Explicit Filtering Research Articles

Explicit filtering and exact reconstruction of the sub-filter stresses in large eddy simulation

Explicit filtering has the effect of reducing numerical or aliasing errors near the grid scale in large eddy simulation (LES). We use a differential filter, namely the inverse Helmholtz operator, which is readily applied to unstructured meshes. The filter is invertible, which allows the sub-filter scale (SFS) stresses to be exactly reconstructed in terms of the filtered solution. Unlike eddy viscosity models, the method of filtering and reconstruction avoids making any physical assumptions and is therefore valid in any flow regime. The sub-grid scale (SGS) stresses are not recoverable by reconstruction, but the second-order finite element method used here is an adequate source of numerical dissipation in lieu of an SGS model. Results for incompressible turbulent channel flow at Re τ = 180 are presented which show that explicit filtering and exact SFS reconstruction is a significant improvement over the standard LES approach of implicit filtering and eddy-viscosity SGS modelling.

Continuous-Time Delta-Sigma ADCs With Improved Interferer Rejection

This paper reviews and analyzes the state of the art of Delta-Sigma modulators for receiver applications. Receiver ADCs require not only steadily increased bandwidth, low power and area consumption, but especially face strong interferer signals. These are outside the band of interest, but they most often determine the overall receiver dynamic range and linearity requirements. In order to avoid or at least relax explicit filtering in front of the ADC, Delta-Sigma architectures have been presented with improved robustness to interferers by filtering. This paper intends to review the motivation, to give a tutorial of the state of the art, as well as to introduce a deeper analysis for DSM with interferer robustness. For this, an introduction to the requirements of Delta-Sigma modulators in receivers is given, and a method is introduced which allows to analyze and to scale the internal states meeting the requirements of the interferer scenarios. The paper additionally analyzes state-of-the-art techniques of modulators with improved interferer rejection in order to outline more clearly their possibilities and drawbacks.

Improving Large-Eddy Simulation of Neutral Boundary Layer Flow across Grid Interfaces

Abstract Increasing computational power has enabled grid resolutions that support large-eddy simulation (LES) of the atmospheric boundary layer. These simulations often use grid nesting or adaptive mesh refinement to refine the grid in regions of interest. LES generates errors at grid refinement interfaces, such as resolved energy accumulation, that may compromise solution accuracy. In this paper, the authors test the ability of two LES formulations and turbulence closures to mitigate errors associated with the use of LES on nonuniform grids for a half-channel approximation to a neutral atmospheric boundary layer simulation. Idealized simulations are used to examine flow across coarse–fine and fine–coarse interfaces, as would occur in a two-way nested configuration or with block structured adaptive mesh refinement. Specifically, explicit filtering of the advection term and the mixed model are compared to a standard LES formulation with an eddy viscosity model. Errors due to grid interfaces are evaluated by comparison to uniform grid solutions. It is found that explicitly filtering the advection term provides significant benefits, in that it allows both mass and momentum to be conserved across grid refinement interfaces. The mixed model reduces unphysical perturbations generated by wave reflection at the interfaces. These results suggest that the choice of LES formulation and turbulence closure can be used to help control grid refinement interface errors in atmospheric boundary layer simulations.

H∞ filter design for fuzzy systems with quantized measurements

This paper addresses the problem of H∞ filtering for a class of discrete time T–S model based fuzzy systems with quantized measurements. The measurement signal is quantized by a logarithmic quantizer. By using basis dependent Lyapunov function, a sufficient condition is provided to ensure the stability of the filtering error system and to guarantee a given H∞ performance level. Based on this analysis result of the filtering error system, an explicit filter design approach is proposed and the basis dependent filtering algorithm is further improved by using a kind of relaxed technique. Two numerical examples are also presented to show that the filtering algorithm based on the basis dependent Lyapunov function has less conservative than the one based on the basis independent Lyapunov function.

