Search Results (121)

In the reconstruction problem of compressed sensing, to address the challenge of adapting common sparse constraints to diverse data, we propose a data-driven inverse-weighted regularization for adaptive data matching to enhance the ability of sparse constraints. Specifically, we formulate a weighted regularization term based on the data transform domain, positing that higher values in the sparsity-promoting transform domain correspond to a greater probability of effective signals. Therefore, when solving sparse optimization problems, we inversely weight this portion based on the inverse relationship with the coefficient magnitude, thereby reducing its impact and mitigating damage to effective signals. However, recognizing that noise and other irrelevant signals are sparse and approximately uniformly distributed in the transform domain, we can increase the weight of this portion to boost the sparsity constraint in the transform domain, thereby enhancing noise suppression. Consequently, we presented the corresponding solution algorithm and convergence proof for inverse-weighted sparse regularization, along with an application example in the context of the Radon transform. Experimental data tests indicate that inverse-weighted sparse regularization enhances the capability of sparse constraints, protects effective signals, suppresses noise, and improves the recovery accuracy of compressive sensing algorithms, as demonstrated in natural image enhancement and seismic multiple suppression. Full article

We introduce the two-point propagation field (TPPF)—a real-valued, phase-sensitive quantity defined as the functional derivative of the single-photon detection probability with respect to an infinitesimal opaque perturbation placed between the source and detection slits. The TPPF is analytically derived and shown to exhibit a stable, high-frequency sinusoidal structure with periods of 4~7 nm near the X-ray detection slit. This structure enables shot-noise-limited displacement detection with ∼200 pm precision for 6 keV X-rays using total photon counts on the order of 1 × ${10}^7$ and detector photon counting as low as 287. Beyond displacement detection, the TPPF physically performs a Fourier–Radon transformation of the projection data, providing a pathway to non-iterative frequency-domain tomography. Two conceptual strategies—a central blocker and off-axis multi-slit arrays—are estimated to lower the required incident photon budget by more than one order of magnitude each, yielding combined reductions of two to three orders of magnitude with near-term detector development. The TPPF concept, originally developed in a perturbative study of single-particle propagation, bridges quantum measurement questions with practical high-resolution X-ray physics. This work provides the foundational physics required for future discrete sampling and 3D numerical reconstruction algorithms. Full article

Metal artifact reduction (MAR) remains a long-standing challenge in computed tomography (CT) reconstruction. Metallic implants introduce inconsistencies between the acquired projection data and the ideal Radon transform, resulting in severe streaking artifacts in images reconstructed using the conventional filtered back projection (FBP) algorithm. In this work, we propose a nonlinear weighted anisotropic total variation (NWATV) regularization method to mitigate metal artifacts and improve CT image quality. The effectiveness of the NWATV method is evaluated through three experiments, and the results demonstrate that it achieves superior reconstruction performance compared to the conventional linear interpolation method, the normalized metal artifact reduction method and the anisotropic total variation (TV) regularization method. Full article

The Hough transform (HT) is widely used in computer vision, tomography, and neural networks. Numerous algorithms for HT computation have been proposed, making their systematic comparison essential. However, existing comparative methodologies are either non-universal and limited to certain HT formulations or task-oriented, relying on application-specific criteria that do not fully capture algorithmic properties. This paper introduces a novel unified methodology for the systematic comparison of HT algorithms. It evaluates key characteristics, including computational complexity, accuracy, and auxiliary space complexity, while explicitly accounting for the property of self-adjointness. The methodology integrates both implementation-level and theoretical considerations related to the interpretation of HT as a discrete approximation of the Radon transform. A set of mathematically justified evaluation functions, not previously described in the literature, is proposed to support our methodology. Importantly, the methodology is universal, applicable across diverse HT paradigms, encompasses pattern-based and Fourier-based fast HT (FHT) algorithms, and offers a comprehensive alternative to existing task-specific methodologies. Its application to several state-of-the-art FHT algorithms ($FHT2DT$, $FHT2SP$, $ASD2$, $KHM$, and Fast Slant Stack) yields new experimentally confirmed theoretical insights, identifies $ASD2$ as the most balanced algorithm, and provides practical guidelines for algorithm selection. In particular, the methodology reveals that for image sizes up to 3000, the maximum normalized computational complexity increases as follows: $FHT2DT$ (1.1), $ASD2$ (15.3), and $KHM$ (30.6), while the remaining algorithms exhibit at least 1.1 times higher values. The maximum orthotropic approximation error equals 0.5 for $ASD2$, $KHM$, and Fast Slant Stack; lies between 0.5 and 1.5 for $FHT2SP$; and reaches 2.1 for $FHT2DT$. In terms of worst-case normalized auxiliary space complexity, the lowest values are achieved by $FHT2DT$ (2.0), Fast Slant Stack (4.0, lower bound), and $ASD2$ (6.8), with all other algorithms requiring at least 8.2 times more memory. Full article

