Multidimensional Filter Research Articles

Plasticity of Multidimensional Receptive Fields in Core Rat Auditory Cortex Directed by Sound Statistics

Sensory cortical neurons can nonlinearly integrate a wide range of inputs. The outcome of this nonlinear process can be approximated by more than one receptive field component or filter to characterize the ensuing stimulus preference. The functional properties of multidimensional filters are, however, not well understood. Here we estimated two spectrotemporal receptive fields (STRFs) per neuron using maximally informative dimension analysis. We compared their temporal and spectral modulation properties and determined the stimulus information captured by the two STRFs in core rat auditory cortical fields, primary auditory cortex (A1) and ventral auditory field (VAF). The first STRF is the dominant filter and acts as a sound feature detector in both fields. The second STRF is less feature specific, preferred lower modulations, and had less spike information compared to the first STRF. The information jointly captured by the two STRFs was larger than that captured by the sum of the individual STRFs, reflecting nonlinear interactions of two filters. This information gain was larger in A1. We next determined how the acoustic environment affects the structure and relationship of these two STRFs. Rats were exposed to moderate levels of spectrotemporally modulated noise during development. Noise exposure strongly altered the spectrotemporal preference of the first STRF in both cortical fields. The interaction between the two STRFs was reduced by noise exposure in A1 but not in VAF. The results reveal new functional distinctions between A1 and VAF indicating that (i) A1 has stronger interactions of the two STRFs than VAF, (ii) noise exposure diminishes modulation parameter representation contained in the noise more strongly for the first STRF in both fields, and (iii) plasticity induced by noise exposure can affect the strength of filter interactions in A1. Taken together, ascertaining two STRFs per neuron enhances the understanding of cortical information processing and plasticity effects in core auditory cortex.

Three-dimensional image volumes from two-dimensional digitally reconstructed radiographs: A deep learning approach in lower limb CT scans.

Three-dimensional (3D) reconstructions of the human anatomy have been available for surgery planning or diagnostic purposes for a few years now. The different image modalities usually rely on several consecutive two-dimensional (2D) acquisitions in order to reconstruct the 3D volume. Hence, such acquisitions are expensive, time-demanding and often expose the patient to an undesirable amount of radiation. For such reasons, along the most recent years, several studies have been proposed that extrapolate 3D anatomical features from merely 2D exams such as x rays for implant templating in total knee or hip arthroplasties. The presented study shows an adaptation of a deep learning-based convolutional neural network to reconstruct 3D volumes from a mere 2D digitally reconstructed radiograph from one of the most extensive lower limb computed tomography datasets available. This novel approach is based on an encoder-decoder architecture with skip connections and a multidimensional Gaussian filter as data augmentation technique. The results achieved promising values when compared against the ground truth volumes, quantitatively yielding an average of 0.77±0.05 structured similarity index. A novel deep learning-based approach to reconstruct 3D medical image volumes from a single x-ray image was shown in the present study. The network architecture was validated against the original scans presenting SSIM values of 0.77±0.05 and 0.78±0.06, respectively for the knee and the hip crop.

Multi-GNSS inter-system model for complex environments based on optimal state estimation

When calibrating inter-system biases (ISB), especially the fractional part of inter-system phase biases (F-ISPB), a multi-GNSS inter-system model can effectively improve positioning performance under a complex environment. Usually, the F-ISPB is estimated after fixing the intra-system ambiguities. However, this approach seems inapplicable when it is difficult to obtain intra-system ambiguities under a complex environment. A multi-dimensional particle filter (PF)-based F-ISPB estimate method has been proposed to overcome the problem. Nevertheless, the multi-dimensional PF involves a great quantity of computations. In this contribution, four state optimal estimate-based F-ISPB handling schemes are proposed: step-by-step PF, step-by-step particle swarm optimization (PSO), multi-dimensional PF, and multi-dimensional PSO-based F-ISPB estimate methods. Two baselines were selected to investigate the F-ISPB estimate performance in both open and complex environments. The results show that due to the potential of the wrong F-ISPB to bring about the maximum ratio for a long time during the initial stage, the step-by-step PF method can achieve better performance than step-by-step PSO. Besides, the two-dimensional results show that all of the F-ISPB still cannot be extracted under complex environments by multi-dimensional PSO. Furthermore, compared with step-by-step PF, the multi-dimensional PF method costs too much to obtain the right value. For example, in the two-dimensional case, the step-by-step PF searches 200 times for each epoch, while the two-dimensional PF requires 40 000 times for each epoch, so it is difficult for receivers to provide hardware support for this method. In addition, the step-by-step PF can obtain the right F-ISPB with about 100 epochs no matter what scenario. Thus, under challenging observation scenarios, a step-by-step PF method is recommended to extract the F-ISPB.

