Multidimensional Filter Research Articles

Static bending deflection and free vibration analysis of moderate thick symmetric laminated plates using multidimensional wave digital filters

Abstract This paper aims to develop a multidimensional wave digital filtering network for predicting static and dynamic behaviors of composite laminate based on the FSDT. The resultant network is, thus, an integrated platform that can perform not only the free vibration but also the bending deflection of moderate thick symmetric laminated plates with low plate side-to-thickness ratios ( = 20 ). Safeguarded by the Courant-Friedrichs-Levy stability condition with the least restriction in terms of optimization technique, the present method offers numerically high accuracy, stability and efficiency to proceed a wide range of modulus ratios for the FSDT laminated plates. Instead of using a constant shear correction factor (SCF) with a limited numerical accuracy for the bending deflection, an optimum SCF is particularly sought by looking for a minimum ratio of change in the transverse shear energy. This way, it can predict as good results in terms of accuracy for certain cases of bending deflection. Extensive simulation results carried out for the prediction of maximum bending deflection have demonstratively proven that the present method outperforms those based on the higher-order shear deformation and layerwise plate theories. To the best of our knowledge, this is the first work that shows an optimal selection of SCF can significantly increase the accuracy of FSDT-based laminates especially compared to the higher order theory disclaiming any correction. The highest accuracy of overall solution is compared to the 3D elasticity equilibrium one.

Optimal Heading Estimation Based Multidimensional Particle Filter for Pedestrian Indoor Positioning

Localization capability is a challenging task in global navigation satellite system-degraded or denied environments. Alternatively, today’s smartphones have an increased number of integrated sensors that can act as terminals for indoor personal positioning solutions such as pedestrian dead reckoning (PDR). However, magnetic interference, poor sensor measurements, and diverse handling of smartphone quickly decrease the performance for indoor PDR. This paper proposes a comprehensive and novel pedestrian indoor positioning solution in which heading estimation is improved by using simplified magnetometer calibration, by calculating projected acceleration along the moving direction using frequency-domain features and by applying direction constrains to indoor accessible paths. Moreover, compared with an ordinary particle filter (OPF) and a Kalman filter, this paper proposes a multidimensional particle filter (MPF) algorithm, namely MPF, which includes high-dimensional variables such as position, heading, step length parameters, motion label, lifetime, number of current particles, and factor. An MPF can handle more uncertain parameters than the OPF. Therefore, positioning with an MPF can achieve lower errors using low-quality sensors, mitigate interference introduced from surrounding environments, and reduce heading ambiguities due to different modes of carrying a smartphone. Consequently, field tests show that the proposed algorithm obtains robust performance for heading estimation and positioning.

Chebyshev approximation problem of multidimensional IIR digital filters in the frequency domain

This paper investigates the problem of simultaneous approximation of a prescribed multidimensional frequency response. The frequency responses of multidimensional IIR digital filters are used as nonlinear approximating functions. Chebyshev approximation theory and the notion of line homotopy are used to reveal the approximation properties of this set of IIR functions. A sign condition is derived to characterize a convex stable domain in this set. This sign condition can be incorporated into the optimization of the Chebyshev simultaneous approximation. The generally sufficient global Kolmogorov criterion is shown to be a necessary condition, for the characterization of best approximation, in the considered set of approximating functions. Thus, it can be incorporated, as a stopping constraint, in the design of the optimal filter. Moreover, the local Kolmogorov criterion is shown to be also necessary for the set of approximating functions. Finally, it is proved that the best approximation is a global minimum.

