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A compressed positive quadrature filter (CPQF) is proposed in this technical note. Accuracy, efficiency, and numerical stability are three main concerns for quadrature-based nonlinear Gaussian filtering, but desirable performance in all these three aspects can hardly be simultaneously achieved in previously proposed nonlinear Gaussian filters, such as unscented Kalman filter (UKF), Gauss-Hermite quadrature filter (GHQF), and sparse grid quadrature filter (SGQF). To improve the overall capacity of nonlinear Gaussian filtering techniques, the CPQF is proposed by numerically solving the constrained moment matching equations. By enforcing the positivity of the quadrature weights, the CPQF is numerically as stable as the GHQF. Through exploiting the underlying sparsity while solving the moment matching equations, the CPQF can also achieve the same level of accuracy as the GHQF using far fewer quadrature points. Simulations are conducted to evaluate the effectiveness of the CPQF, and the numerical results demonstrate its superior performance over conventional Gaussian filters.

The dynamic estimation of epidemic spreading on networks is essential for controlling morbidity. Nonlinear Kalman filters, which are capable of estimating the hidden state of a nonlinear system, can be utilized for dynamic state estimation of epidemic spreading. Traditional nonlinear Kalman filters perform optimization using the minimum mean square error (MMSE) criterion. Since observable measurements are generally corrupted by non-Gaussian noise, maximum correntropy criterion (MCC)-based nonlinear Kalman filters have been used for improving robustness against non-Gaussian noise. In comparison with the MCC, generalized correntropy is more robust and flexible in the presence of non-Gaussian noise. In this article, epidemic spreading is described by a compartmental model, i.e., susceptible-infected-recovered-susceptible model. Based on the compartmental model, the generalized correntropy-based sparse Gauss-Hermite quadrature filter (GCSGHQF) is proposed for epidemic tracking on homogeneous networks. The GCSGHQF approximates the Gaussian-weighted integrals by utilizing the sparse Gauss-Hermite quadrature rule. In addition, the generalized correntropy is applied to enhancing robustness in the presence of non-Gaussian noise. Simulation results show that the GCSGHQF exhibits a higher filtering accuracy and improves robustness compared to traditional nonlinear Kalman filters.

In this study, a novel M-estimation based sparse grid quadrature filter (MSGQF) is proposed to improve the robust performance of the nonlinear system. We present a systematic formulation of the sparse grid quadrature filter (SGQF), and extend it to the discrete-time nonlinear system with abnormal measurement values. The M-estimation method is introduced in the SGQF, which uses the Huber’s cost function to update the measurement covariance. Convergence on the modified robust SGQF is established and proved. The sufficient conditions are shown to ensure stochastic stability of the MSGQF. A target tracking problem has been conducted to demonstrate the accuracy of the MSGQF. When measurement abnormal values appear, it outperforms the unscented Kalman filter (UKF), the cubature Kalman filter (CKF) and the SGQF. Theoretical analysis and simulation results prove that the MSGQF provides significant performance improvement in the robustness of the nonlinear system.

To improve the filtering effect of the sparse grid quadrature filter (SGQF) under non-Gaussian conditions, the Gaussian sum technique is introduced, and the Gaussian sum sparse grid quadrature filter (GSSGQF) is developed. We present a systematic formulation of the SGQF and extend it to the discrete-time nonlinear system with the non-Gaussian noise. The proposed algorithm approximates the non-Gaussian probability densities by a finite number of weighted sums of Gaussian densities, and takes the SGQF as the Gaussian sub-filter to conduct the time and measurement update for each Gaussian component. An application in the discrete-time nonlinear system with the non-Gaussian noise has been shown to demonstrate the accuracy of the GSSGQF. It outperforms the unscented Kalman filter (UKF), the cubature Kalman filter (CKF) and the SGQF. Theoretical analysis and simulation results prove that the GSSGQF provides significant performance improvement in the calculation accuracy for nonlinear non-Gaussian filtering problems.