Метод синтезу оптимального багатовимірного фільтру для виділення регулярного сигналу на фоні випадкових перешкод

In terms of [1] we formulate the problem of synthesis of a complex system of allocation of a useful regular signal. Suppose that a multidimensional stationary filter best processes the input information about the same regular signal r(t), which is obtained by several "non-ideal" meters, and the result is transmitted to the evaluation system. In this article, a multi-channel measurement system, which is connected to the input of a multidimensional data transmission system, the dynamics of which is described by a system of linear differential equations. The input of the measuring system receives an n-dimensional vector of measured signals r (t), the components of which are deterministic functions. The vector r (t) belongs to the main group of "non-ideal" meters. Measurements are accompanied by interference, which is a random stationary process with zero mathematical expectation and a known fractional-rational matrix of spectral densities. An integral indicator of the quality of the system is the sum of the weighted integral quadratic error of the regular signal estimation and the variance of the random component of the error. Thus, a new algorithm for the synthesis of a complete optimal regular signal extraction system against the background of a multidimensional stationary random interference is obtained, which allows to find the structure and parameters of a multidimensional optimal filter taking into account the dynamics of the information transmission system.

Real-Time Point Process Filter for Multidimensional Decoding Problems Using Mixture Models

There is an increasing demand for a computationally efficient and accurate point process filter solution for real-time decoding of population spiking activity in multidimensional spaces. Real-time tools for neural data analysis, specifically real-time neural decoding solutions open doors for developing experiments in a closed-loop setting and more versatile brain-machine interfaces. Over the past decade, the point process filter has been successfully applied in the decoding of behavioral and biological signals using spiking activity of an ensemble of cells; however, the filter solution is computationally expensive in multi-dimensional filtering problems. Here, we propose an approximate filter solution for a general point-process filter problem when the conditional intensity of a cell’s spiking activity is characterized using a Mixture of Gaussians. We propose the filter solution for a broader class of point process observation called marked point-process, which encompasses both clustered – mainly, called sorted – and clusterless – generally called unsorted or raw– spiking activity. We assume that the posterior distribution on each filtering time-step can be approximated using a Gaussian Mixture Model and propose a computationally efficient algorithm to estimate the optimal number of mixture components and their corresponding weights, mean, and covariance estimates. This algorithm provides a real-time solution for multi-dimensional point-process filter problem and attains accuracy comparable to the exact solution. Our solution takes advantage of mixture dropping and merging algorithms, which collectively control the growth of mixture components on each filtering time-step. We apply this methodology in decoding a rat’s position in both 1-D and 2-D spaces using clusterless spiking data of an ensemble of rat hippocampus place cells. The approximate solution in 1-D and 2-D decoding is more than 20 and 4,000 times faster than the exact solution, while their accuracy in decoding a rat position only drops by less than 9% and 4% in RMSE and 95% highest probability coverage area (HPD) performance metrics. Though the marked-point filter solution is better suited for real-time decoding problems, we discuss how the filter solution can be applied to sorted spike data to better reflect the proposed methodology versatility.