Hexagonal Smoothness-Increasing Accuracy-Conserving Filtering

Discontinuous Galerkin (DG) methods are a popular class of numerical techniques to solve partial differential equations due to their higher order of accuracy. However, the inter-element discontinuity of a DG solution hinders its utility in various applications, including visualization and feature extraction. This shortcoming can be alleviated by postprocessing of DG solutions to increase the inter-element smoothness. A class of postprocessing techniques proposed to increase the inter-element smoothness is SIAC filtering. In addition to increasing the inter-element continuity, SIAC filtering also raises the convergence rate from order $$k + 1$$ to order $$2k + 1$$ . Since the introduction of SIAC filtering for univariate hyperbolic equations by Cockburn et al. (Math Comput 72(242):577–606, 2003), many generalizations of SIAC filtering have been proposed. Recently, the idea of dimensionality reduction through rotation has been the focus of studies in which a univariate SIAC kernel has been used to postprocess a two-dimensional DG solution (Docampo-Sanchez et al. in Multi-dimensional filtering: reducing the dimension through rotation, 2016. arXiv preprint arXiv:1610.02317 ). However, the scope of theoretical development of multidimensional SIAC filters has never gone beyond the usage of tensor product multidimensional B-splines or the reduction of the filter dimension. In this paper, we define a new SIAC filter called hexagonal SIAC (HSIAC) that uses a nonseparable class of two-dimensional spline functions called hex splines. In addition to relaxing the separability assumption, the proposed HSIAC filter provides more symmetry to its tensor-product counterpart. We prove that the superconvergence property holds for a specific class of structured triangular meshes using HSIAC filtering and provide numerical results to demonstrate and validate our theoretical results.

New constructions of nonseparable tight wavelet frames

We present two methods for constructing new nonseparable multidimensional tight wavelet frames by combining the ideas of sum of squares representations of nonnegative trigonometric polynomials with the coset sum method of generating nonseparable multidimensional lowpass filters from univariate lowpass filters. In effect, these methods allow one to select a univariate lowpass filter and generate nonseparable multidimensional tight wavelet frames from it in any dimension n≥2, under certain conditions on the input filter which are given explicitly. We construct sum of hermitian squares representations for a particular class of trigonometric polynomials f in several variables, each related to a coset sum generated lowpass mask τ in that nonnegativity of f implies the sub-QMF condition for τ, in two ways: for interpolatory inputs to the coset sum method satisfying the univariate sub-QMF condition, we find this representation using the Fejér–Riesz Lemma; and in the general case, by writing f=x⁎Px, where x is a vector of complex exponential functions, and P is a constant positive semidefinite matrix that is constructed to reduce the number of generators in this representation. The generators of this representation of f may then be used to generate the filters in a tight wavelet frame with lowpass mask τ. Several examples of these representations and the corresponding frames are given throughout.

Reverse engineering aggregation queries

Query reverse engineering seeks to re-generate the SQL query that produced a given query output table from a given database. In this paper, we solve this problem for OLAP queries with group-by and aggregation. We develop a novel three-phase algorithm named REGAL 1 for this problem. First, based on a lattice graph structure, we identify a set of group-by candidates for the desired query. Second, we apply a set of aggregation constraints that are derived from the properties of aggregate operators at both the table-level and the group-level to discover candidate combinations of group-by columns and aggregations that are consistent with the given query output table. Finally, we find a multi-dimensional filter, i.e., a conjunction of selection predicates over the base table attributes, that is needed to generate the exact query output table. We conduct an extensive experimental study over the TPC-H dataset to demonstrate the effectiveness and efficiency of our proposal.

Fast and Complete Conflict Detection for Packet Classifiers

Packet classification filters are used to classify packets based on header fields. A filter conflict occurs when two or more filters overlap, causing an ambiguity in packet classification. These conflicts may cause quality-of-service failures, security vulnerabilities, or routing errors in network services, e.g., differentiated services and firewalls. There are two types of conflicts, i.e., overlapping and subset. While the subset conflict problem can be solved by reordering filters, overlapping conflicts are resolved by inserting resolve filters. None of the existing algorithms detects both types of conflicts for multidimensional filters with arbitrary-range fields. To fill the research gap, we present a series of algorithms based on a previous algorithm that reports all overlapping filters without identifying overlapping conflicts. We improve the previous algorithm to extract overlapping conflicts by modifying either data structures or operations. To further reduce the cost of conflict detection, we define new data structures to process range fields with their boundary addresses. The algorithm based on new bit vectors can detect partial overlaps between multidimensional filters with arbitrary ranges. Our experimental results show that the new algorithm is two times faster than the algorithms based on the original data structures in detecting both types of conflicts.