We develop a geometric approach to financial risk based on Crofton’s idea and the tools of the Radon transform. The trajectory of a financial instrument is defined with respect to a frame of reference (money, benchmark). A central role is played by simple instruments, inspired by the annual percentage rate (APR) concept, whose graphs in a fixed reference frame are line segments. Risk is interpreted transactionally as the density of exchange dilemmas that arise when the instrument’s trajectory intersects the trajectories of simple instruments. This perspective leads to a risk measure given by the trajectory length in the Crofton–Steinhaus sense. We also introduce new notions, such as geometric volatility, transactional entropy, and trajectory temperature, associated with the distribution of the number of intersections, enabling thermodynamic analogies to be incorporated into the description of risk and market complexity. Full article

Long-term monitoring of radon (²²²Rn) and thoron (²²⁰Rn) radioactive gases has been used in earthquake forecasting. Seismic activity before earthquakes raises the levels of these gases, causing abnormalities in the baseline values of radon and thoron time series (RTTS) data. This study reports applications of kernel density estimation (KDE) and wavelet-based density estimation (WBDE) to detect anomalies in radon, thoron, and meteorological time-series data. Anomalies appearing in the RTTS data have been assessed for their potential correlation with seismic events. Using KDE and WBDE, radon anomalies were observed on 12 March, 15 August, 17 September, in the year 2017, and 19 January 2018. Thoron anomalies were recorded on 12 March, 15 August, 17 September 2017, and 28 February 2018. Irregularities in RTTS were observed several days before seismic events. Anomalies in RTTS, detected using KDE, successfully correlated five out of nine seismic events while WBDE identified four anomalies in RTTS which were successfully correlated with the corresponding seismic events. The wavelet transform has been used to reduce noise at higher decomposition levels in radon and thoron time series. Findings of the study reveal the potential of radon and thoron time series that can be used as precursors for earthquake forecasting. Full article

The Apex-Shifted Hyperbolic Radon Transform (ASHRT) is a variant of the Radon Transform. In the field of seismic exploration, it can be applied to simultaneous source separation, diffraction- and reflection-wave separation, seismic data reconstruction, among other purposes. This paper primarily investigates the application of ASHRT in the separation of diffraction and reflection waves. Detailed exploration of complex structures using diffraction wave imaging has become a new trend, thereby necessitating the separation of diffraction wave fields. The conventional ASHRT based on the Stolt operator, due to its weak sparsity, increasingly struggles to meet current separation requirements. Compared to conventional ASHRT, the Stolt-based ASHRT enables fast, efficient computation; however, the Stolt operator exhibits relatively weaker sparseness and fidelity. To address this issue, replacing the Stolt operator with the PS operator for performing ASHRT allows the transform to achieve both high sparseness and high fidelity simultaneously. In this study, synthetic data were used to investigate the advantages of the PS operator over the Stolt operator. Furthermore, both operators were applied to separate diffraction and reflection waves in marine seismic data and land seismic data, respectively. The research demonstrates that, in the separation of diffraction and reflection waves using the ASHRT method, the PS operator provides significant advantages over the Stolt operator in terms of both sparseness and fidelity. Full article

Focused ultrasound (FU) technology is extensively employed in clinical applications such as tumor ablation, Parkinson’s disease treatment, and neuropathic pain management. The safety and efficacy of FU therapy critically depend on the accurate quantification of the acoustic field, particularly the high-pressure distribution in focal region. To address the limitations of existing acoustic measurement techniques—including invasiveness, inability to measure high sound pressure, and system complexity—this study proposes a non-invasive method termed Laser Deflection Acoustic Field Quantification (LDAQ), based on the laser deflection principle. An experimental system was constructed utilizing the acousto-optic deflection effect, which incorporates precision displacement control, rotational scanning, and synchronized triggering. Through tomographic scanning, laser deflection images of the acoustic field were acquired at multiple orientations. An inversion algorithm using Radon transforms was proposed to reconstruct the refractive index gradient distributions from the variations of light intensity and spot displacement. An adaptive weighted fusion strategy was then employed to map these optical signals to the sound pressure field. To validate the LDAQ technique, an acoustic field generated by an FU transducer operating at 0.84 MHz was measured. The reconstructed results were compared with both hydrophone measurements and numerical simulations. The findings demonstrated high consistency among all three results within the focal zone. Full-field analysis yielded a root mean square error (RMSE) of 0.1102 between LDAQ and simulation, and an RMSE of 0.1422 between LDAQ and hydrophone measurements. These results confirm that LDAQ enables non-invasive and high-precision quantification of megapascal-level focused acoustic fields, offering a reliable methodology for acoustic field characterization to support FU treatment optimization and device standardization. Full article

