Smoothing Algorithm Research Articles

High-resolution vasomotion analysis reveals novel arteriole physiological features and progressive modulation of cerebral vascular networks by stroke

Spontaneous cerebral vasomotion, characterized by ∼0.1 Hz rhythmic contractility, is crucial for brain homeostasis. However, our understanding of vasomotion is limited due to a lack of high-precision analytical methods to determine single vasomotion events at basal levels. Here, we developed a novel strategy that integrates a baseline smoothing algorithm, allowing precise measurements of vasodynamics and concomitant Ca2+ dynamics in mouse cerebral vasculature imaged by two-photon microscopy. We identified several previously unrecognized vasomotion properties under different physiological and pathological conditions, especially in ischemic stroke, which is a highly harmful brain disease that results from vessel occlusion. First, the dynamic characteristics between SMCs Ca2+ and corresponding arteriolar vasomotion are correlated. Second, compared to previous diameter-based estimations, our radius-based measurements reveal anisotropic vascular movements, enabling a more precise determination of the latency between smooth muscle cell (SMC) Ca2+ activity and vasoconstriction. Third, we characterized single vasomotion event kinetics at scales of less than 4 seconds. Finally, following pathological vasoconstrictions induced by ischemic stroke, vasoactive arterioles entered an inert state and persisted despite recanalization. In summary, we developed a highly accurate technique for analyzing spontaneous vasomotion, and our data suggested a potential strategy to reduce stroke damage by promoting vasomotion recovery.

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Detection the internal quality of watermelon seeds based on terahertz imaging technology combined with image smoothing and enhancement algorithm

AbstractThe cultivation processes of watermelon seed are often affected by issues such as empty shells and defects, resulting in significant losses. To obtain high‐quality seeds, the terahertz imaging technology combined with image smoothing and enhancement algorithm was proposed to reduce the noise and non‐obvious features caused by the influence in the imaging process and realize the non‐destructive, efficient, and accurate detection of the internal quality of watermelon seeds. Initially, a terahertz imaging system with a spatial resolution of 0.4 mm was used to acquire images of watermelon seeds with varying levels of fullness. Subsequently, denoising techniques, including Gaussian filtering, median filtering, bilateral filtering, discrete wavelet transformation denoising, wavelet denoising, and principal component analysis denoising, were used to handle the terahertz spectral images of watermelon seeds in the frequency range of 1–1.5 THz, respectively. Image enhancement operations, involving segmented linear gray‐level transformation and fractional‐order differentiation, were performed on the terahertz images of watermelon seeds after denoising. The optimal image processing approach was determined based on defect assessment through threshold segmentation. Finally, the validation was conducted at a spatial resolution of 0.2 mm. The images at a spatial resolution of 0.4 mm were subjected to wavelet denoising and window slicing in segmented linear gray‐level transformation (WS‐SLT) enhancement; the results exhibited the following improvements in defect accuracy compared with untreated THz images. A 7.74% increase in accuracy was observed for empty seeds, along with a 6.29% increase in the defect ratio for defective seeds 1. The defect ratio for intact seeds was 0, and there was no significant difference in defect ratio accuracy for defective seeds 2. At a spatial resolution of 0.2 mm, the average defect ratio error of THz imaging handled by wavelet denoising and WS‐SLT was approximately 5.04%. In conclusion, the terahertz imaging technology coupled with wavelet denoising and WS‐SLT methods can be used to enhance the accuracy of internal defect detection in watermelon seeds, and it provides a technical foundation and reference for assessing watermelon seed fullness.

Iterative smoothing for change-point regression function estimation

Understanding wildfire spread in Canada is critical to promoting forest health and protecting human life and infrastructure. Quantifying fire spread from noisy images, where change-point boundaries separate regions of fire, is critical to accurately estimating fire spread rates. The challenge lies in denoising the fire images and accurately identifying highly non-linear fire lines without smoothing over boundaries. In this paper, we develop an iterative smoothing algorithm for change-point data that utilizes oversmoothed estimates of the underlying data generating process to inform re-smoothing. We demonstrate its effectiveness on simulated one- and two-dimensional change-point data, and robustness to response outliers. Then, we apply the methodology to fire spread images from laboratory micro-fire experiments and show that the regions fuel, burning and burnt-out are smoothed while boundaries are preserved.