An approach based on dwindling filter method for positive definite generalized eigenvalue problem

In this paper, we present a new spectral residual method for solving large-scale positive definite generalized eigenvalue problems. The proposed algorithm is equipped with a dwindling multidimensional nonmonotone filter, in which the envelope dwindles as the step length decreases. We have also employed a relaxed nonmonotone line search technique in the structure of the algorithm which allows it to enjoy the nonmonotonicity from scratch. Under some mild and standard assumptions, the global convergence property of the proposed algorithm is established. An implementation of the new algorithm on some test problems shows the efficiency and effectiveness of the proposed algorithm in practice.

Software-defined microwave photonic filter with high reconfigurable resolution.

Microwave photonic filters (MPFs) are of great interest in radio frequency systems since they provide prominent flexibility on microwave signal processing. Although filter reconfigurability and tunability have been demonstrated repeatedly, it is still difficult to control the filter shape with very high precision. Thus the MPF application is basically limited to signal selection. Here we present a polarization-insensitive single-passband arbitrary-shaped MPF with ~GHz bandwidth based on stimulated Brillouin scattering (SBS) in optical fibre. For the first time the filter shape, bandwidth and central frequency can all be precisely defined by software with ~MHz resolution. The unprecedented multi-dimensional filter flexibility offers new possibilities to process microwave signals directly in optical domain with high precision thus enhancing the MPF functionality. Nanosecond pulse shaping by implementing precisely defined filters is demonstrated to prove the filter superiority and practicability.

Synthesis of optimal multidimensional digital filter

Demonstrated is one of efficient methods of digital realization of analogue multidimensional filter. Worked out on the basis of this method is software of digital realization of analogue multidimensional filter. The efficiency of the proposed method is demonstrated by the example of digital realization of optimal filter structure in the channel of angular velocity measurement of snap down inertia navigation

Performance-Aware Architectures for Parallel 4D Color fMRI Filtering Algorithm: A Complete Performance Indices Package

A parallel 4D fMRI filtering algorithm is proposed to overcome the bottlenecks of large 4D volumetric fMRI data and its overlapping segments by input decimation, multidimensional intensive computation by parallel processing and the boundary conditions by output interpolation. Three spatial convolution architectures implement this parallel multidimensional filtering algorithm in Virtex-6 FPGA board, as automated 4D fMRI filtering systems. These three automated filtering systems are devised as “plug and develop” processors to filter any 4D volumetric data. Then, two sets of generic Edge and noise smoothing filtering operators are prototypically plugged and developed to be improved for filtering a dementia case study of color 256 × 256 × 4 × 3 volumetric fMRI. Accordingly, performance indices of the three architectures are evaluated as a complete package of area, speed, dynamic power, and throughput. Significant improvements have been achieved in keeping a stable speed, decreasing power consumption and increasing throughput in color fMRI filtering applications. All three architectures have an operating (225 MHz) maximum frequency. The power consumption improved more than two-fold using architecture 2 compared to 3. The highest throughput is achieved by architectures 2 and 3 almost (2.5) times than that of architecture 1. Evidently, all three architectures are performance-aware processors, and architecture 2 is optimal.

Evaluating the Improvement in Shear Wave Speed Image Quality Using Multidimensional Directional Filters in the Presence of Reflection Artifacts.