In this paper, a bulk driven quadrature filter is proposed for low power applications. A 3rd complex filter is designed by cascade connection of 2nd order right shifted Low Pass Filter with first order right shifted notch filter, which helps in improving the selectivity of the filter. The quadrature filter is implemented by employing Fully Differential Current Conveyor (FDCCII) as a basic building block. The proposed quadrature filter achieves a −3 dB bandwidth of 1.3 MHz with an Image Rejection Ratio (IRR) of 22.5 dB. The design consumes a total power of 10.94 μW with Total Harmonic Distortion (THD) of 0.121 $$\%$$ . The Figure Of Merit (FOM) of the proposed filter is 0.002fJ with a SFDR of 61 dB. The output noise of the design at 2 MHz centre frequency is 89.12 nV/ $$\sqrt{Hz}$$ and integrated Input Referred noise is 36.89 $$\upmu V_{rms}$$ . The design is simulated using a 180 nm CMOS technology with a supply voltage of 0.5 V. The proposed quadrature filter is used for low-Intermediate Frequency (IF) receiver for standard IEEE 802.15.1 (Bluetooth) applications.

To effectively improve the computation efficiency in the strapdown inertial navigation system (SINS) alignment process, the authors propose a marginalised adaptive sparse-grid quadrature filter (MASGQF). The filtering method combines the virtues of marginalisation technique and accuracy level switching structure to decrease the computational burden and improve the filtering precision simultaneously. With the adaptation criterion and the predefined tolerance value, different integration rules corresponding to the different accuracy levels nested in the proposed filtering method can be adjusted autonomously. It is proved that the MASGQF is exponentially bounded by theoretical analysis. The performance comparison of different filtering methods is demonstrated by the numerical results of the simulation and offline experiment. On the basis of the data performance of the online test, the validity of the proposed MASGQF is verified in the SINS alignment application.

In this paper, a composite weighted average consensus filtering (CWACF) algorithm is proposed for space object tracking by combining two distributed heterogeneous nonlinear filters. In light of the sensors' different sensing accuracy and computational capability, extended Kalman filter (EKF) and sparse-grid quadrature filter (SGQF) are compositely adopted on different sensors as local filters. Then, estimates from neighbours are fused based on the weighted average consensus framework to attain better estimation performance. Moreover, it is proved that the estimation error is exponentially bounded in mean square. The performances of the proposed algorithm, the distributed extended Kalman filtering (DEKF) and the distributed sparse-grid quadrature filter (DSGQF) are compared in a space object tracking problem.

In this work, new nonlinear filtering algorithms based on Gaussian sum framework is formulated and then applied to track a ballistic target on reentry. Other than representing the predicted and updated probability density function of states given measurements as a sum of weighted Gaussian densities, a weight update scheme in time update step is also considered. This weight update scheme is based on a quadratic optimization problem that minimizes the integral square error between the true and the approximated prior density. The Gaussian densities in the weighted sum is realized using various quadrature filters. These filters are applied to track a ballistic target on reentry using measurements from an inbuilt seeker of an interceptor missile, where a 6 degrees of freedom state-dependent coefficient model (SDC) of target–interceptor dynamics is considered. Further, the estimated states are provided to a guidance law for generating interceptor missile accelerations. For performance analysis, root mean square error (RMSE) of relative states and also the range between target and interceptor when they cross each other (miss-distance) are considered. It was found that the miss-distances obtained from the Gaussian filters are smaller than that of the conventional EKF. Further, the Gaussian sum and its weight adaptation scheme with quadrature filter proposals provided far better results, with the weight adaptation filters giving more accurate miss-distances.

