Spatial Smoothing Research Articles

Manifold Regularizer for High-Resolution fMRI Joint Reconstruction and Dynamic Quantification.

Oscillating Steady-State Imaging (OSSI) is a recently developed fMRI acquisition method that can provide 2 to 3 times higher SNR than standard fMRI approaches. However, because the OSSI signal exhibits a nonlinear oscillation pattern, one must acquire and combine nc (e.g., 10) OSSI images to get an image that is free of oscillation for fMRI, and fully sampled acquisitions would compromise temporal resolution. To improve temporal resolution and accurately model the nonlinearity of OSSI signals, instead of using subspace models that are not well suited for the data, we build the MR physics for OSSI signal generation as a regularizer for the undersampled reconstruction. Our proposed physics-based manifold model turns the disadvantages of OSSI acquisition into advantages and enables joint reconstruction and quantification. OSSI manifold model (OSSIMM) outperforms subspace models and reconstructs high-resolution fMRI images with a factor of 12 acceleration and without spatial or temporal smoothing. Furthermore, OSSIMM can dynamically quantify important physics parameters, including R2∗ maps, with a temporal resolution of 150 ms.

Forward-backward spatial smoothing for snapshot matrix construction of blade tip timing signal

Forward-backward spatial smoothing for snapshot matrix construction of blade tip timing signal

Joint Weighted Schatten-p Norm and Spatial Smoothness Regularization for Hyperspectral and Multispectral Image Fusion With Spectral Variability

Joint Weighted Schatten-<i>p</i> Norm and Spatial Smoothness Regularization for Hyperspectral and Multispectral Image Fusion With Spectral Variability

Learning Unified Anchor Graph for Joint Clustering of Hyperspectral and LiDAR Data.

The joint clustering of multimodal remote sensing (RS) data poses a critical and challenging task in Earth observation. Although recent advances in multiview subspace clustering have shown remarkable success, existing methods become computationally prohibitive when dealing with large-scale RS datasets. Moreover, they neglect intrinsic nonlinear and spatial interdependencies among heterogeneous RS data and lack generalization ability for out-of-sample data, thereby restricting their applicability. This article introduces a novel unified framework called anchor-based multiview kernel subspace clustering with spatial regularization (AMKSC). It learns a scalable anchor graph in the kernel space, leveraging contributions from each modality instead of seeking a consensus full graph in the feature space. To ensure spatial consistency, we incorporate a spatial smoothing operation into the formulation. The method is efficiently solved using an alternating optimization strategy, and we provide theoretical evidence of its scalability with linear computational complexity. Furthermore, an out-of-sample extension of AMKSC based on multiview collaborative representation-based classification is introduced, enabling the handling of larger datasets and unseen instances. Extensive experiments on three real heterogeneous RS datasets confirm the superiority of our proposed approach over state-of-the-art methods in terms of clustering performance and time efficiency. The source code is available at https://github.com/AngryCai/AMKSC.

Stereotaxic Coordinates of Human Hypothalamic Nuclei Used for Region of Interest Analyses in Functional Magnetic Resonance Imaging.

The hypothalamus maintains homeostasis by controlling various organs and the central nervous system, but analyzing the human hypothalamic nuclei is challenging. Our previous studies applied areal parcellation to high-resolution functional magnetic resonance imaging (fMRI) data to delineate hypothalamic nuclei boundaries. This article presents stereotaxic coordinates of these nuclei for fMRI analyses, offering guidance on defining regions of interest and appropriate spatial smoothing kernel sizes. The provided coordinates aid future research in nuclear level hypothalamus analyses.

SpconfShiny: An R Shiny application for calculating the spatial scale of smoothing splines for point data.

Epidemiological analyses of environmental exposures often benefit from including spatial splines in models to account for confounding by spatial location. Understanding how the number of splines relates to physical spatial differences is not always intuitive and can be context-dependent. To address this, we developed a R Shiny application, spconfShiny, that provides a user-friendly platform to calculate an effective bandwidth metric that quantifies the relationship between spatial splines and the range of implied spatial smoothing. spconfShiny can be accessed at https://g2aging.shinyapps.io/spconfShiny/. We illustrate the procedure to compute the effective bandwidth and demonstrate its use for different numbers of spatial splines across England, India, Ireland, Northern Ireland, and the United States. Using spconfShiny, we show the effective bandwidth increases with the size of the region and decreases with the number of splines. Including 10 splines on a 10km grid corresponds to effective bandwidths of 92.2km in Ireland and 927.7km in the United States.

Spatio-temporal variation in prostate cancer testing in Stockholm: A population-based study.