Noise Reduction of Enhanced Images UsingDual Tree Complex Wavelet Transform and Shrinkage Filter

The project presents that noise reduction of enhanced images using Dual tree complex wavelet transform and Bivariate shrinkage filter.Enhanced image gets affected during contrast enhancement process.So the denoising process will be handled to reduce distortion under Dual tree complex wavelet transform domain. Initially noisy image pixels are decorrelated to obtain coarser and finer components and more noise details are contaminated in high frequency subbands. In order to reduce the spatial distortion during filtering, bivariate shrinkage function used in the DTCWT domain.The effect of noise in the images can be reduced by using either spatial filtering or transform domain filtering. In transform domain wavelet method provide better de-noising while preserving the details of images like edges. In order to increase the quality of the super resolved image, preserving the edges is essential.The guided filter is not directly applicable for sparse inputs like strokes. It also shares a common limitation of other explicit filter,it may have halos near some edges.In order to overcome these disadvantages Dual Tree Complex Wavelet Transform (DTCWT) is used which provide perfect reconstruction over the traditional wavelet transform.Experimental results show that the resultant algorithms produce images with better visual quality and at the same time performance can be improved.Evaluation is carried out in terms of various parameters such as Peak Signal to Noise Ratio, mean Structural Similarity and Coefficient of Correlation.

Explicit Filtering Based Low-Dose Differential Phase Reconstruction Algorithm with the Grating Interferometry.

X-ray grating interferometry offers a novel framework for the study of weakly absorbing samples. Three kinds of information, that is, the attenuation, differential phase contrast (DPC), and dark-field images, can be obtained after a single scanning, providing additional and complementary information to the conventional attenuation image. Phase shifts of X-rays are measured by the DPC method; hence, DPC-CT reconstructs refraction indexes rather than attenuation coefficients. In this work, we propose an explicit filtering based low-dose differential phase reconstruction algorithm, which enables reconstruction from reduced scanning without artifacts. The algorithm adopts a differential algebraic reconstruction technique (DART) with the explicit filtering based sparse regularization rather than the commonly used total variation (TV) method. Both the numerical simulation and the biological sample experiment demonstrate the feasibility of the proposed algorithm.

Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization

In this paper, we propose a robust sequential quadratic programming (SQP) method for nonlinear programming without using any explicit penalty function and filter. The method embeds the modified QP subproblem proposed by Burke and Han (Math Program 43:277---303, 1989) for the search direction, which overcomes the common difficulty in the traditional SQP methods, namely the inconsistency of the quadratic programming subproblems. A non-monotonic technique is employed further in a framework in which the trial point is accepted whenever there is a sufficient relaxed reduction of the objective function or the constraint violation function. A forcing sequence possibly tending to zero is introduced to control the constraint violation dynamically, which is able to prevent the constraint violation from over-relaxing and plays a crucial role in global convergence and the local fast convergence as well. We prove that the method converges globally without the Mangasarian---Fromovitz constraint qualification (MFCQ). In particular, we show that any feasible limit point that satisfies the relaxed constant positive linear dependence constraint qualification is also a Karush---Kuhn---Tucker point. Under the strict MFCQ and the second order sufficient condition, furthermore, we establish the superlinear convergence. Preliminary numerical results show the efficiency of our method.

Subfilter scalar-flux vector orientation in homogeneous isotropic turbulence

The geometric orientation of the subfilter-scale scalar-flux vector is examined in homogeneous isotropic turbulence. Vector orientation is determined using the eigenframe of the resolved strain-rate tensor. The Schmidt number is kept sufficiently large so as to leave the velocity field, and hence the strain-rate tensor, unaltered by filtering in the viscous-convective subrange. Strong preferential alignment is observed for the case of Gaussian and box filters, whereas the sharp-spectral filter leads to close to a random orientation. The orientation angle obtained with the Gaussian and box filters is largely independent of the filter width and the Schmidt number. It is shown that the alignment direction observed numerically using these two filters is predicted very well by the tensor-diffusivity model. Moreover, preferred alignment of the scalar gradient vector in the eigenframe is shown to mitigate any probable issues of negative diffusivity in the tensor-diffusivity model. Consequentially, the model might not suffer from solution instability when used for large eddy simulations of scalar transport in homogeneous isotropic turbulence. Further a priori tests indicate poor alignment of the Smagorinsky and stretched vortex model predictions with the exact subfilter flux. Finally, strong filter dependence of subfilter scalar-flux orientation suggests that explicit filtering may be preferable to implicit filtering in large eddy simulations.

