Spatial Smoothing Technique Research Articles

Geographical variation in prostate cancer testing explained by socio-economic position in Stockholm

Abstract Background Prostate cancer screening using prostate-specific antigen (PSA) testing is controversial but remains prevalent in many countries. Despite its prevalence there is little information in Sweden or globally on the spatial heterogeneity in PSA testing. This study aims to describe the spatio-temporal variation in PSA testing in the Stockholm region specifically at the municipality and small area level. Additionally, it aims to quantify the extent to which socio-economic position (SEP) indicators such as education, income, and country of birth explain the observed variation in PSA testing. Methods A retrospective population-based register study was conducted, encompassing men aged 40 years and older residing in the Stockholm region from 2007 to 2016. Utilizing spatial smoothing techniques, we calculated the age-standardised proportion of men undergoing PSA testing prior to any prostate cancer diagnosis within each area for every calendar year. Furthermore, we used Bayesian logistic regression models with spatial random effects to estimate the individual-level association between PSA testing and socio-economic position. The proportion of variance in PSA testing explained by various measures of SEP was also estimated at both the municipality and small area levels. Results Significant geographical disparities in PSA testing were observed across small areas within Stockholm. The proportion of variance explained in PSA testing at the small area level was highest for income (32.6%), followed by education (9.7%) and country of birth (7.4%). Incorporating all SEP measures led to a higher proportion of explained variance at the small area level (41.6%) compared to the municipality level (24.8%). Conclusions PSA testing was significantly associated with various socio-economic indicators and some of the spatial variation could be explained by SEP. It would be useful to ascertain whether similar patterns are observed in other regions or countries. Key messages • The findings suggested widespread and consistent opportunistic prostate cancer screening practices within the Stockholm region, raising concerns regarding potential overdiagnosis and overtreatment. • The socio-economic differences in prostate cancer screening could partially explain the differences in cancer incidence and mortality.

Noncircular Distributed Source DOA Estimation with Nested Arrays via Reduced-Dimension MUSIC

This paper focuses on the direction-of-arrival (DOA) estimation for noncircular coherently distributed (CD) sources with nested arrays. Usually, for point sources, sparse arrays have the potential to improve the estimation performance of algorithms by obtaining more degrees of freedom. However, algorithms have to be reconsidered for CD sources with sparse arrays and many problems arise. One thorny problem is the disappearance of displacement invariance of the virtual array manifold constructed by the virtualization technique. To deal with this issue, a nested array processing method for CD sources transmitting noncircular signals is proposed in this paper. Firstly, we construct the virtual sum-and-difference co-array by leveraging the noncircular quality of signals with a nested array. Then, an approximation is made to degrade CD sources into point sources. In this way, spatial smoothing techniques can be applied to restore the rank. Finally, in order to reduce the complexity, we modify the reduced-dimension MUSIC to estimate DOAs through a one-dimensional peak-searching procedure. The simulation results prove the superiority of our algorithm against other competitors.

Real-time ultrasound AR 3D visualization toward better topological structure perception for hepatobiliary surgery.

Ultrasound serves as a crucial intraoperative imaging tool for hepatobiliary surgeons, enabling the identification of complex anatomical structures like blood vessels, bile ducts, and lesions. However, the reliance on manual mental reconstruction of 3D topologies from 2D ultrasound images presents significant challenges, leading to a pressing need for tools to assist surgeons with real-time identification of 3D topological anatomy. We propose a real-time ultrasound AR 3D visualization method for intraoperative 2D ultrasound imaging. Our system leverages backward alpha blending to integrate multi-planar ultrasound data effectively. To ensure continuity between 2D ultrasound planes, we employ spatial smoothing techniques to interpolate the widely spaced ultrasound planes. A dynamic 3D transfer function is also developed to enhance spatial representation through color differentiation. Comparative experiments involving our AR visualization of 3D ultrasound, alongside AR visualization of 2D ultrasound and 2D visualization of 3D ultrasound, demonstrated that the proposed method significantly reduced operational time(110.25 ± 27.83s compared to 292 ± 146.63s and 365.25 ± 131.62s), improved depth perception and comprehension of complex topologies, contributing to reduced pressure and increased personal satisfaction among users. Quantitative experimental results and feedback from both novice and experienced physicians highlight our system's exceptional ability to enhance the understanding of complex topological anatomy. This improvement is crucial for accurate ultrasound diagnosis and informed surgical decision-making, underscoring the system's clinical applicability.