Reconstructing a Short-Term Indicator by State-Space Models: An Application to Estimate Hours Worked by Quarterly National Accounts

ISTAT has recently released an updated version of short-term statistics on hours worked in Italy, which are used in labor input estimates by the Quarterly National Accounts (QNA). The coverage of these statistics has been expanded from larger-than-ten workers firms to include the entire universe of Italian private firms. To include the updated indicator within estimates by QNA, the series must be reconstructed back to 1995 first quarter (1995q1) due to methodological requirements of QNA. In this paper, we first reconstruct the updated indicator using the Kalman filter and smoother algorithms applied to a state-space representation of a multivariate structural model (SUTSE). Next, we comparatively assess the performance of the new indicator against the non-updated one. This assessment is based on estimates of quarterly per-employee hours worked using temporal disaggregation methods for seven economic sections spanning the non-agricultural private business economy over the period 1995q1 to 2020q4. Compared to the previous indicator, the reconstructed indicator (i) implies improvements in temporal disaggregation model fitting in the majority of economic sections considered; (ii) returns smaller forecast errors in the 64.3% of the estimations, based on MAE; (iii) ensures a higher correlation between the estimated quarterly series to the indicator in the 71.4% of the estimates.

Validation of Inertial-Measurement-Unit-Based Ex Vivo Knee Kinematics during a Loaded Squat before and after Reference-Frame-Orientation Optimisation.

Recently, inertial measurement units have been gaining popularity as a potential alternative to optical motion capture systems in the analysis of joint kinematics. In a previous study, the accuracy of knee joint angles calculated from inertial data and an extended Kalman filter and smoother algorithm was tested using ground truth data originating from a joint simulator guided by fluoroscopy-based signals. Although high levels of accuracy were achieved, the experimental setup leveraged multiple iterations of the same movement pattern and an absence of soft tissue artefacts. Here, the algorithm is tested against an optical marker-based system in a more challenging setting, with single iterations of a loaded squat cycle simulated on seven cadaveric specimens on a force-controlled knee rig. Prior to the optimisation of local coordinate systems using the REference FRame Alignment MEthod (REFRAME) to account for the effect of differences in local reference frame orientation, root-mean-square errors between the kinematic signals of the inertial and optical systems were as high as 3.8° ± 3.5° for flexion/extension, 20.4° ± 10.0° for abduction/adduction and 8.6° ± 5.7° for external/internal rotation. After REFRAME implementation, however, average root-mean-square errors decreased to 0.9° ± 0.4° and to 1.5° ± 0.7° for abduction/adduction and for external/internal rotation, respectively, with a slight increase to 4.2° ± 3.6° for flexion/extension. While these results demonstrate promising potential in the approach's ability to estimate knee joint angles during a single loaded squat cycle, they highlight the limiting effects that a reduced number of iterations and the lack of a reliable consistent reference pose inflicts on the sensor fusion algorithm's performance. They similarly stress the importance of adapting underlying assumptions and correctly tuning filter parameters to ensure satisfactory performance. More importantly, our findings emphasise the notable impact that properly aligning reference-frame orientations before comparing joint kinematics can have on results and the conclusions derived from them.

Application and characterization of digital Sallen–Key filter in nuclear spectrum smoothing

In the nuclear spectrum analysis processing, spectrum smoothing can remove the statistical fluctuation in the spectrum, which is beneficial for peak detection and peak area calculation. In this work, a spectrum smoothing algorithm is proposed based on digital Sallen–Key filter, which contains four parameters (m, n, k, D). The amplitude–frequency response curve of Sallen–Key filter is deduced and the filtering performance is analyzed. Meanwhile, the effects of the four parameters on the shape of the smoothed spectrum are explored: D affects the counts and peak areas of the spectrum, and the peak area can be corrected by the peak area correction function S’. The parameters of m, n and k affect the peak position after smoothing, making the peak position shift to the right, and the peak position correction function P’ can be used to correct the peak position, when n¿2, the spectrum data appear negative after smoothing, when k¿2, the smoothed spectrum broadening degree is greater than 20%. Smoothness (R), noise smoothing factor (NSF), spectrum count ratio before and after smoothing (PER), and comprehensive evaluation factor (Q) are used to evaluate the smoothing effect of the algorithm. The parameters of the algorithm are optimally selected: about the gamma spectrum of 137Cs and 60Co, the optimal parameters are m=1.5 n=2 k=2 D=1, about the characteristic X-ray spectrum of Fe and quasi-geological sample (TiMnFeNiCuZn), the optimal parameters are m=1.1 n=1.1 k=1.3 D=1. Based on Sallen–Key smoothing method, Fourier transform method, Gaussian function method, wavelet transformation method, center of gravity method and least squares method, the gamma spectrum of 137Cs is smoothed and denoised in this paper. The results show that the Sallen–Key method has better spectrum denoising effect (R=0.6056) and comprehensive performance indicators (Q=0.6104), which can be further applied for the smoothing of nuclear spectrum data.

