on Si substrates. These comprise partially fused SiGe microcrystals that are tens of micrometres high, multiple-quantum-well structures grown on SiGe microcrystals and pyramid-shaped GaAs/Ge microcrystals on top of Si micropillars.

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Heart disease has a higher fatality rate than any other disease. Increased Atrial fat on the left atrium has been discovered to cause Atrial Fibrillation (AF) in most patients. AF can put one's life at risk and eventually lead to death. AF might worsen over time; therefore, it is crucial to have an early diagnosis and treatment. To evaluate the left atrium fat tissue pattern using Radon descriptor-based machine learning. This study developed a bridge between the Radon transform framework and machine learning to distinguish two distinct patterns. Motivated by a Radon descriptor-based machine learning approach, the patches of eight patients from CT images of the heart were used and categorized into "epicardial fat tissue" and "nonfat tissue" groups. The 10 feature vectors are extracted from each big patch using Radon descriptors and then fed into a traditional machine learning model. The results show that the proposed methodology discriminates between fat tissues and nonfat tissues clearly. KNN has shown the best performance with 96.77% specificity, 98.28% sensitivity, and 97.50% accuracy. To our knowledge, this study is the first attempt to provide a Radon transform-based machine learning method to distinguish between fat tissue and nonfat tissue on the left atrium. Our proposed research method could be potentially used in advanced interventions.

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We synthesized an alcohol-based liquid scintillator (AbLS), and we implemented an auxiliary monitoring system with short calibration intervals using AbLS for particle therapy. The commercial liquid scintillator used in previous studies did not allow the user to control the chemical ratio and its composition. In our study, the chemical ratio of AbLS was freely controlled by simultaneously mixing water and alcohol. To make an equivalent substance to the human body, 2-ethoxyethanol was used. There was no significant difference between AbLS and water in areal density. As an application of AbLS, the range was measured with AbLS using an electron beam in an image analysis that combined AbLS and a digital phone camera. Given a range-energy relationship for the electron expressed as areal density, the electron beam range (cm) in water can be easily estimated. To date, no literature report for the direct comparison of a pixel image analysis and Monte Carlo (MC) simulation has been published. Furthermore, optical tomography of the inverse problem was performed with AbLS and a mobile phone camera. Analyses of optical tomography images provide deeper insight into Radon transformation. In addition, the human phantom, which is difficult to compose with semiconductor diodes, was easily implemented as an image acquisition and analysis system.

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We study the symplectic Radon transform from the point of view of the metaplectic representation of the symplectic group and its action on the Lagrangian Grassmannian. We give rigorous proofs in the general setting of multi-dimensional quantum systems. We interpret the Radon transform of a quantum state as a generalized marginal distribution for its Wigner transform; the inverse Radon transform thus appears as a "demarginalization process" for the Wigner distribution.