2-D DOA Estimation of Coherent Signals Using the Dual-Size Spreading Array

Abstract We introduce a novel approach for high-precision estimation of two-dimensional (2-D) Direction-of-Arrival (DOA) under conditions of coherent interference. This study innovatively devises an antenna configuration, termed the Dual-Size Spreading Array, specifically tailored to estimate DOAs in such environments. The method involves integrating a subarray with the primary array to create a Dual-Size Extended Array structure. This integration allows for a transformation of the covariance matrix into a new form, where its rank solely depends on the number of impinging waves. Both the subarray and primary array must have a scale no less than the number of incoming wavefronts. This proposed technique not only amplifies the effective aperture but also significantly reduces the computational intricacy associated with DOA estimation procedures. The efficacy of our methodology has been substantiated through simulation results, which demonstrate that it outperforms the conventional spatial smoothing techniques. Moreover, we provide several practical guidelines designed to enhance estimation accuracy while concurrently minimizing computational demands. In summary, this research presents an advanced solution that effectively addresses challenges in 2D DOA estimation under coherent scenarios, achieving improved performance and computational efficiency compared to existing methods.

A stochastic framework for rainfall intensity–time scale–return period relationships. Part ΙΙ: point modelling and regionalization over Greece

ABSTRACT In this work, we formulate a regionalization framework for rainfall intensity–time scale–return period relationships which is applied over the Greek territory. The methodology for single-site estimation is based on a stochastic framework for multi-scale modelling of rainfall intensity which is outlined in the companion paper. Five parameters are first fitted independently for each site and the resulting parameter variability is assessed. Following a systematic investigation of uncertainty and variability patterns, two parameters, i.e. the tail-index and a time scale parameter, are identified as constant in space and estimated using data pooling techniques. The other three parameters are regionalized over Greece by means of spatial interpolation and smoothing techniques that are assessed through cross-validation in a multi-model framework. The regionalization scheme is implemented in a sequential order that allows exploiting rainfall information both from rainfall stations with sub-daily resolution and from the more reliable network of daily raingauges.

An Improved Spatial Smoothing Technique Based on Cross-covariance for Coherent Signals DOA Estimation

An Improved Spatial Smoothing Technique Based on Cross-covariance for Coherent Signals DOA Estimation

Enhanced Coprime Array Structure and DOA Estimation Algorithm for Coherent Sources.

This paper presents a new enhanced coprime array for direction of arrival (DOA) estimation. Coprime arrays are capable of estimating the DOA using coprime properties and outperforming uniform linear arrays. However, the associated algorithms are not directly applicable for estimating the DOA of coherent sources. To overcome this limitation, we propose an enhanced coprime array in this paper. By increasing the number of array sensors in the coprime array, it is feasible to enlarge the aperture of the array and these additional array sensors can be utilized to achieve spatial smoothing, thus enabling estimation of the DOA for coherent sources. Additionally, applying the spatial smoothing technique to the signal subspace, instead of the conventional spatial smoothing method, can further improve the ability to reduce noise interference and enhance the overall estimation result. Finally, DOA estimation is accomplished using the MUSIC algorithm. The simulation results demonstrate improved performance compared to traditional algorithms, confirming its feasibility.

DOA-Estimation Method Based on Improved Spatial-Smoothing Technique

To improve the data utilization of the sensor array and direction-of-arrival-(DOA)-estimation performance for coherent signals, a DOA-estimation method with a modified spatial-smoothing technique is proposed. The covariance matrix of the received data of the sensor array is decomposed to obtain the signal subspace vectors, and the obtained vectors are smoothed in the proposed method. Then, a new data covariance matrix is constructed by using the autocorrelation covariance matrix of the intra-subarrays and the cross-correlation covariance matrix of the inter-subarrays. Finally, the DOA of the incident signal is estimated, using the new data covariance matrix with the multiple-signal-classification-(MUSIC) algorithm. The data-processing results of the simulation and lake test show that the modified method has stronger decoherence ability, as it utilizes more comprehensive coherent signal information. It also has better azimuth-estimation performance and robustness in the case of a low signal-to-noise ratio (SNR), few snapshots, and small incident-angle intervals when compared to the traditional method. Therefore, the modified method has great engineering application value.

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.

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.

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.

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.