Mobile Robot Path Planning Algorithm Based on NSGA-II

Path planning for mobile robots is a key technology in robotics. To address the issues of local optima trapping and non-smooth paths in mobile robot path planning, a novel algorithm based on the NSGA-II (Non-dominated Sorting Genetic Algorithm II) is proposed. The algorithm utilizes a search window approach for population initialization, which improves the quality of the initial population. An innovative fitness function is designed as the objective function for optimization iterations. A probability-based selection strategy is employed for population selection and optimization, enhancing the algorithm’s ability to escape local minima and preventing premature convergence to suboptimal solutions. Furthermore, a path smoothing algorithm is developed by incorporating Bézier curves. By connecting multiple segments of Bézier curves, the problem of the high computational complexity associated with high-degree Bézier curves is addressed, while simultaneously achieving smooth paths. Simulation results demonstrated that the proposed path planning algorithm exhibited fewer iterations, superior path quality, and path smoothness. Compared to other methods, the proposed approach demonstrated better overall performance and practical applicability.

Robust Recursive Least-Squares Fixed-Point Smoother and Filter using Covariance Information in Linear Continuous-Time Stochastic Systems with Uncertainties

This study develops robust recursive least-squares (RLS) fixed-point smoothing and filtering algorithms for signals in linear continuous-time stochastic systems with uncertainties. The algorithms use covariance information, such as the cross-covariance function of the signal with the observed value and the autocovariance function of the degraded signal. A finite Fourier cosine series expansion approximates these functions. Additive white Gaussian noise is present in the observation of the degraded signal. A numerical simulation compares the estimation accuracy of the proposed robust RLS filter with the robust RLS Wiener filter, showing similar mean square values (MSVs) of the filtering errors. The MSVs of the proposed robust RLS fixed-point smoother are also compared to those of the proposed robust RLS filter.

Smooth morphing of immersed spherical curves and application to ruled surfaces

In this paper, we realize a rapid, smooth iterative morphing algorithm between two immersed and closed spherical curves of arbitrary turning numbers. By compensating in turning numbers, we linearly interpolate between geodesic curvatures and the side lengths of their accurate spherical polygons approximation. Our algorithm is essentially based on a geometrical closure condition for a flow of spherical polygons involving the variation of both sides and exterior angles. A curvature smoothing flow using discrete geodesic curvature is adopted for smooth curve generation. To demonstrate the good properties of the method, a morphing of spherical curves and ruled surfaces is illustrated.

Application of mobile laser measurement system in railway inspection

Abstract Given the time constraints and demanding precision requirements of railway measurements, traditional measurement methods struggle to meet the inspection needs for the future expansion and renovation of extensive rail networks. This paper presents a railway data collection and processing system developed by using mobile laser scanning technology. To address the issue of error accumulation exceeding predefined limits in the positioning algorithm, we conducted a comprehensive study and utilized smoothing algorithms to correct acceleration and attitude angles. This optimization process not only enhances trajectory data but also improves the accuracy of the point cloud. The results indicate that this system holds significant importance in the realms of railway digital survey and design, as well as digital renovation and related areas.