Data analysis is a necessary part of practical applications as well as of pure research. The problem of data analysis is of great interest in engineering areas such as signal processing, speech recognition, vibration analysis, time series modelling, etc. Sensing of physical effects transformed to time series of voltage represents measured reality for us. However, the knowledge of time characteristics of measured data is often quite insufficient for description of real signal properties. Therefore, frequency analysis, as an alternative signal description approach, has been engaged in signal processing methods. Unfortunately, data from real applications are mostly non-stationary and represent non-linear processes in general. This fact has leaded to introduction of joint time-frequency representation of measured signals. Former time-frequency methods dealing with non-stationary data analysis, such as the short-time Fourier transform, repeatedly use a block of data processing with the assumption that frequency characteristics are time-invariant and/or a process is stationary within the usage of the data block. The resolution of such methods is then given by the HeisenbergGabor uncertainty principle. This limitation is mainly addressed by Fourier pairs and by the block processing. In this chapter, the definition of instantaneous frequency introduces a new approach to acquire a proper time-frequency representation of a signal. The description of limitations which have to be taken into account in order to achieve meaningful results is also given there. The section that deals with the instantaneous frequency phenomenon is followed by the part describing the construction of the signal model. A signal is modelled as an output of a system that consists of sum of auto-regressive (AR), linear time-invariant (LTI), secondorder subsystems. In fact, such a model corresponds to a system of resonators formed in parallel. The reason for such model selection is simplicity in matrix implementation as well as preservation of a physical meaning of decomposed signal components. The signal model is developed in state space and there is also demonstrated how to select adequately all system matrices. The estimation of particular signal components is then obtained through the adaptive Kalman filtering which is based on the previously defined state space model. The Kalman filter recursively estimates time-varying signal components in a complex form. The complex form is required in order to compute the instantaneous frequency and amplitude of the O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

Dynamic phenomena in electric power systems require fast and accurate algorithms for processing signals. The processing results include synchrophasor parameters, e.g., varying amplitude, phase or frequency of sinusoidal voltage or current signals. This paper presents a novel estimation method of synchrophasor parameters that comply with the requirements of IEEE/IEC standards. The authors analyzed an algorithm for measuring the phasor magnitude by means of a selected artificial neural network (ANN), an algorithm for estimating the phasor phase and frequency that makes use of the zero-crossing method. The original components of the presented approach are: the method of the synchrophasor magnitude estimation by means of a suitably trained and applied radial basic function (RBF), the idea of using two algorithms operating simultaneously to estimate the synchrophasor magnitude, phase and frequency that apply identical calculation methods are different in that the first one filters the input signal using the FIR filter and the second one operates without any filter, and the algorithm calculating corrections of the phase shift between the input and output signal and the algorithm calculating corrections of the magnitude estimation. The error results obtained from the applied algorithms were compared with those of the quadrature filter method and the ones presented in literature, as well as with the permissible values of the errors. In all cases, these results were lower than the permissible values and at least equal to the values found in the literature.

Guidewires are thin wires used in coronary angioplasty to guide different tools to access and repair the obstructed artery. The whole procedure is monitored using fluoroscopic (real-time X-ray) images. Due to the guidewire being thin in the low quality fluoroscopic images, it is usually poorly visible. The poor quality of the X-ray images makes the guidewire detection a challenging problem in image-guided interventions. Localizing the guidewire could help in enhancing its visibility and for other automatic procedures. Guidewire localization methods usually contain a first step of computing a pixelwise guidewire response map on the entire image. In this paper, we present a steerable Convolutional Neural Network (CNN), which is a Fully Convolutional Neural Network (FCNN) that can detect objects rotated by an arbitrary 2D angle, without being rotation invariant. In fact, the steerable CNN has an angle parameter that can be changed to make it sensitive to objects rotated by that angle. We present an application of this idea to detecting the guidewire pixels, and compare it with an FCNN trained to be invariant to the guidewire orientation. Results reveal that the proposed method is a good choice, outperforming some popular filter-based and learning-based approaches such as Frangi Filter, Spherical Quadrature Filter, FCNN and a state of the art trained classifier based on hand-crafted feature.

There has been increasing interest in the analysis of corneal nerve fibers to support examination and diagnosis of many diseases, and for this purpose, automated nerve fiber segmentation is a fundamental step. Existing methods of automated corneal nerve fiber detection continue to pose difficulties due to multiple factors, such as poor contrast and fragmented fibers caused by inaccurate focus. To address these problems, in this paper we propose a novel weighted local phase tensor-based curvilinear structure filtering method. This method not only takes into account local phase features using a quadrature filter to enhance edges and lines, but also utilizes the weighted geometric mean of the blurred and shifted responses to allow better tolerance of curvilinear structures with irregular appearances. To demonstrate its effectiveness, we apply this framework to 1578 corneal confocal microscopy images. The experimental results show that the proposed method outperforms existing state-of-the-art methods in applicability, effectiveness, and accuracy.