Convergence Analysis of a Trust-Region Multidimensional Filter Method for Nonlinear Complementarity Problems

For solving nonlinear complementarity problems, a new algorithm is proposed by using multidimensional filter techniques and a trust-region method. The algorithm is shown to be globally convergent under the reasonable assumptions and does not depend on any extra restoration procedure. In particular, it shows that the subproblem is a convex quadratic programming problem, which is easier to be solved. The results of numerical experiments show its efficiency.

A Filter and Nonmonotone Adaptive Trust Region Line Search Method for Unconstrained Optimization

In this paper, a new nonmonotone adaptive trust region algorithm is proposed for unconstrained optimization by combining a multidimensional filter and the Goldstein-type line search technique. A modified trust region ratio is presented which results in more reasonable consistency between the accurate model and the approximate model. When a trial step is rejected, we use a multidimensional filter to increase the likelihood that the trial step is accepted. If the trial step is still not successful with the filter, a nonmonotone Goldstein-type line search is used in the direction of the rejected trial step. The approximation of the Hessian matrix is updated by the modified Quasi-Newton formula (CBFGS). Under appropriate conditions, the proposed algorithm is globally convergent and superlinearly convergent. The new algorithm shows better performance in terms of the Dolan–Moré performance profile. Numerical results demonstrate the efficiency and robustness of the proposed algorithm for solving unconstrained optimization problems.

PERCEPTIVE DATA HEURISTIC CLASSIFICATION ALGORITHM BASED BRAIN TUMOR DETECTION FOR MEDICAL APPLICATIONS

Brain tumors are a tissue that grows out of control in an unusual and abandoned spread of cells due to some issues of human health. A brain tumor may be reflected among the most stimulating tumors to treat, as it includes the organ which is not only in control of the body. In recent years the detection of brain tumors is increasing, and because the level of the disease is challenging to identify. The proposed automated brain tumor detection algorithm consists of several steps which are namely preprocessing, segmentation, and classification of the brain images. First, a multidimensional filter based preprocessed input image is fed to the Multi-model Image Clustering Technique (MICT) based segmentation block, which is used to separate the rough outline of affected brain tissues. Then the segmented image is categorized using Perceptive Data Heuristic Classification Algorithm (PDHCA), which is used to classify the pathology and normal output brain image. An efficient Perceptive Data Heuristic Classification Algorithm (PDHCA) is proposed for brain tumor detection based on different digital image processing steps. Hence the results of PDHCA are tested and classify the tumor using MATLAB 2019a.

All-relevant feature selection using multidimensional filters with exhaustive search

This paper describes a method for the identification of informative variables in an information system with discrete decision variables. It is targeted specifically towards the discovery of variables that are non-informative when considered alone, but informative when the synergistic interactions between multiple variables are considered. To this end, mutual entropy of all possible k-tuples of variables with a decision variable is computed. Then, for each variable, the maximum information gain due to interactions with other variables is obtained. For non-informative variables, this quantity conforms to well-known statistical distributions. This allows for discerning the truly informative variables from the non-informative ones. To demonstrate this approach, the method is applied to several synthetic datasets that involve complex multidimensional interactions between variables. The performance of the method is also validated on a real-world dataset. It is shown that the method is capable of identifying the most important informative variables, even when the dimensionality of the analysis is smaller than the true dimensionality of the problem. What is more, the high sensitivity of the algorithm allows for the detection of the influence of nuisance variables on the response variable.

Effects of numerical anti-diffusion in closed unsteady flows governed by two-dimensional Navier-Stokes equation