With the continuous development of cities and the increasing utilization of underground space, ambient noise seismic imaging has become an essential approach for exploring and monitoring the urban subsurface. The integration of Distributed Acoustic Sensing (DAS) with ambient noise imaging offers a more convenient and effective solution for investigating shallow subsurface structures in urban environments. To overcome the limitations of conventional ambient noise seismic nodes, which are costly and incapable of achieving high-density data acquisition, this work makes use of existing urban telecommunication fibers to record ambient noise and perform sliding-window cross-correlation on it. Then the Phase-Weighted Stack (PWS) technique is applied to enhance the quality and stability of the cross-correlation signals, and fundamental-mode Rayleigh wave dispersion curves are extracted from the cross-correlation functions through the High-Resolution Linear Radon Transform (HRLRT). In the inversion stage, an adaptive regularization strategy based on automatic L-curve corner detection is introduced, which, in combination with the Preconditioned Steepest Descent (PSD) method, enables efficient and automated dispersion inversion, resulting in a well-resolved near-surface S-wave velocity structure. The results indicate that the proposed workflow can extract useful surface-wave dispersion information under typical urban noise conditions, achieving a feasible level of subsurface velocity imaging and providing a practical technical means for urban underground space exploration and utilization. Full article

Recent advances in forward-looking sonar (FLS) have enabled the acquisition of high-resolution acoustic images. However, the accuracy of image-based rotation estimation remains limited owing to speckle noise, perceptual ambiguity, and shadows. In recent years, object-based path reconstruction has become increasingly important for underwater inspection tasks, and in such scenarios, reliably estimating rotation from static seabed objects is essential for ensuring the robustness of autonomous underwater vehicle (AUV) missions. Accordingly, we present a rotation estimation method that adaptively extracts a region of interest (ROI) and applies the Radon transform. The proposed approach automatically selects sonar image regions containing objects and emphasizes high projection values in the resulting sinogram. By computing the shift between the high projection values of two sinograms, the method achieves robust rotation estimation even under low contrast and severe speckle noise. Experimental results demonstrate that our method consistently achieves lower estimation errors than existing approaches, particularly in scenarios involving static seabed objects. These findings highlight its practical value for object-based path reconstruction, high-precision mapping, and other underwater navigation tasks. Full article

The Shizhuyuan polymetallic deposit in Hunan Province, China, is a world-class ore field rich in tungsten (W), tin (Sn), molybdenum (Mo), and bismuth (Bi), now facing resource depletion due to prolonged exploitation. This study addresses the limitations of traditional geological prediction methods in complex terrain by integrating multi-source datasets—including γ-ray spectrometry, high-precision magnetometry, induced polarization (IP), and soil radon measurements—across 5049 samples. Unsupervised factor analysis was employed to extract five key ore-indicating factors, explaining 82.78% of data variance. Based on these geological features, predictive models including Support Vector Machine (SVM), Random Forest (RF), and Extreme Gradient Boosting (XGBoost) were constructed and compared. SHAP values were employed to quantify the contribution of each geological feature to the prediction outcomes, thereby transforming the machine learning “black-box models” into an interpretable geological decision-making basis. The results demonstrate that machine learning, particularly when integrated with multi-source data, provides a powerful and interpretable approach for deep mineral prospectivity mapping in concealed terrains. Full article

Background: Radon, a naturally occurring radioactive gas, is increasingly recognized as a major risk factor for lung cancer (LC), especially among non-smokers. The objective of this study was to identify serum biomarkers for the early detection of LC in individuals at high risk due to prolonged residential radon exposure in Chiang Mai, Thailand, and to assess whether the use of single or combined biomarkers improves the sensitivity and specificity of detection. Methods: A total of 15 LC patients and 30 healthy controls (HC) were enrolled. The HC group was further stratified into two subgroups: low radon (LR, n = 15) and high radon (HR, n = 15) exposure. All participants were non-smokers or former smokers. Serum levels of cytokeratin 19 fragment (CYFRA 21-1), carcinoembryonic antigen (CEA), interleukin-6 (IL-6), interleukin-8 (IL-8), transforming growth factor-alpha (TGF-alpha), and indoleamine 2,3-dioxygenase-1 (IDO-1) were measured using the Milliplex^® Kit on a Luminex^® Multiplexing Instrument (MAGPIX^® System). Results: Serum CEA, IL-6 and IL-8 levels were significantly higher in LC patients compared to the HC group (p < 0.05). Among analyzed biomarkers, only IL-8 was significantly elevated in LC patients compared to the HR group (p = 0.04). Notably, CYFRA 21-1 was the only biomarker that significantly differed between LR and HR groups (p = 0.004). The diagnostic potential of these biomarkers was evaluated using receiver operating characteristic (ROC) analysis. Individually, IL-6 showed the highest discriminative ability for differentiating LC patients from both HC and HR groups, with high specificity but moderate sensitivity. Combining IL-6 and IL-8 improved specificity and increased the area under the ROC curve (AUC), though it did not enhance sensitivity for distinguishing LC from HC. For distinguishing LC from HR individuals, IL-6 and CYFRA 21-1 exhibited strong diagnostic performance. Their combination significantly improved diagnostic accuracy, yielding the highest AUC, sensitivity, and specificity. In contrast, CEA, IL-8, TGF-alpha, and IDO-1 demonstrated limited diagnostic utility. Conclusions: Based on the available literature, this is the first study to evaluate the combined use of IL-6 and CYFRA 21-1 as potential biomarkers for LC screening in individuals with high residential radon exposure. Our findings highlight their utility, particularly in combination, for improving diagnostic accuracy in this high-risk population. Full article