A wide range of applications needs the analysis of biomedical images as a fundamental task to extract meaningful information and allow high throughput measurements. A new method for the detection of curve-like structures in biomedical images is presented by exploiting local phase vector and the structural anisotropy information at various directions. We introduce an oriented gaussian derivative quadrature filter not only for estimating the local phase vectors, which include line features, but also for its immunity to inhomogeneous intensity and its capability to enhance curved structures having various diameters, leading to more reliable hessian analysis. A novel measure function-based hessian tensor is proposed to detect curvilinear patterns by incorporating the anisotropic indices (coherence and linearity) of curved features, producing a uniform and strong response. Over multiple orientations, the responses are maximized to achieve a rotationally invariant response, and to detect target structures with different widths and illuminations. The evaluation of the proposed method on the extraction of retinal vessels and leaf venation patterns exhibits its superior performance against state-of-the-art methods.

This brief proposes a new unbiased finite impulse response (FIR) filter with improved robustness for state-space models in continuous time. The FIR filter proposed in this brief is called the unbiased FIR filter based on the Frobenius norm and exponential weight (UFFFNE). A new integral cost function based on the Frobenius norm for the filter gain function with exponential weight is introduced to improve its robustness. It is shown that the UFFFNE design problem can be cast into the constrained minimum-energy optimal control problem. A new analytic expression for the gain function of the UFFFNE is also proposed. The higher robustness of the proposed UFFFNE is demonstrated through a comparison with the existing minimum variance unbiased FIR filter and the conventional Kalman-Bucy filter based on a numerical example.

This paper presents a novel active element, namely dual-X current conveyor transconductance amplifier. The CMOS implementation, parasitic model and characteristic performance parameters of the proposed dual-X current conveyor transconductance amplifier have been explored. The proposed active element has the advantages of good operational bandwidth, good dynamic range and low power consumption. Additionally, current-mode multifunction filter and quadrature oscillator are proposed to examine the applicability of the newly proposed active element. The proposed current-mode multifunction filter provides the responses, low-pass, high-pass and band-pass simultaneously without any circuit modification. The proposed quadrature oscillator circuit simultaneously generates three current outputs and three voltage outputs. The non-ideal analyses of both current-mode multifunction filter and quadrature oscillator are also included. Moreover, the active and passive sensitivities of both current-mode multifunction filter and quadrature oscillator are calculated which are found to be less than unity in magnitude. HSPICE simulation results are depicted to confirm the theoretical analyses. Moreover, practicality of novel dual-X current conveyor transconductance amplifier is examined through the experimental results of the proposed quadrature oscillator.

A novel robust filter referred as maximum correntropy sparse Gauss–Hermite quadrature filter (MCSGHQF) is proposed. The novel algorithm makes use of the sparse Gauss–Hermite quadrature (SGHQ) rule to numerically compute Gaussian-weighted integrals, which are propagated through non-linear state equation, and then a weighted means and covariance is taken. As the sensor measurements are always corrupted by non-Gaussian noise which is typically glint noise or mixed Gaussian-impulsive noise, the measurement update is redesigned based on the maximum correntropy criterion instead of minimum mean square error. Therefore, the MCSGHQF could exhibit robustness to the non-Gaussian measurement noise, especially impulsive noise. In addition, the study proposes the use of MCSGHQF for ballistic missile tracking during midcourse phase to deal with the non-Gaussian noise. The tracking performance is compared with that of SGHQ filter (SGHQF), Huber-based filter and extended Kalman filter by Monte-Carlo simulations. The simulation results demonstrate that the MCSGHQF is effective in glint noise case and exhibits superior to Huber-based filter in mixed Gaussian-impulsive noise case.