SOHD-LOAM: Suppress odometry height drift lidar odometry and mapping on undulating road

In the process of mapping outdoor undulating and flat roads, existing LiDAR SLAM systems often encounter issues such as map distortion and ghosting. These problems arise due to the low vertical resolution of multi-line LiDAR, which easily leads to the occurrence of odometry height drift during the mapping process. To address this challenge, this study propose a novel LiDAR SLAM system named SOHD-LOAM, designed specifically to suppress odometry height drift. This system encompasses several critical components, including data preprocessing, front-end LiDAR odometry, back-end LiDAR mapping, loop detection, and graph optimization. SOHD-LOAM leverages the road gradient limitation algorithm and the height smoothing algorithm as its core, while also integrating the Kalman filter, loop detection, and graph optimization techniques. To evaluate the performance of SOHD-LOAM, the comprehensive experiments are conducted with using KITTI datasets and real-world scenes. The experimental results demonstrate that SOHD-LOAM achieves superior accuracy and robustness in global odometry compared to the state-of-the-art LEGO-LOAM. Specifically, the height error of the sequences 00, 05 experiment was found to be 40.62% and 61.92% lower than that of LEGO-LOAM. Additionally, the maps generated by SOHD-LOAM exhibit no distortion or ghosting, thereby significantly enhancing map quality.

Qualitative and quantitative detection of microplastics in soil based on LIF technology combined with OOA-ELM/SPA-PLS

Traditional methods for detecting soil microplastics include chemical digestion, density separation, staining, etc. These methods often only provide qualitative analysis of microplastics and are difficult to accurately quantify. To address this issue, laser induced fluorescence (LIF) technology is introduced, which can achieve high sensitivity, non-destructive, and rapid detection, and improve the accuracy and efficiency of qualitative and quantitative analysis of soil microplastics. Therefore, based on LIF technology, a qualitative prediction model for optimizing Extreme Learning Machine (ELM) using Osprey Optimization Algorithm (OOA) and a quantitative prediction model combining Continuous Projection Algorithm (SPA) with Partial Least Squares Algorithm (PLS) were established. Qualitative analysis used eight types of microplastics, with AS, PA66, ABS, PS, POM, PBT, PET, and PVC as experimental samples. Initially, spectral data is obtained using LIF technology and the raw spectral data is pre-processed using polynomial smoothing algorithm (SG) and moving average (MA) methods. Subsequently, factor analysis (FA) and local linear embedding (LLE) techniques are applied to dimensionality reduction and then input into the ELM model. At the same time, the ELM parameter is optimized by using OOA algorithm. In the quantitative analysis, PA66 powder and soil are mixed in different proportions (10:0, 8:2, 5:5, 2:8, 0:10), SG and MA pre-processing are performed on the spectral data obtained by LIF technology, and SPA is used to select the spectral characteristic wavelength for the original data and the pre-processed spectral data, and then a linear regression model is established combined with PLS. In order to facilitate the comparison of data, the experimental results are reserved to 5 decimal places, the experimental results indicate that LIF technology is faster than traditional methods in extracting raw data. The convergence of the OOA-optimized ELM model is better than that of the PSO-optimized ELM model. Among all the models of qualitative analysis, SG-LLE-OOA-ELM had the best prediction effect, with mean square error (MSE) of 0.00834, coefficient of determination (R2) of 0.99841, root mean square error (RMSE) of 0.09134, and mean absolute error (MAE) of 0.07038. Among the models of quantitative analysis, the best effect is SG-SPA-PLS model with R2 of 0.99951.

Bayesian Inference of Recurrent Switching Linear Dynamical Systems with Higher-Order Dependence

Many complicated dynamical events may be broken down into simpler pieces and efficiently described by a system that shifts among a variety of conditionally dynamical modes. Building on switching linear dynamical systems, we develop a new model that extends the switching linear dynamical systems for better discovering these dynamical modes. In the proposed model, the linear dynamics of latent variables can be described by a higher-order vector autoregressive process, which makes it feasible to evaluate the higher-order dependency relationships in the dynamics. In addition, the transition of switching states is determined by a stick-breaking logistic regression, overcoming the limitation of a restricted geometric state duration and recovering the symmetric dependency between the switching states and the latent variables from asymmetric relationships. Furthermore, logistic regression evidence potentials can appear as conditionally Gaussian potentials by utilizing the Pólya-gamma augmentation strategy. Filtering and smoothing algorithms and Bayesian inference for parameter learning in the proposed model are presented. The utility and versatility of the proposed model are demonstrated on synthetic data and public functional magnetic resonance imaging data. Our model improves the current methods for learning the switching linear dynamical modes, which will facilitate the identification and assessment of the dynamics of complex systems.