Shear waves propagating through interfaces where there is a change in stiffness cause reflected waves that can lead to artifacts in shear wave speed (SWS) reconstructions. Two-dimensional (2-D) directional filters are commonly used to reduce in-plane reflected waves; however, SWS artifacts arise from both in- and out-of-imaging-plane reflected waves. Herein, we introduce 3-D shear wave reconstruction methods as an extension of the previous 2-D estimation methods and quantify the reduction in image artifacts through the use of volumetric SWS monitoring and 4-D-directional filters. A Gaussian acoustic radiation force impulse excitation was simulated in phantoms with Young’s modulus (E) of 3 kPa and a 5-mm spherical lesion with E = 6, 12, or 18.75 kPa. The 2-D-, 3-D-, and 4-D-directional filters were applied to the displacement profiles to reduce in-and out-of-plane reflected wave artifacts. Contrast-to-noise ratio and SWS bias within the lesion were calculated for each reconstructed SWS image to evaluate the image quality. For 2-D SWS image reconstructions, the 3-D-directional filters showed greater improvements in image quality than the 2-D filters, and the 4-D-directional filters showed marginal improvement over the 3-D filters. Although 4-D-directional filters can further reduce the impact of large magnitude out-of-plane reflection artifacts in SWS images, computational overhead and transducer costs to acquire 3-D data may outweigh the modest improvements in image quality. The 4-D-directional filters have the largest impact in reducing reflection artifacts in 3-D SWS volumes.

A New Approach to Video Coding Using 3D Directional Filter Bank

The high resolution 3-D and higher dimensional volumetric data are increasingly used in a wide variety of applications including biomedical imaging, video processing and compression. Multidimensional filter banks and its associated constructions provide a framework and serve as an efficient computational tool in the formation, representation, and processing of multidimensional data sets. This paper focuses on the construction of 3-D directional filter banks (DFB) and its signal representations for scalable video coding. In this paper we consider five such DFBs and analyse the performance to find the best suitable one for scalable video coding. The five different filters includes: Maxflat filter, Vk filter, kos filter, Sinc filter and Haar filter. The performance evaluation has been done which quantifies the factors like Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE). In order to achieve better compression, a comparative study between RLC and Huffman coding schemes has been performed and the average codeword length is measured and tabulated. Among the five filters and two compression scheme it is observed that Kos filters with Huffman coding provide better compression and low Average codeword length.

An Innovative Ultrasound Technique for Evaluation of Tumor Vascularity in Breast Cancers: Superb Micro-Vascular Imaging.

Tumor vascularity is an important indicator for differential diagnosis, tumor growth, and prognosis. Superb micro-vascular imaging (SMI) is an innovative ultrasound technique for vascular examination that uses a multidimensional filter to eliminate clutter and preserve extremely low-velocity flows. Theoretically, SMI could depict more vessels and more detailed vascular morphology, due to the increased sensitivity of slow blood flow. Here, we report the early experience of using SMI in 21 breast cancer patients. We evaluated tumor vascular features in breast cancer and compared SMI and conventional color or power Doppler imaging. SMI was superior to color or power Doppler imaging in detecting tumor vessels, the details of vessel morphology, and both peripheral and central vascular distribution. In conclusion, SMI is a promising ultrasound technique for evaluating microvascular information of breast cancers.

Young Investigator Award session – Basic Science3433D printed models for surgical planning in complex congenital heart disease344Ultrafast doppler imaging of intramyocardial coronary arteries345Quantification of mitral regurgitation with multiple jets: in vitro comparison of two-dimensional PISA techniques346Non-invasive ultrasonic chordal cutting

Young Investigator Award session – Basic Science3433D printed models for surgical planning in complex congenital heart disease344Ultrafast doppler imaging of intramyocardial coronary arteries345Quantification of mitral regurgitation with multiple jets: in vitro comparison of two-dimensional PISA techniques346Non-invasive ultrasonic chordal cutting

Higher order feasible building blocks for lattice structure of multidimensional linear phase biorthogonal filter banks