A high precision indoor positioning system of BLE AOA based on ISSS algorithm

This paper investigates the Bluetooth direction finding technique and combines it with the improved signal subtraction subspace (ISSS) algorithm for precise indoor positioning. First, the phase offset caused by the electronic switch is solved by the phase compensation algorithm. Then, the ISSS algorithm is proposed by combining the spatial smoothing techniques algorithm, the density-based spatial clustering of applications with noise (DBSCON) techniques and the signal subtraction subspace (SSS), which reduces the interference of coherent signals and caused by moving between people in the room. Finally, different placement methods for receivers in different spatial shapes are proposed. In this paper, the positioning accuracy of the algorithm is tested using Silicon Labs' Bluetooth device. The results show that the average positioning errors are 0.92 m for single receivers and 0.30 m for dual receivers in a room size of 3 m * 3 m. Therefore, the method has a promising application in achieving accurate indoor positioning.

An Enhanced Spatial Smoothing Technique of Coherent DOA Estimation with Moving Coprime Array.

This paper investigates the direction of arrival (DOA) estimation of coherent signals with a moving coprime array (MCA). Spatial smoothing techniques are often used to deal with the covariance matrix of coherent signals, but they cannot be used in sparse arrays. Therefore, super-resolution algorithms such as multiple signal classification (MUSIC) cannot be applied in the DOA estimation of coherent signals in sparse arrays. In this study, we propose an enhanced spatial smoothing method specifically designed for MCA. Firstly, we combine the signals received by the MCA at different times, which can be regarded as a sparse array with a larger number of array sensors. Secondly, we describe how to compute the covariance matrix, derive the signal subspace by eigenvalue decomposition, and prove that the signal subspace is also equivalent to a received signal. Thirdly, we apply enhanced spatial smoothing to the signal subspace and construct a rank recovered covariance matrix. Finally, the DOA of coherent signals are well estimated by the MUSIC algorithm. The simulation results validate the improved performance of the proposed algorithm compared with traditional methods, particularly in scenarios with low signal-to-noise ratios.

Enhanced DOA Estimation With Co-Prime Array in the Scenario of Impulsive Noise: A Pseudo Snapshot Augmentation Perspective

Co-prime array configuration is popular in the recent development of array signal processing by exploiting the sparse arrangement of arrays and the co-prime feature of the number of subarray elements. However, the assumption of Gaussian noise in most co-prime array processing research might lead to model mismatch in practical scenarios of impulsive noise, and therefore have an adverse impact on the estimation of direction of arrival (DOA). Moreover, co-prime array builds an enlarged virtual array by vectorizing the covariance matrix of the received signals, where the equivalent received signals of the virtual array have only a single snapshot. In this paper, we propose an enhanced fractional low-order method (EFLOM) for co-prime array configuration in scenarios of impulsive noise, from the perspective of pseudo snapshot increment. Since impulsive noise does not have finite second-order statistics or high-order cumulant, we construct a series of equivalent covariance matrices by using phased fractional low-order moments with different orders of the received signals. Then, the vectorization of multiple equivalent covariance matrices can be formed as the equivalent received signals of the virtual array with multiple snapshots. Since the reformed observations of the equivalent received signals are from the same sources, additional spatial smoothing preprocessing operations are still needed for decorrelation. While in this paper, we propose an improved spatial smoothing (ISS) technique by applying the information of both autocorrelation and cross subarray correlation of the covariance matrix. Afterwards, the classical multiple signal classification (MUSIC) is applied for the estimation of DOAs. The performance of the proposed method is theoretically verified and simulations are also provided to show its effectiveness in terms of the generalized signal to noise ratio (GSNR), parameter of impulsive noise, and angle separation.

Investigating local variation in disease rates within high-rate regions identified using smoothing.

Exploratory disease maps are designed to identify risk factors of disease and guide appropriate responses to disease and helpseeking behaviour. However, when produced using aggregatelevel administrative units, as is standard practice, disease maps may mislead users due to the Modifiable Areal Unit Problem (MAUP). Smoothed maps of fine-resolution data mitigate the MAUP but may still obscure spatial patterns and features. To investigate these issues, we mapped rates of Mental Health- Related Emergency Department (MHED) presentations in Perth, Western Australia, in 2018/19 using Australian Bureau of Statistics (ABS) Statistical Areas Level 2 (SA2) boundaries and a recent spatial smoothing technique: the Overlay Aggregation Method (OAM). Then, we investigated local variation in rates within high-rate regions delineated using both approaches. The SA2- and OAM-based maps identified two and five high-rate regions, respectively, with the latter not conforming to SA2 boundaries. Meanwhile, both sets of high-rate regions were found to comprise a select number of localised areas with exceptionally high rates. These results demonstrate how, due to the MAUP, disease maps that are produced using aggregate-level administrative units are unreliable as a basis for delineating geographic regions of interest for targeted interventions. Instead, reliance on such maps to guide responses may compromise the efficient and equitable delivery of healthcare. Detailed investigation of local variation in rates within high-rate regions identified using both administrative units and smoothing is required to improve hypothesis generation and the design of healthcare responses.