Numerical methods producing acceptable results for a long time abruptly blow up, without providing any indication of localized onset of sudden numerical instability. This has been identified as focusing problem in literature. It is noted that the scale selection of error does not depend on the relevant excited physical space-time scales. While this has been encountered in weather prediction studies, it is not widely reported from the solution of Navier-Stokes equation (NSE). Recently, in “Focusing phenomenon in numerical solution of two-dimensional Navier-Stokes equation, In: Pirozzoli S., Sengupta T. (eds) High-Performance Computing of Big Data for Turbulence and Combustion, CISM International Centre for Mechanical Sciences (Courses and Lectures), vol 592. Springer, Cham (2019)”, focusing was demonstrated for a steady fluid flow and its mechanism was identified from global spectral analysis (GSA) of 2D convection diffusion equation (CDE). Focusing was shown to be due to the anti-diffusion caused by the discretization of diffusion term for the chosen numerical scheme. The present work consolidates the one-to-one correspondence between numerical anti-diffusion of 2D CDE and focusing for unsteady flows by solving flow inside a 2D lid driven cavity (LDC) for the Reynolds number of 10,000. We also present a method to remove numerical anti-diffusion using multi-dimensional filters. Detailed analysis of space-time discretization with filters is also provided to explain the cure of focusing.

A New Filter Nonmonotone Adaptive Trust Region Method for Unconstrained Optimization

In this paper, a new filter nonmonotone adaptive trust region with fixed step length for unconstrained optimization is proposed. The trust region radius adopts a new adaptive strategy to overcome additional computational costs at each iteration. A new nonmonotone trust region ratio is introduced. When a trial step is not successful, a multidimensional filter is employed to increase the possibility of the trial step being accepted. If the trial step is still not accepted by the filter set, it is possible to find a new iteration point along the trial step and the step length is computed by a fixed formula. The positive definite symmetric matrix of the approximate Hessian matrix is updated using the MBFGS method. The global convergence and superlinear convergence of the proposed algorithm is proven by some classical assumptions. The efficiency of the algorithm is tested by numerical results.

Spatial GNSS Spoofing Against Drone Swarms With Multiple Antennas and Wiener Filter

Spoofing of global-navigation satellite system (GNSS) signals to induce a target position estimate is a relevant security threat to the navigation of drones. However, spoofing multiple drones simultaneously as they move in a swarm, without disrupting their formation, is a complex task. In this paper, we propose to transmit spoofing signals from the ground, such that the fake position can be estimated in any point of an area of the plane where the swarm is moving. To this end we filter the satellite-generated GNSS signals with a multidimensional linear filter, and transmit the filtered signal with multiple ground antennas. The multidimensional filter is designed according to a generalized Wiener-filter criterion, such that the fake signal is accurately reproduced (in terms of mean squared error (MSE)) in the whole spoofed area. We investigate the impact of various design parameters (among others, the size of the spoofed area, the number of ground antennas, and the number of spoofed satellites) on both the MSE, and the probability of acquisition of the spoofed signal by the drones.

Quaternion broad learning system: A novel multi-dimensional filter for estimation and elimination tremor in teleoperation

In this paper, a novel quaternion broad learning system is proposed in this paper for tremor estimation and elimination in teleoperation. In the new proposed QBLS, the architecture can be divided into three layers, including quaternion feature layer, enhancement layer and the output layer. In quaternion feature layer, a quaternion-value auto-encoder (QAE) based on the quaternion algebra is proposed and employed to extract the unsupervised features in quaternion domain. Moreover, the enhancement nodes are mapped to improve the system’s regression ability in enhancement layer. In the output layer, the nodes of feature layer and enhancement layer are concatenated to map the output of QBLS. The weight parameters of output layer can be calculated by the minimum norm least squares solutions. In addition, the semi-physical simulation experiment is completed and the new proposed QBLS has been compared with some existing methods. Finally, the effectiveness and efficiency of QBLS are demonstrated by experimental results.

New design approach of three-dimensional IIR notch filter using all-pass sections

ABSTRACTThis paper investigates the design problem of a multidimensional IIR notch filter. To address this issue, a 3-D recursive digital notch filter is considered. A closed-form analytical solution of the notch filter is firstly derived and used for its realisation. The latter is achieved through two types of filters: i) a 3-D IIR straight line filter and ii) 3-D IIR filter with order 111 based on all-pass sections. The straight-line filter is designed by frequency transformation of 3-D analogue prototype filter where a prescribed notch frequency is localised. The IIR filter is realised in proposed lattice structure as a cascade of all-pass sections where the 3-dB bandwidth of the notch filter can be adjusted by the lattice coefficient of the IIR filter independently.