A multidimensional (MD) linear phase biorthogonal filter bank (LPBOFB) with higher order feasible (HOF) building blocks is reported. Basically, there are two ways to design filter banks with large filter supports. One way is to use a cascade of degree-1 building blocks, and the other way is to use a cascade of order-1 building blocks. Unfortunately, both methods have high implementation costs in terms of the number of parameters, especially for the multidimensional case. A previously reported HOF building block has now been applied to MD LPBOFBs. Their generalized structural design supports both an even and odd number of channels. It is shown that the HOF structure cannot be factored into a cascade of order-1 building blocks. The proposed MD LPBOFB has larger filters and uses fewer building blocks than the traditional degree-1 and order-1 structures.

Lesion Area Detection (LAD) using Superpixel Segmentation

Nowadays, in biomedical field, imaging techniques are used to discover the abnormalities in the particular region. Lesion is an area in an organ or tissue, which has suffered from damage through injury or disease, such as a wound, ulcer, abscess, or tumor. Lesion area of the tissue is detected using source images. Wireless capsule endoscopy image of the gastrointestinal tract is used to find the lesion. Preprocessing of image is done using denoising by multidimensional filter. Denoised image is edge detected during which the edge points in an image differentiation is highlighted by Sobel edge detection. The value of each pixel in the edge detected image is evaluated based on the comparison of corresponding pixel in the input image with its neighboring pixels by the morphological operation. Erosion and dilation operation erodes and adds pixels respectively to the edge detected image, so that the value of the output pixel has the maximum pixel value. During segmentation, the pixels are grouped using superpixel algorithm to reduce the complexity while maintaining high diagnostic accuracy. As a final point, the Correlation coefficient test finds the spoiled area between healthy tissue and abnormal tissue by color encoding. This intends to identify the suspected abnormal areas (lesion) from the source images.

Sparsity optimization in design of multidimensional filter networks

Filter networks are a powerful tool for reducing image processing time and maintaining high image quality. They are composed of sparse sub-filters whose high sparsity ensures fast image processing. The filter network design is related to solving a sparse optimization problem where a cardinality constraint bounds below the sparsity level. In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated. The cardinality constraint makes the problem even more difficult to solve. An approach for approximately solving the cardinality-constrained MLLS problem is presented. It is then applied to solving a bi-criteria optimization problem in which both the time and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

Multidimensional digital smoothing filters for target detection

Recursive, causal and non-causal, multidimensional digital filters, with infinite impulse responses and maximally flat magnitude and delay responses in the low-frequency region, are designed to negate correlated clutter and interference in the ‘background’ and to accumulate power due to dim targets in the ‘foreground’ of a surveillance sensor. Expressions relating mean impulse-response duration, frequency selectivity and group delay, to low-order linear-difference-equation coefficients are derived using discrete Laguerre polynomials and discounted least-squares regression, then verified through simulation.

Neuronal oscillations as a mechanistic substrate of auditory temporal prediction.

Neuronal oscillations are comprised of rhythmic fluctuations of excitability that are synchronized in ensembles of neurons and thus function as temporal filters that dynamically organize sensory processing. When perception relies on anticipatory mechanisms, ongoing oscillations also provide a neurophysiological substrate for temporal prediction. In this article, we review evidence for this account with a focus on auditory perception. We argue that such "oscillatory temporal predictions" can selectively amplify neuronal sensitivity to inputs that occur in a predicted, task-relevant rhythm and optimize temporal selection. We elaborate this argument for a prototypic example, speech processing, where information is present at multiple time scales, with delta, theta, and low-gamma oscillations being specifically and simultaneously engaged, enabling multiplexing. We then consider the origin of temporal predictions, specifically the idea that the motor system is involved in the generation of such prior information. Finally, we place temporal predictions in the general context of internal models, discussing how they interact with feature-based or spatial predictions. We propose that complementary predictions interact synergistically according to a dominance hierarchy, shaping perception in the form of a multidimensional filter mechanism.