Geoelectrical image of the Sabalan geothermal reservoir from magnetotelluric studies

The magnetotelluric (MT) survey of the Sabalan geothermal zone, which includes 22 stations along three traverse profiles across the main prospect zone, was conducted in 2007. The geophysical investigation utilized sharp boundary inversion of processed MT data due to the high contrast of electrical resistivity between embedded layers. This method was preferred to suppress the smeared-out impact of the smooth inversion algorithm on retrieving geological layering. The analysis of MT data led to the use of a 2D inversion algorithm to visualize the geothermal reservoir. Additionally, the geoelectrical strike of the main geothermal target was determined, showing some inconsistency across the profiles. The simulation of synthetic numerical models is conducted to evaluate the effectiveness of sharp boundary inversion compared to a smooth algorithm in sharp gradient mediums, specifically in terms of electrical characteristics, for plausible geothermal scenarios. The Finite Element method (FEM) was employed to construct these models, followed by running the 2D forward and inversion processes. The meshing and initial parameters of the modeling were set based on information obtained from prior geological and geophysical investigations. A sharp boundary inversion can be accurately implemented by introducing layering constraints along each profile surrounding the probable sought geothermal reservoir target. These layering constraints encompass the conductive cap, topsoil, and basement rocks, which are the key components of a plausible geothermal configuration. The results of the comparison indicate that the sharp boundary inversion technique effectively restored the boundary between neighboring layers that had significant differences in electrical resistivity. This was achieved when the smoothing algorithm failed to produce an accurate representation of the layered model. Ultimately, conceptual geological models were developed to illustrate the plausible structures corresponding to each profile, focusing on the sought geothermal reservoir targets. It can be deduced that many misunderstandings in the smoothing inversion algorithm will be omitted if the sharp boundary algorithm is used in highly electrical gradient structures. Based on the outcomes, a trachyandesite, andesite, and altered andesite reservoir exists at an elevation of 1600 to −2000 m. The reservoirs were recovered precisely with sharp and discriminable interfaces. Therefore, accurate interfaces led us to determine the conductive cap, heat source, and topsoil stacking as the main components of the geothermal system.

Auxiliary two-filter particle smoothing for one generalized hidden Markov model

This paper develops two-filter particle smoothing (TFPS) algorithms for the nonlinear fixed-interval smoothing problem of one generalized hidden Markov model (GHMM), where the current observation depends not only on the current state, but also on one-step previous state. Firstly, by Bayesian approach, the two-filter smoothing (TFS) formula for GHMM is established to calculate smoothing densities. In this TFS formula, the backward information prediction density is generally not a density of the state. This results in a difficulty that the normal sequential Monte Carlo (SMC) sampling technique cannot be directly applied to design corresponding TFPS algorithms based on the TFS formula. To solve this difficulty, a generalized TFS formula for GHMM is then proposed by introducing a sequence of artificial densities. By combining this generalized TFS formula, SMC, and the auxiliary variable sampling technique, a basic auxiliary TFPS (ATFPS) algorithm with quadratic computational complexity is proposed, and a simplified ATFPS algorithm with linear computational complexity is further developed. Finally, the effectiveness and superiority of the two proposed ATFPS algorithms for GHMM are verified via simulation examples and real experimental data.

An optimal “Trade-Online-Deliver-Offline” strategy for recycling unwanted medicines by reutilizing the existent informative pharmaceutical sales network

Circular economy and sustainable development resort to creating friendly and profitable environment of recycling unwanted goods in practice. This research aims to design a novel “Trade-Online-Deliver-Offline” (TODO) system to recycle unwanted medicines (UMs) by reutilizing the existent informative pharmaceutical sales network, which is the first dual-channel recycle system with synergies of manufacturer, chain drugstores and governments. Cross-selling effect, i.e., the additional sales from the customers who visit the drugstores for returning UMs, is also considered in this system. With a given revenue-sharing contract, a bi-level programming model is built to formulate such a recycle system, where the drugmaker is the leader and the chain drugstores are the followers within a decision mode of the Stackelberg game. Through reformulating, this complicated model is solved by developing an efficient smoothing algorithm. Scenario analysis and sensitivity analysis are employed to validate the built model and reveal valuable managerial insights. Main findings include: Compared with the existing modes, the proposed TODO mode is more efficient in terms of the recycled UM quantity and the reduced government burden; Cross-selling effects enhance the profit of drugstores without damage of customer’s surplus, but without significant impacts on the drugmaker’s profit; An increasing revenue-sharing ratio is beneficial to the drugstores in certain scenarios, but reduces the total profit of the recycle system; Resale prices of UMs and governmental tax relief policies both dominate the drugmaker’s optimal ratio of the resold and donated UMs.