A Study on the Filtering Approach and Turbulence Modeling for LES

the past decades, Large-Eddy Simulation (LES) has been demonstrated to be a useful research tool for understanding the physics of turbulence as well as an accurate and sophisticated predictive method for flows of engineering interest. The LES is numerical technique and is based on the separation between large and small scales in which the large- scale motion is exactly calculated and the effects of small sales or so called sub grid-scale motions are modelled. It is also important to note that the explicit or implicit filter representations like spectral cut-offs or numerical discretizations are commonly used in LES of turbulent flows. Strictly we can say that in LES we need to filter the Navier- Stokes equations in turbulence. Therefore, the study on the filtering approach in turbulence is the main objects of the present research, and in this study we have elaborately studied on this filtering approach and analyzed some general algebraic properties of the filtered representations. It is shown that the averaged equations are the same in terms of the generalized central moments, and then we have defined the resolved turbulence using these average properties. The algebraic consistency rules related with the resolved quantities to the turbulent stresses are derived and their possible use in sub grid-scale modelling is examined. In this study, we have also discussed about the standard Smagorinsky model for LES and then we derived an expression to determine the Smagorinsky constant dynamically, which suppose to be assured the consistency between the filter and the sub grid-scale model. Finally, we have derived the governing equations for LES by applying the filtering approach to the Navier-Stokes equations.

Implementation of a Nonlinear Attitude Estimator for Aerial Robotic Vehicles

Attitude estimation is a key component of the avionics suite of any aerial robotic vehicle. This paper details theoretical and practical solutions in order to obtain a robust nonlinear attitude estimator for flying vehicles equipped with low-cost sensors. The attitude estimator is based on a nonlinear explicit complementary filter that has been significantly enhanced with an effective gyro-bias compensation via the design of an anti-windup nonlinear integrator. A measurement decoupling strategy is proposed in order to make roll and pitch estimation robust to magnetic disturbances that are known to cause errors in yaw estimation. In addition, this paper discusses the fixed-point numerical implementation of the algorithm. Finally, simulation and experimental results confirm the performance of the proposed method.

Green channel guiding denoising on bayer image.

Denoising is an indispensable function for digital cameras. In respect that noise is diffused during the demosaicking, the denoising ought to work directly on bayer data. The difficulty of denoising on bayer image is the interlaced mosaic pattern of red, green, and blue. Guided filter is a novel time efficient explicit filter kernel which can incorporate additional information from the guidance image, but it is still not applied for bayer image. In this work, we observe that the green channel of bayer mode is higher in both sampling rate and Signal-to-Noise Ratio (SNR) than the red and blue ones. Therefore the green channel can be used to guide denoising. This kind of guidance integrates the different color channels together. Experiments on both actual and simulated bayer images indicate that green channel acts well as the guidance signal, and the proposed method is competitive with other popular filter kernel denoising methods.

Large-eddy simulation of decaying isotropic turbulence across a grid refinement interface using explicit filtering and reconstruction

This paper explores numerical errors that arise when large-eddy simulation (LES) is used with adaptive mesh refinement (AMR). LES and AMR combined can reduce the computational cost of turbulence simulations compared to direct numerical simulations, but are rarely used together due to complications that arise with the application of the turbulence closure model at different grid resolutions. Errors appear at grid refinement interfaces due to dependence of computed quantities on the LES filter width and insufficient smoothness of the solution at the grid scale. Here, explicit filtering and approximate reconstruction of the unfiltered velocity field are used to mitigate the effects of these errors in a simulation of decaying isotropic turbulence advected past a grid refinement interface. In particular, different explicit filter types and levels of reconstruction are tested. Explicit filtering with zero-level reconstruction is found to produce the best long-term convergence to a uniform grid solution with minimum perturbation at the interface. Higher levels of reconstruction yield better near-interface convergence. When explicit filtering is used, the explicit filter width transition is more important than the grid spacing transition in terms of solution convergence and interface perturbation. These results inform the use of LES on more complicated AMR grids.