Prostate cancer screening using prostate-specific antigen (PSA) testing is controversial but remains prevalent in many countries. There is little information in Sweden or elsewhere on the spatial variation in PSA testing. This study aims to describe the spatio-temporal variation in PSA testing prior to a prostate cancer diagnosis in the Stockholm region at the municipality and small area levels. A population-based register study comprised men aged 40 years and over living in the Stockholm region during 2007-2016. For Stockholm in 2016, we reported the proportion of men who had a PSA test for the preceding one, two, five and ten years by ten-year age groups. The age-standardised proportion of men having a PSA test was reported for municipalities by calendar years. We used spatial smoothing for calculating the age-standardised proportion of men having a PSA test in a small area for each calendar year. In 2016, 74.0% and 77.8% of men aged 60-69 and 70-79 years respectively had taken a PSA test in the previous ten years. The municipalities of Danderyd and Ekerö showed high proportions of PSA testing. A marked heterogeneity in such proportions within each municipality was observed. The odds ratio for having a PSA test for those born in Sweden was 2.22 (95% CI 2.00-2.52). Opportunistic PSA testing is widespread with three quarters of men in their sixties and seventies having had a test in the preceding decade. We found evidence for marked geographical heterogeneity, where more affluent and metropolitan areas had higher levels of testing. Variations in PSA testing was associated with socio-economic position and demographic factors including education, income and country of birth.

4D High-Resolution Imagery of Point Clouds for Automotive mmWave Radar

In the community of automotive millimeter wave radar, the recently developed concept of four-dimensional (4D) radar can provide high-resolution point clouds image with enhanced imaging performance. Currently, the density of point clouds for single-frame image is usually too sparse to satisfy the demands of target classification and recognition due to the limitation of Doppler and angle resolutions. To address the aforementioned issues, a novel algorithm is proposed for 4D high-resolution imagery generation of point clouds with extremely high Doppler and angle resolutions in this paper. For high Doppler resolution with high-dynamic, a novel velocity ambiguity resolution algorithm is proposed using a dual pulse repetition frequency (dual-PRF) waveform design embedded in an innovative time-division multiplexing & Doppler-division multiplexing MIMO (TDM-DDM-MIMO) framework. Meanwhile, an attractive complex-valued deep convolutional network (CV-DCN) of super-resolution direction-of-arrival (DOA) estimation is proposed only using single-frame data. To be specific, a spatial smoothing operator on array data is applied as input of the network, and a CV-DCN is designed to learn the transformation of the spatial spectrum from the end-to-end to effectively protect the spectrum extraction. Furthermore, experimental analysis is performed to confirm the effectiveness of the proposed super-resolution DOA estimation algorithm. Finally, the 4D high-resolution imagery of point clouds is obtained by experiments in the parking lot.

Estimating neuronal firing density: A quantitative analysis of firing rate map algorithms.

The analysis of neurons that exhibit receptive fields dependent on an organism's spatial location, such as grid, place or boundary cells typically begins by mapping their activity in space using firing rate maps. However, mapping approaches are varied and depend on multiple tuning parameters that are usually chosen qualitatively by the experimenter and thus vary significantly across studies. Small changes in parameters such as these can impact results significantly, yet, to date a quantitative investigation of firing rate maps has not been attempted. Using simulated datasets, we examined how tuning parameters, recording duration and firing field size affect the accuracy of spatial maps generated using the most widely used approaches. For each approach we found a clear subset of parameters which yielded low-error firing rate maps and isolated the parameters yielding 1) the least error possible and 2) the Pareto-optimal parameter set which balanced error, computation time, place field detection accuracy and the extrapolation of missing values. Smoothed bivariate histograms and averaged shifted histograms were consistently associated with the fastest computation times while still providing accurate maps. Adaptive smoothing and binning approaches were found to compensate for low positional sampling the most effectively. Kernel smoothed density estimation also compensated for low sampling well and resulted in accurate maps, but it was also among the slowest methods tested. Overall, the bivariate histogram, coupled with spatial smoothing, is likely the most desirable method in the majority of cases.