Multi-dimensional particle filter-based estimation of inter-system phase biases for multi-GNSS real-time integer ambiguity resolution

In multi-GNSS integration, fixing inter-system double-difference ambiguities to integers is still a challenge due to the existence of inter-system biases (ISB) when mixed types of GNSS receivers are used. It has been shown that when ISB is known, the inter-system ambiguities can be fixed and the reliability of ambiguity fixing can be improved significantly, especially under poor conditions when the number of observed satellites is small. In traditional methods, the intra-system ambiguity is fixed first; then, the ISB is estimated to ultimately fix the inter-system ambiguity. In our work, we use the particle filter-based method to estimate the ISB parameter and fix the inter-system ambiguities to integers at the same time. This method shows higher reliability and higher ambiguity fixing rate. Nevertheless, the existing particle filter approach for ISB parameter estimation is a one-dimensional algorithm. When satellites from three or more systems are observed, there are two or more ISB parameters. We extend the current one-dimensional particle filter approach to multi-dimensional case and estimate multi-ISB parameters in this study. We first present a multi-dimensional particle filter approach that can estimate multi-ISB parameters simultaneously. We also show that the RATIO values can be employed to judge the quality of multi-dimensional ISB values. Afterward, a two-dimensional particle filter approach is taken as an example to validate this approach. For example, in the experiment of GPS L5, Galileo E5a and QZSS L5 integration with 6 satellites using the IGS baseline SIN0-SIN1, only three ambiguities are resolved to integer when the ISBs are unknown. The integer ambiguity fixing rate is 41.0% with 53% of the ambiguity-fixed solutions having positioning errors larger than 3 cm. However, when our approach is adopted, the number of integer ambiguity parameters increases to five. The integer ambiguity fixing rate increases to 99.7% with 100% of ambiguity-fixed solutions having positioning errors smaller than 3 cm.

Symmetry Incorporated Cost-Effective Architectures for Two-Dimensional Digital Filters

Professor Fettweis as far back as 1977 published a paper generalizing McClellan transformation to obtain circular symmetry in 2-D and spherical, hyper-spherical symmetries in multidimensional digital filters [1]. This survey paper presents stateof-the-art two-dimensional (2-D) VLSI digital filter architectures possessing various symmetries in the filter magnitude response. Preceding the symmetry structures, a generalized formulation is given that allows the derivation of various new 2-D VLSI filter structures of any order without global broadcast. Following this, two types (namely, Type 1 [20] and Type 3 [21], [25], [26]) of cost-effective 2-D magnitude symmetry filter architectures possessing diagonal, four-fold rotational, quadrantal, and octagonal symmetries with reduced number of multipliers are given. By combining the identities of the Types-1 and 3 symmetry filter structures, multimode 2-D symmetry filters which enable the above four symmetry modes are discussed. The Type-1 and Type-3 multimode filters can result in a 65.3% cost reduction in terms of number of multipliers compared with the sum of the multipliers of the four individual Type-1 symmetry filter structures studied in this paper. Furthermore, Type-3 has shorter critical path than Type-1 multimode filter. The paper is concluded with the presentation of a 2-D filter design example and a corresponding structure.

On a robust and accurate localized artificial diffusivity scheme for the high-order flux-reconstruction method