Guided Image Filtering

In this paper, we propose a novel explicit image filter called guided filter. Derived from a local linear model, the guided filter computes the filtering output by considering the content of a guidance image, which can be the input image itself or another different image. The guided filter can be used as an edge-preserving smoothing operator like the popular bilateral filter [1], but it has better behaviors near edges. The guided filter is also a more generic concept beyond smoothing: It can transfer the structures of the guidance image to the filtering output, enabling new filtering applications like dehazing and guided feathering. Moreover, the guided filter naturally has a fast and nonapproximate linear time algorithm, regardless of the kernel size and the intensity range. Currently, it is one of the fastest edge-preserving filters. Experiments show that the guided filter is both effective and efficient in a great variety of computer vision and computer graphics applications, including edge-aware smoothing, detail enhancement, HDR compression, image matting/feathering, dehazing, joint upsampling, etc.

Near-wall turbulent fluctuations in the absence of wide outer motions

AbstractNumerical experiments that remove turbulent motions wider than ${ \lambda }_{z}^{+ } \simeq 100$ are carried out up to ${\mathit{Re}}_{\tau } = 660$ in a turbulent channel. The artificial removal of the wide outer turbulence is conducted with spanwise minimal computational domains and an explicit filter that effectively removes spanwise uniform eddies. The mean velocity profile of the remaining motions shows very good agreement with that of the full simulation below ${y}^{+ } \simeq 40$, and the near-wall peaks of the streamwise velocity fluctuation scale very well in the inner units and remain almost constant at all the Reynolds numbers considered. The self-sustaining motions narrower than ${ \lambda }_{z}^{+ } \simeq 100$ generate smaller turbulent skin friction than full turbulent motions, and their contribution to turbulent skin friction gradually decays with the Reynolds number. This finding suggests that the role of the removed outer structures becomes increasingly important with the Reynolds number; thus one should aim to control the large scales for turbulent drag reduction at high Reynolds numbers. In the near-wall region, the streamwise and spanwise velocity fluctuations of the motions of ${ \lambda }_{z}^{+ } \leq 100$ reveal significant lack of energy at long streamwise lengths compared to those of the full simulation. In contrast, the losses of the wall-normal velocity and the Reynolds stress are not as large as those of these two variables. This implies that the streamwise and spanwise velocities of the removed motions penetrate deep into the near-wall region, while the wall-normal velocity and the Reynolds stress do not.

Filtering Quantized Measurements

The problem of estimating the states of a linear system with quantized measurements is investigated. By introducing the concept of the so-called grid function, it is shown that the quantization effects may be interpreted as a modification of the nonquantized Bayesian posterior distribution. A new filter is obtained by approximating the grid function with a certain class of functions. An explicit filter representation resembling Gaussian sum filters is derived. It is shown that the grid function may also serve as a tool for characterizing well-known filters. We conclude by comparing the filter structure and performance with these well-known filters.

A sub-grid surface dynamics model for sub-filter surface tension induced interface dynamics

This paper presents a novel model for the sub-filter surface tension induced motion of interfaces separating immiscible fluids. A key feature of the proposed Sub-Grid Surface Dynamics (SGSD) model is to take the sub-filter interface dynamics fully into account by employing a dual-scale approach. Instead of modeling the sub-filter interface geometry, it is resolved on an auxiliary grid using the Refined Level Set Grid approach. The required sub-filter velocity field on the auxiliary grid is reconstructed solving a PDE in a narrow band surrounding the interface. With the fully resolved interface geometry available, the previously unclosed surface tension term in the filtered Navier–Stokes equations can be directly closed using explicit filtering. The novel model shows excellent results for different test cases, including sub-grid oscillations of drops, the sub-grid Rayleigh–Plateau instability, and the viscous capillary breakup of a ligament.