This study presents denoising of phases signal by comb filter. Signal phase is widely used in biomedical and communications engineering, and has become increasingly important over the past few years. In particular, steady-state visual evoked potential (SSVEP) of electroencephalogram (EEG) and quadrature amplitude modulation (QAM) uses phase to distinguish channel and data. For signal processing, the filter is usually adopted. In this study, the usefulness of comb and bandpass filters in detecting the phase of a signal is compared by using simulated and real signals to verify phase signal denoising. Experimental data show that comb filters had a higher signal to noise ratio (SNR) of phase signal. However, even if a comb filter performs well, the delay time of a digital comb filter will be limited by the sampling rate. It is possible to solve this problem, but doing so is inconvenient within the context of real-time applications. Using a variable delay (VD) approached to fractional delay for digital comb filter, it is both simple and easy to use.

We develop an error-free, nonuniform phase-stepping algorithm (nPSA) based on principal component analysis (PCA). PCA-based algorithms typically give phase-demodulation errors when applied to nonuniform phase-shifted interferograms. We present a straightforward way to correct those PCA phase-demodulation errors. We give mathematical formulas to fully analyze PCA-based nPSA (PCA-nPSA). These formulas give a) the PCA-nPSA frequency transfer function (FTF), b) its corrected Lissajous figure, c) the corrected PCA-nPSA formula, d) its harmonic robustness, and e) its signal-to-noise-ratio (SNR). We show that the PCA-nPSA can be seen as a linear quadrature filter, and as consequence, one can find its FTF. Using the FTF, we show why plain PCA often fails to demodulate nonuniform phase-shifted fringes. Previous works on PCA-nPSA (without FTF), give specific numerical/experimental fringe data to "visually demonstrate" that their new nPSA works better than competitors. This often leads to biased/favorable fringe pattern selections which "visually demonstrate" the superior performance of their new nPSA. This biasing is herein totally avoided because we provide figures-of-merit formulas based on linear systems and stochastic process theories. However, and for illustrative purposes only, we provide specific fringe data phase-demodulation, including comprehensive analysis and comparisons., 10 pages, 8 figures

In this paper, a dimensionality reduction Gauss-Hermite quadrature filter (DRGHQF) is proposed. Compared with the conventional GHQF algorithm and with the Rao-Blackwellised particle filter (RBPF), the proposed DRGHQF performs better in terms of computational cost and accuracy. The simulation results indicate that the DRGHQF can significantly reduce the computational cost without incurring a loss in accuracy.

Blade Tip Timing (BTT) is a non-intrusive measurement technique that can be used to estimate the vibration characteristics of rotor blades during turbomachine operation. BTT uses proximity probes mounted into the turbomachine casing to measure the Time-of-Arrival (ToA) of rotor blades at these proximity probes. The ToAs are determined using a triggering criterion on the proximity probe signal. Rotor blade tip displacements are then calculated from these ToAs. It is therefore imperative that the triggering criterion be as accurate as possible. This article proposes a new method to determine the tip displacement of rotor blades from a proximity probe signal. The method first converts the signal into the angular domain and then obtains the tip deflection through manipulation of the instantaneous phase in the signal. Three experimental tests are conducted where existing triggering criteria are compared to the proposed method. It is found that the proposed method is highly accurate in determining the tip deflections for a constant rotor speed.

In this note, a novel tunable bandpass filter/phase shifter implementation (with a Hilbert transformer as a special case) is proposed. The filter can also be used to synthesize a bandpass analytic signal from a real-valued signal. The novelty is the simple, yet elegant implementation that exploits the even and odd symmetry of the in-phase and quadrature carrier modulation. HighlightsAlternate tunable bandpass phase shifter implementation is proposed.Exploits even and odd symmetry of in-phase and quadrature carrier modulation.Novel, simple yet elegant, architecture to shift the phase by any arbitrary angle.Hilbert transform computation of a bandpass signal as a specific case is presented.