The high-order flux reconstruction (FR) method on unstructured hexahedral grids is coupled with the localized artificial diffusivity (LAD) scheme for aiming at accurate simulation of shock-turbulence interaction. In order to overcome known robustness issues particularly with the high-order (r>0) derivative formulation, important properties of the artificial bulk viscosity (ABV) profile affecting the solution are investigated first. For the purpose of comparison, an approximated Gaussian filter and modified restriction-prolongation (RP) filters are developed and tested for the present FR-LAD approach. Then, we propose a multidimensional RP filter on unstructured quadrilateral and hexahedral grids to address the issues on non-Cartesian grids. It is shown that a simple extension of a one-dimensional RP filter for two-dimensional grids may result in insufficient smoothing of ABV with r=2, and that the proposed multidimensional RP filter can provide smooth ABV with both r=0 and r=2. The proposed FR-LAD scheme is tested for typical shock-related problems, including the 1D shock tube, 1D shock-entropy wave interaction, 2D steady shock flows, and 2D shock-vortex interaction. The FR-LAD scheme has favorable properties of subcell shock capturing with the length scale of O(h/p) and superior preservation of high-order accuracy for smooth flows. Finally, LES of an overexpanded supersonic jet is performed to demonstrate its capability for practical applications. The proposed FR-LAD scheme can be an attractive candidate for LES or DNS of compressible flows involving shocks, contact discontinuities, turbulence, and their interactions on unstructured meshes.

Alias-Free Products of Signals Near Nyquist Rate

Products of time-series signals have found wide-spread application in many fields of signal processing. For example, they are often used in modeling and compensating distortions generated by analog and mixed-signal components. Without excess bandwidth, the products of time-series signals will produce aliased artifacts that do not represent the physical phenomenology of the components being modeled. To ameliorate the effects of these potentially unwanted, aliased distortion products, we compare two multidimensional filters: the first is a simple one-dimensional (1-D) polyphase filter that is used to generate excess bandwidth; the second is a multidimensional (M-D) filter that is convolved with the time-series product. We demonstrate that the 1-D polyphase filter, although computationally simple, still produces unwanted aliasing when applied to signals near Nyquist rate, which can adversely affect modeling and/or compensation performance. By contrast, the M-D filter is computationally expensive, but is capable of most closely matching the ideal antialias filter response.

Multidimensional Seismic Data Reconstruction Using Frequency-Domain Adaptive Prediction-Error Filter

Seismic data interpolation and reconstruction play an important role in seismic data processing. Seismic data are often inadequately sampled along various spatial axes. We have developed a new approach to interpolate aliased multidimensional seismic data based on the multidimensional adaptive prediction-error filter in frequency domain. First, we estimate the adaptive prediction-error filter coefficients, then interpolate missing traces using the estimated coefficients. Shaping regularization is used to control the smoothness of frequency-domain multidimensional adaptive prediction-error filter coefficients. Instead of estimating prediction-error filter coefficients only along one direction space, we estimate the prediction-error filter coefficients using more information along different direction spaces. So, multidimensional adaptive prediction-error filter using regularized nonstationary autoregression can adaptively estimate seismic events whose slopes vary in multidimensional space. The frequency-domain multidimensional interpolation method can input data at temporal frequency, which can save computer memory and time. For multidimensional seismic data, which miss different number of traces regularly in different axes, the proposed method can be used to interpolate missing traces to obtain more accurate results. The proposed method improves the calculation efficiency by applying shaping regularization and implementation in the frequency domain. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples.

Multidimensional directional steerable filters — Theory and application to 3D flow estimation

In this paper, a thorough theoretical analysis on the construction of multi-dimensional directional steerable filters is given. Steerable filters have been constructed for up to three dimensions. We extend the relevant theory to multiple dimensions and construct multi-dimensional steerable filters, as well as quadrature pairs of such filters. Formulating the multi-dimensional motion estimation problem in the spatiotemporal frequency domain, it is shown that motion manifests itself as energy concentration along “motion hyper-planes” in that domain. Subsequently, using the constructed multi-dimensional filters, we formulate the “hyper-donut” mechanism, i.e. a mechanism to efficiently “measure” the “motion energy” on a “motion hyper-plane”. On top of that, rigorous mathematical analysis on the use of the constructed filters in the dense flow estimation task is given. Based on the theoretical developments, a steerable filter-based algorithm is formulated, in its simplest possible form, for estimating 3D flow in sequences of volumetric or point-cloud data. Experimental results on simulated and real-world data verify the validity of our arguments and the effectiveness of the proposed method.