Quasi-disjoint pentadiagonal matrix systems for the parallelization of compact finite-difference schemes and filters

This paper proposes a novel systematic approach for the parallelization of pentadiagonal compact finite-difference schemes and filters based on domain decomposition. The proposed approach allows a pentadiagonal banded matrix system to be split into quasi-disjoint subsystems by using a linear–algebraic transformation technique. As a result the inversion of pentadiagonal matrices can be implemented within each subdomain in an independent manner subject to a conventional halo-exchange process. The proposed matrix transformation leads to new subdomain boundary (SB) compact schemes and filters that require three halo terms to exchange with neighboring subdomains. The internode communication overhead in the present approach is equivalent to that of standard explicit schemes and filters based on seven-point discretization stencils. The new SB compact schemes and filters demand additional arithmetic operations compared to the original serial ones. However, it is shown that the additional cost becomes sufficiently low by choosing optimal sizes of their discretization stencils. Compared to earlier published results, the proposed SB compact schemes and filters successfully reduce parallelization artifacts arising from subdomain boundaries to a level sufficiently negligible for sophisticated aeroacoustic simulations without degrading parallel efficiency. The overall performance and parallel efficiency of the proposed approach are demonstrated by stringent benchmark tests.

Integration Filter for APS, DVL, IMU and Pressure Gauge for Underwater Vehicles

High-accuracy underwater navigation is important in order to automate motion control of remotely operated vehicles (ROVs). An observer that estimates the vehicle states (position, velocity, attitude and turn rates) is proposed for closed-loop control. Measurements from an acoustic positioning system (APS), a Doppler velocity log (DVL), an inertial measurement unit (IMU) and a pressure gauge (PG) are used in the proposed observer. The observer is divided into an attitude observer and a translational motion observer with interconnections. The attitude observer is an explicit complementary filter (ECF). Results from simulation are presented.

Mixed-motion Segmentation Using Helmholtz Decomposition

Motion segmentation plays a central role in video analysis, such as the surveillance, human-computer interaction, action recognition, etc. Extensive studies have been done on the stationary camera scenarios. Recently, more attentions are focusing on dynamic backgrounds with several moving objects in the scene. In many applications, the background motion is of much less interest, and solely the local object motion is expected. Several approaches have been proposed for global motion estimation and motion segmentation (the global motion and the object motion are also named as inlier and outlier, respectively). The work in [6] introduced a parametric form which assumed the global motion model from simple translation to general perspective transformation using different parameters. A joint global motion estimation and segmentation method was proposed in [2]. It iteratively updates the inlier model by segmenting the outlier out. A regression scheme, using gradient descent (GD) [6] or least squares (LS) [5], is also applied to refine the inlier model. An outlier rejection filter in [1] explicit filters motion vectors by checking their similarity in a pre-defined window. RANSAC in [3] is a statistical method which estimates the inlier model by iteratively updating the probability of inlier. All above methods are 2D based methods. They require the multiple motions to be independent. But for interdependent motions, they may fail to deal with. Considering this, it is better to place different motions on different layers in higher dimensional space. To this end, our method transforms 2D motion field into 3D surfaces. Local extremes on the surface such as peaks, ridges and valleys depict local motions while smoothing places represent the global motion. The 3D surface is calculated using Helmoholtz decomposition. In [4], a particle filter based on Helmholtz decomposition was proposed for flow estimation. Following is its fundamental theory. For an arbitrary flow field ξ, it is decomposed into two components: curl-free (divergence) component ∇E and divergence-free (curl) component ∇ × W , where E and W are what we want to obtain the 3D potential surfaces. The

Time-domain analysis of frequency dependent inertial wave forces on cylinders

Mono-pile structures are attractive for small well-head platforms and foundation of offshore wind turbines at moderate water depth. Their diameter of several meters makes them prone to simultaneous occurrence of frequency-dependent inertial forces and non-linear drag. The present paper presents a simple time-domain procedure for the inertial force, in which the frequency dependence is represented via a simple explicit time filter on the wave particle acceleration or velocity. The frequency dependence of the inertia coefficient is known analytically as a function of the wave-number, and the relevant range of waves shorter than about six times the diameter typically corresponds to deep water waves. This permits a universal non-dimensional frequency representation, that is converted to rational form to provide the relevant filter equation. Simple time-domain simulations demonstrate the reduction of the resonant part of the response for natural structural frequencies above the dominating wave frequency.