Mapping the prevalence of cancer risk factors at the small area level in Australia

BackgroundCancer is a significant health issue globally and it is well known that cancer risk varies geographically. However in many countries there are no small area-level data on cancer risk factors with high resolution and complete reach, which hinders the development of targeted prevention strategies.MethodsUsing Australia as a case study, the 2017–2018 National Health Survey was used to generate prevalence estimates for 2221 small areas across Australia for eight cancer risk factor measures covering smoking, alcohol, physical activity, diet and weight. Utilising a recently developed Bayesian two-stage small area estimation methodology, the model incorporated survey-only covariates, spatial smoothing and hierarchical modelling techniques, along with a vast array of small area-level auxiliary data, including census, remoteness, and socioeconomic data. The models borrowed strength from previously published cancer risk estimates provided by the Social Health Atlases of Australia. Estimates were internally and externally validated.ResultsWe illustrated that in 2017–2018 health behaviours across Australia exhibited more spatial disparities than previously realised by improving the reach and resolution of formerly published cancer risk factors. The derived estimates revealed higher prevalence of unhealthy behaviours in more remote areas, and areas of lower socioeconomic status; a trend that aligned well with previous work.ConclusionsOur study addresses the gaps in small area level cancer risk factor estimates in Australia. The new estimates provide improved spatial resolution and reach and will enable more targeted cancer prevention strategies at the small area level. Furthermore, by including the results in the next release of the Australian Cancer Atlas, which currently provides small area level estimates of cancer incidence and relative survival, this work will help to provide a more comprehensive picture of cancer in Australia by supporting policy makers, researchers, and the general public in understanding the spatial distribution of cancer risk factors. The methodology applied in this work is generalisable to other small area estimation applications and has been shown to perform well when the survey data are sparse.

Evaluation of the Influence of the Spatial Smoothing Procedure of the Correlation Matrix on the Efficiency of the 2D-MUSIC Method

The occurrence of correlations between radio signals arriving at the antenna array of the base station reduces the effectiveness of subspace methods for positioning user devices in wireless communication networks. For the purpose of radiation sources decorrelation, a spatial smoothing algorithm can be applied dividing the base station antenna array into sub-arrays and then averaging the signal correlation matrices obtained for these sub-arrays. In this paper, we investigate the impact of various ways of dividing a flat equidistant antenna array into subarrays on the performance of the 2D-MUSIC multiple signal classification method in the scenario of ultra-dense networks operating in the FR2 band.

Altitude measurement method of VHF radar based on spatial smoothing of correlation matrix

For very high frequency (VHF) phased array radar, the key problem to be solved in altitude measurement is the super-resolution spatial spectrum estimation under the condition of coherent sources. The spatial smoothing algorithm is a kind of decorrelation algorithm with excellent properties, but the decorrelation process is at the expense of the effective array aperture. Because it only uses the autocorrelation information of the subspace, its performance is significantly reduced, when the positions of the coherent sources are very close. In order to solve the above problems, this paper proposes an altitude measurement method of VHF radar based on the space smoothing of autocorrelation and cross-correlation matrix, which is used to realize the correlation and super-resolution processing of echo signals and multipath signals. The proposed method does not need to construct a weighting matrix, and can make full use of the received data, enhance the signal components in the equivalent spatial smoothing matrix, reduce the impact of noise, and improve the resolution of coherent sources. The simulation results show that the weighted spatial smoothing method proposed in this paper is correct and effective.

Efficient DOA-polarization estimation for 2-D mirrored array based on the hybrid aperture expansion

At present, there are fewer studies on the polarization-sensitive mirrored array (PS-MA). Meantime, the estimation accuracy will decrease when the array element spacing is lower than half wavelength. This paper focuses on the aperture expansion of the PS-MA to improve the estimation accuracy. To this end, we establish the received signal model of the 2-D PS-MA with two perpendicular reflectors. Unlike the existing virtual array without polarization information, a novel model of the polarization-sensitive virtual array (PS-VA) is suggested based on the hybrid coarray technique. Additionally, the spatial smoothing (SS) technique is used to recover the rank of the covariance matrix, and the modulus value boundedness (MVB) of the polarization vector is used to reduce the dimension of the polarization-spatial spectrum. Then, the MVB-MA-SS algorithm is proposed for polarization-DOA estimation, which is much more efficient than the standard group-lasso algorithm used in the 1-D PS-MA. Numerical experiments show that the proposed algorithm can provide satisfactory estimation accuracy with significantly reduced computational complexity.

Spatio-temporal smoothing and dynamics of different electricity flexibility options for highly renewable energy systems—Case study for Norway

In this article, we investigate the mismatch of renewable electricity production to demand and how flexibility options enabling spatial and temporal smoothing can reduce risks of variability. As a case study we pick a simplified (partial) 2-region representation of the Norwegian electricity system and focus on wind power. We represent regional electricity production and demand through two stochastic processes: the wind capacity factors are modelled as a two-dimensional Ornstein–Uhlenbeck process and electricity demand consists of realistic base load and temperature-induced load coming from a deseasonalised autoregressive process. We validate these processes, that we have trained on historical data, through Monte Carlo simulations allowing us to generate many statistically representative weather years. For the investigated realisations (weather years) we study deviations of production from demand under different wind capacities, and introduce different scenarios where flexibility options like storage and transmission are available. Our analysis shows that simulated loss values are reduced significantly by cooperation between regions and either mode of flexibility. Combining storage and transmission leads to even more synergies and helps to stabilise production levels and thus reduces likelihoods of inadequacy of renewable power systems.