This article describes the interactions between radon emissions and tectonic movements that accompany seismic activity as a function of time. The interpretation is based on advanced data analysis methods, such as Fourier wavelet transform, SGolay correlation analysis, and time-based data categorization. The dataset comprised the measurement results of ²²²Rn activity concentrations and the effects of the tectonic activity of rock masses acquired from two water-tube tiltmeters and five SRDN-3 radon probes. The analysis included four seismic events with moderate and light magnitudes (≥4.0), with a hypocenter at a depth of 1–10 km, located approximately 75 km from the research site. Each seismic shock had a different distribution of rock mass phases recorded by the integrated (probe-tiltmeter) measurement system. The results indicate that at the research site, the radon-tectonic signal is best identified between 25 and 48 h and between 49 and 72 h before the seismic shock. Positive correlations between the tectonic signal and the radon signal associated with the tension phase in the rock mass and negative correlations between the tectonic signal and the radon signal associated with the compression phase allow the description of the behavior of the rock mass before the seismic shock. Mixed correlations (positive and negative) indicate that both the stress and strain phases of the rock mass are recorded. The observed correlations seem particularly promising, as they can be recorded already 1–3 days before the seismic event, allowing an appropriately early response to the expected seismic event. Full article

This study presents a comprehensive methodology for the detection and characterization of fractures in geological samples using X-ray computed tomography (CT). By combining convolution-based image processing techniques with advanced neural network-based segmentation, the proposed approach achieves high precision in identifying complex fracture networks. The method was applied to a marly limestone sample from the Maiolica Formation, part of the Umbria–Marche stratigraphic succession (Northern Apennines, Italy), a geological context where fractures often vary in size and contrast and are frequently filled with minerals such as calcite or clays, making their detection challenging. A critical part of the work involved addressing multiple sources of uncertainty that can impact fracture identification and measurement. These included the inherent spatial resolution limit of the CT system (voxel size of 70.69 μm), low contrast between fractures and the surrounding matrix, artifacts introduced by the tomographic reconstruction process (specifically the Radon transform), and noise from both the imaging system and environmental factors. To mitigate these challenges, we employed a series of preprocessing steps such as Gaussian and median filtering to enhance image quality and reduce noise, scanning from multiple angles to improve data redundancy, and intensity normalization to compensate for shading artifacts. The neural network segmentation demonstrated superior capability in distinguishing fractures filled with various materials from the host rock, overcoming the limitations observed in traditional convolution-based methods. Overall, this integrated workflow significantly improves the reliability and accuracy of fracture quantification in CT data, providing a robust and reproducible framework for the analysis of discontinuities in heterogeneous and complex geological materials. Full article

High-density component-induced metal artifacts in industrial computed tomography (CT) severely impair image quality and make further analysis more difficult. To suppress artifacts and improve image quality, this research suggests a practical approach that combines lightweight attention-enhanced super-resolution networks with Radon-domain artifact elimination. First, the original CT slices are subjected to bicubic interpolation, which enhances resolution and reduces sampling errors during transformation. The Radon transform, which detects and suppresses metal artifacts in the Radon domain, is then used to convert the interpolated pictures into sinograms. The artifact-suppressed sinograms are then reconstructed at better resolution using a lightweight Enhanced Deep Super-Resolution (EDSR) network with a channel attention mechanism, which consists of only one residual block. The inverse Radon transform is used to recreate the final CT images. An average peak signal-to-noise ratio (PSNR) of 40.39 dB and an average signal-to-noise ratio (SNR) of 29.75 dB, with an SNR improvement of 15.48 dB over the original artifact-laden images, show the success of the suggested strategy in experiments. This method offers a workable and effective way to improve image quality in industrial CT applications that involve intricate structures that incorporate metal. Full article