Establishment and preliminary application of personalized three-dimensional reconstruction of thyroid gland with automatic detection of thyroid nodules based on ultrasound videos.

A well display of the spatial location of thyroid nodules in the thyroid is important for surgical path planning and surgeon-patient communication. The aim of this study was to establish a three-dimensional (3D) reconstruction method of the thyroid gland, thyroid nodule, and carotid artery with automatic detection based on two-dimensional (2D) ultrasound videos, and to evaluate its clinical value. Ultrasound videos, including the thyroid gland with nodule, isthmus of thyroid gland, and ipsilateral carotid artery, were recorded. BC-UNet, MTN-Net, and RDPA-U-Net network models were innovatively employed for segmentation of the thyroid glands, the thyroid nodules, and the carotid artery respectively. Marching Cubes algorithm was used for reconstruction, while Laplacian smoothing algorithm was employed to smooth the 3D model surface. Using this model, 20 patients and 15 surgeons completed surveys on the effectiveness of this model for the pre-surgery demonstration of nodule location as well as surgeon-patient communication. The thyroid gland with nodule, isthmus of gland, and carotid artery were reconstructed and displayed. With the 3D model, the understanding of the spatial location of thyroid nodules improved in all three surgeon groups, eliminating the influence of professional levels. In the patient survey, the patients' understanding of the thyroid nodule location and procedure for surgery were significantly improved. In addition, with the 3D model, the time for doctors to explain to patients was significantly reduced (16.75 vs. 8.85min, p=0.001). To our knowledge, this is the first report of constructing a 3D thyroid model using a deep learning technique for personalized thyroid segmentation based on 2D ultrasound videos. The preliminary clinical application showed that it was conducive to the comprehension of the location of thyroid nodules for surgeons and patients, with significant improvement on the efficiency of surgeon-patient communication.

Towards Large Certified Radius in Randomized Smoothing Using Quasiconcave Optimization

Randomized smoothing is currently the state-of-the-art method that provides certified robustness for deep neural networks. However, due to its excessively conservative nature, this method of incomplete verification often cannot achieve an adequate certified radius on real-world datasets. One way to obtain a larger certified radius is to use an input-specific algorithm instead of using a fixed Gaussian filter for all data points. Several methods based on this idea have been proposed, but they either suffer from high computational costs or gain marginal improvement in certified radius. In this work, we show that by exploiting the quasiconvex problem structure, we can find the optimal certified radii for most data points with slight computational overhead. This observation leads to an efficient and effective input-specific randomized smoothing algorithm. We conduct extensive experiments and empirical analysis on CIFAR-10 and ImageNet. The results show that the proposed method significantly enhances the certified radii with low computational overhead.

Deep Reconstruction Transfer Convolutional Neural Network for Rolling Bearing Fault Diagnosis.

Deep transfer learning has been widely used to improve the versatility of models. In the problem of cross-domain fault diagnosis in rolling bearings, most models require that the given data have a similar distribution, which limits the diagnostic effect and generalization of the model. This paper proposes a deep reconstruction transfer convolutional neural network (DRTCNN), which satisfies the domain adaptability of the model under cross-domain conditions. Firstly, the model uses a deep reconstruction convolutional automatic encoder for feature extraction and data reconstruction. Through sharing parameters and unsupervised training, the structural information of target domain samples is effectively used to extract domain-invariant features. Secondly, a new subdomain alignment loss function is introduced to align the subdomain distribution of the source domain and the target domain, which can improve the classification accuracy by reducing the intra-class distance and increasing the inter-class distance. In addition, a label smoothing algorithm considering the credibility of the sample is introduced to train the model classifier to avoid the impact of wrong labels on the training process. Three datasets are used to verify the versatility of the model, and the results show that the model has a high accuracy and stability.