Mapping Seismic Hazard for Canadian Sites Using Spatially Smoothed Seismicity Model

The estimated seismic hazard based on the delineated seismic source model is used as the basis to assign the seismic design loads in Canadian structural design codes. An alternative for the estimation is based on a spatially smoothed source model. However, a quantification of differences in the Canadian seismic hazard maps (CanSHMs) obtained based on the delineated seismic source model and spatially smoothed model is unavailable. The quantification is valuable to identify epistemic uncertainty in the estimated seismic hazard and the degree of uncertainty in the CanSHMs. In the present study, we developed seismic source models using spatial smoothing and historical earthquake catalogue. We quantified the differences in the estimated Canadian seismic hazard by considering the delineated source model and spatially smoothed source models. For the development of the spatially smoothed seismic source models, we considered spatial kernel smoothing techniques with or without adaptive bandwidth. The results indicate that the use of the delineated seismic source model could lead to under or over-estimation of the seismic hazard as compared to those estimated based on spatially smoothed seismic source models. This suggests that an epistemic uncertainty caused by the seismic source models should be considered to map the seismic hazard.

The impact of breathing patterns on CSF flow and global brain BOLD signal while awake: A study using real‐time phase‐contrast MRI and fast rsfMRI

AbstractBackgroundThe cardiac and respiratory cycles have been suggested as major drivers of cerebrospinal fluid(CSF) flow. The glymphatic system, one of the mechanisms for the clearance of amyloid‐beta and tau proteins, relies heavily on the movement(flow) of the CSF, and thus, investigating the forces that modulate the CSF flow is essential for understanding the glymphatic flux. Because breathing is trainable through exercise and self‐directed methods, various breathing methods may enhance the CSF flow.MethodReal‐time phase‐contrast MRI(pc‐MRI) was used to measure the CSF flow at the foramen magnum on a 3T. Fast resting‐state fMRI(rsfMRI;TR400ms) was conducted on a compact 3T. Under an IRB‐approved protocol, participants were instructed to breathe slowly and deeply, and subsequently switch to their spontaneous breathing. For rsfMRI data preprocessing, we performed motion correction, skull stripping, spatial smoothing(4mm), temporal filtering(0.01 to 0.1Hz), and linear and quadratic temporal trends removal. fMRI time courses were then normalized to Z‐score at each voxel before being averaged. On the pcMRI, the phase was summed in a CSF region‐of‐interest and plotted vs time. Additionally, we confirmed for possible confounding effects such as head motion or motion‐induced susceptibility changes.ResultrsfMRI findings showed that deep breathing promoted large oscillations in the CSF flow in the ventricles, while spontaneous breathing did not(Figure 1). Additionally, deep breathing resulted in large oscillations in lobar cortical regions. Similar results were observed in the pcMRI, with larger CSF velocity through the foramen magnum during the deep breathing compared to the spontaneous breathing(Figure 2A‐B). The cumulative summation result showed that the volume of CSF flow was increased during deep breathing(Figure 2C).ConclusionThis study provides new evidence that slow and deep breathing promotes CSF flow and global brain BOLD signal, which may be useful in promoting circulation in the brain. The study’s findings also open new avenues for research in the field of neurovascular coupling and mechanisms associated with glymphatic clearance. As hampered CSF flow and/or worsen glymphatic clearance have been shown to associate with pathological aging and dementia, including Alzheimer’s disease and Parkinson’s disease, future research is needed explore the potential of breathing training methods as a non‐pharmacological intervention to support brain health.

Backward stimulated Brillouin scattering spatial gain with polarization, spatial, and temporal beam smoothing techniques

A recent study [Ruyer et al., Phys. Rev. E 107, 035208 (2023)] modeling the influence of a random phase plate on the backward stimulated Brillouin scattering growth is here supplemented with the effect of temporal and polarization smoothing. Our analytical predictions are validated by a large number of three dimensional Hera paraxial simulations for various beam smoothing techniques and relevant to most high energy laser facilities. Neglecting all non-linear effects apart from the pump depletion, we then reconstruct the system of differential equations that the backward stimulated Brillouin scattering convective amplification of a smoothed beam propagating in a non-homogeneous plasma satisfies. Its resolution is successfully confronted with our simulation data and prepares the accurate modeling, in a ray tracing scheme, of the effect of laser smoothing techniques on laser plasma instabilities.