Simplified Spatial Smoothing for DOA Estimation of Coherent Signals

In coherent direction of arrival (DOA) estimation, subspace-based methods suffer from performance deterioration because of the rank loss of the signal covariance matrix. A variety of spatial smoothing preprocessing techniques have been proposed for decorrelation, among which the enhanced spatial smoothing preprocessing (ESS) technique shows outstanding performance by exploiting the signal subspace. However, ESS is applied by squaring the matrix whose columns span the signal subspace (called signal matrix), which involves unnecessary computational loads. Besides, the smoothed covariance matrix after ESS is a linear combination of the sub-matrices of signal matrix, where the coefficients of the combination may undermine the decorrelation performance. In this context, a simplified spatial smoothing (SSS) technique is proposed for decorrelation by averaging the sub-matrices of the signal matrix directly, and avoids redundant operations in squared signal matrix. The proposed method is tested numerically in terms of the signal-to-noise ratio (SNR), the number of snapshots, angle separation, and the execution time. Simulation results show the improvement of the decorrelation performance, efficiency, and robustness with the proposed method in coherent scenarios, compared with the other spatial smoothing preprocessing based methods.

Accounting for speckle-scale beam bending in classical ray tracing schemes for propagating realistic pulses in indirect drive ignition conditions

We propose a semi-analytical modeling of smoothed laser beam deviation induced by plasma flows. Based on a Gaussian description of speckles, the model includes spatial, temporal, and polarization smoothing techniques, through fits coming from hydrodynamic simulations with a paraxial description of electromagnetic waves. This beam bending model is then incorporated into a ray tracing algorithm and carefully validated. When applied as a post-process to the propagation of the inner cone in a full-scale simulation of a National Ignition Facility (NIF) experiment, the beam bending along the path of the laser affects the refraction conditions inside the hohlraum and the energy deposition, and could explain some anomalous refraction measurements, namely, the so-called glint observed in some NIF experiments.

Direction-of-Arrival Estimation for Nested Acoustic Vector-Sensor Arrays Using Quaternions

There is an increasing interest in direction-of-arrival (DOA) estimation using nested arrays composed of vector sensors. Considering acoustic vector sensors (AVSs) commonly used in underwater applications, this paper proposes a novel algorithm, called augmented nested quaternion-MUSIC (ANQ-MUSIC), to perform DOA estimation. By judiciously arranging the multi-component outputs of AVSs, we model the received signals from the entire nested AVS array as a quaternion observation vector in a compact way to reduce the computational complexity. Next, we formulate a quaternion-based difference co-array (QDCA) model via vectorizing the quaternion covariance matrix (QCM). Based on the obtained insights from the QDCA model, we derive a suitable QCM, which is constructed by applying the spatial smoothing technique. Finally, classical quaternion-MUSIC is logically introduced to estimate the DOA parameters. In simulations, we take into account non-uniform received noise and inter-component correlated noise, which may occur in practical underwater environments. The results demonstrate that the proposed method shows superiority in angular resolution and achieves a desirable trade-off between estimate accuracy and computational burden, besides showing robust performance in the above test scenarios.

Coarray Polarization Smoothing for DOA Estimation with Coprime Vector Sensor Arrays

In this paper, the problem of direction-of-arrival (DOA) estimation of multiple sources using a coprime electromagnetic vector sensor (EMVS) array is addressed. Each EMVS consists of three mutually orthogonal electric dipoles and three mutually orthogonal magnetic loops, all collocated at a single point in space. By exploiting the polarization diversities embedded in the vector sensors, the coarray polarization smoothing (COPS) is presented to increase the degrees of freedom (DOFs) from the polarization coarray domain. In contrast to the widely used spatial smoothing technique, the COPS offers the following insights: (1) it is source polarization-dependent and is proved to offer 20 DOFs at most, (2) it does not reduce the efficient spatial coarray aperture of the coprime array so that it enables the use of all virtual coarray sensors without resorting to the nontrivial sparse recovery or array interpolation operations, and (3) it can be synthesized with the spatial smoothing to get the DOFs multiplied. Finally, the efficacy of the COPS scheme is verified by numerical examples.