Quality Control for Ocean Current Measurement Using High-Frequency Direction-Finding Radar

High-frequency radars (HFRs) are important for remote sensing of the marine environment due to their ability to provide real-time, wide-coverage, and high-resolution measurements of the ocean surface current, wave height, and wind speed. However, due to the intricate multidimensional processing demands (e.g., time, Doppler, and space) for internal data and effective suppression of external noise, conducting quality control (QC) on radar-measured data is of great importance. In this paper, we first present a comprehensive quality evaluation model for both radial current and synthesized vector current obtained by direction-finding (DF) HFRs. In the proposed model, the quality factor (QF) is calculated for each current cell to evaluate its reliability. The QF for the radial current depends on the signal-to-noise ratio (SNR) and DF factor of the first-order Bragg peak region in the range–Doppler (RD) spectrum, and the QF for the synthesized vector current can be calculated using an error propagation model based on geometric dilution of precision (GDOP). A QC method is then proposed for processing HFR-derived surface current data via the following steps: (1) signal preprocessing is performed to minimize the effect of unwanted external signals such as radio frequency interference and ionospheric clutter; (2) radial currents with low QFs and outliers are removed; (3) the vector currents with low QFs are also removed before spatial smoothing and interpolation. The proposed QC method is validated using a one-month-long dataset collected by the Ocean State Monitoring and Analyzing Radar, model S (OSMAR-S). The improvement in the current quality is proven to be significant. Using the buoy data as ground truth, after applying QC, the correlation coefficients (CCs) of the radial current, synthesized current speed, and synthesized current direction are increased by 4.33~102.91%, 1.04~90.74%, and 1.20~62.67%, respectively, and the root mean square errors (RMSEs) are decreased by 2.51~49.65%, 7.86~27.22%, and 1.68~28.99%, respectively. The proposed QC method has now been incorporated into the operational software (RemoteSiteConsole v1.0.0.65) of OSMAR-S.

Computationally efficient localised spatial smoothing of disease rates using anisotropic basis functions and penalised regression fitting

The spatial variation in population-level disease rates can be estimated from aggregated disease data relating to N areal units using Bayesian hierarchical models. Spatial autocorrelation in these data is captured by random effects that are assigned a Conditional autoregressive (CAR) prior, which assumes that neighbouring areal units exhibit similar disease rates. This approach ignores boundaries in the disease rate surface, which are locations where neighbouring units exhibit a step-change in their rates. CAR type models have been extended to account for this localised spatial smoothness, but they are computationally prohibitive for big data sets. Therefore this paper proposes a novel computationally efficient approach for localised spatial smoothing, which is motivated by a new study of mental ill health across N=32,754 Lower Super Output Areas in England. The approach is based on a computationally efficient ridge regression framework, where the spatial trend in disease rates is modelled by a set of anisotropic spatial basis functions that can exhibit either smooth or step change transitions in values between neighbouring areal units. The efficacy of this approach is evidenced by simulation, before using it to identify the highest rate areas and the magnitude of the health inequalities in four measures of mental ill health, namely antidepressant usage, benefit claims, depression diagnoses and hospitalisations.

Self-Position Determination Based on Array Signal Subspace Fitting under Multipath Environments

A vehicle’s position can be estimated with array receiving signal data without the help of satellite navigation. However, traditional array self-position determination methods are faced with the risk of failure under multipath environments. To deal with this problem, an array signal subspace fitting method is proposed for suppressing the multipath effect. Firstly, all signal incidence angles are estimated with enhanced spatial smoothing and root multiple signal classification (Root-MUSIC). Then, non-line-of-sight (NLOS) components are distinguished from multipath signals using a K-means clustering algorithm. Finally, the signal subspace fitting (SSF) function with a P matrix is established to reduce the NLOS components in multipath signals. Meanwhile, based on the initial clustering estimation, the search area can be significantly reduced, which can lead to less computational complexity. Compared with the C-matrix, oblique projection, initial signal fitting (ISF), multiple signal classification (MUSIC) and signal subspace fitting (SSF), the simulated experiments indicate that the proposed method has better NLOS component suppression performance, less computational complexity and more accurate positioning precision. A numerical analysis shows that the complexity of the proposed method has been reduced by at least 7.64dB. A cumulative distribution function (CDF) analysis demonstrates that the estimation accuracy of the proposed method is increased by 3.10dB compared with the clustering algorithm and 11.77dB compared with MUSIC, ISF and SSF under multipath environments.