In this paper, a novel particle filter (PF) which we refer to as the quadrature particle filter (QPF) based on fuzzy c-means clustering is proposed. In the proposed algorithm, a set of quadrature point probability densities are designed to approximate the predicted and posterior probability density functions (pdf) of the quadrature particle filter as a Gaussian. It is different from the Gaussian particle filter that uses the prior distribution as the proposal distribution, the proposal distribution of the QPF is approximated by a set of modified quadrature point probability densities, which can effectively enhance the diversity of samples and improve the performance of the QPF. Moreover, the fuzzy membership degrees provided by a modified version of fuzzy c-means clustering algorithm are used to substitute the weights of the particles, and the quadrature point weights are adaptively estimated based on the weighting exponent and the particle weights. Finally, experiment results show the proposed algorithms have advantages over the conventional methods, namely, the unscented Kalman filter(UKF), quadrature Kalman filter(QKF), particle filter(PF), unscented particle filter(UPF) and Gaussian particle filter(GPF), to solve nonlinear non-Gaussian filtering problems. Especially, to the target tracking in Aperiodic Sparseness Sampling Environment, the performance of the quadrature particle filter is much better than those of other nonlinear filtering approaches.

This letter presents a time-domain equalization method for compensation of chromatic dispersion (CD) using Wiener filter in digital coherent optical receivers. The Wiener filter can compensate CD, filter out the noise from the corrupted signal, and provide an optimal estimate of the signal of interest in the sense of minimum mean square error. The tap weights of the Wiener filter applied to a multirate system are determined by the channel impulse response and the signal-to-noise ratio. Numerical results of 16-ary quadrature amplitude modulation coherent optical multirate transmission systems show that the proposed equalizer outperforms the existing ones.

In this paper, a novel fuzzy quadrature particle filter (FQPF) based on maximum entropy fuzzy clustering for maneuvering target tracking is proposed. The novelties of the fuzzy quadrature particle filter are in the update step in which the predicted and posterior probability density functions are approximated by introducing a set of quadrature point probability densities based on the Gauss–Hermite quadrature rule as a Gaussian. The particle and quadrature point weights can be adaptively estimated based on the weighting exponent and fuzzy membership degrees provided by a modified version of maximum entropy fuzzy clustering algorithm. Unlike the Gaussian particle filter (GPF) using the prior distribution as the proposal distribution, the new FQPF uses a set of modified quadrature point probability densities as the proposal distribution that can effectively enhance the diversity of samples and improve the approximate performance. Finally, simulation results are presented to demonstrate the versatility and improved performance of the fuzzy quadrature particle filter over other nonlinear filtering approaches, namely the unscented Kalman filter, quadrature Kalman filter, particle filter, and GPF, to solve maneuvering target tracking problems.

In this paper, a composite weighted average consensus filtering algorithm (CWACF) is proposed by applying multiple heterogeneous nonlinear filters. In light of the sensors’ different sensing accuracy and computational capability, extended Kalman filter (EKF) and sparse-grid quadrature filter (SGQF) are compositely adopted on different sensors as local filters. Then, estimation from neighbours are fused based on the weighted average consensus framework to attain better estimation performance. Moreover, it has been proved that the estimation error is exponentially bounded in mean square. The performance of the proposed algorithm and distributed extended Kalman filtering (DEKF) are compared by a target localization case through a sensor network.

Edgeworth expansion is an effective method to approximate a non-Gaussian distribution by utilizing higher order cumulants of the statistics, which can be obtained from corresponding moments. The higher order moments can be calculated by numerical integration rules. In this paper, a new nonlinear filtering method that combines higher order moment approximation with the Edgeworth expansion is proposed. The Edgeworth expansion is utilized to correct the weights on the quadrature points in the Gauss-Hermite quadrature filter. This new filter can provide the robustness to non-Gaussianity for nonlinear filters. An adaptive mechanism is adopted in the filtering algorithm to determine which orders of moments need to be used in the Edgeworth expansion based on the measure of non-Gaussianity. The simulation results demonstrate the enhanced performance of this new filter compared with the conventional nonlinear Gaussian filters.

Automated detection of vascular structures is of great importance in understanding the mechanism, diagnosis, and treatment of many vascular pathologies. However, automatic vascular detection continues to be an open issue because of difficulties posed by multiple factors, such as poor contrast, inhomogeneous backgrounds, anatomical variations, and the presence of noise during image acquisition. In this paper, we propose a novel 2-D/3-D symmetry filter to tackle these challenging issues for enhancing vessels from different imaging modalities. The proposed filter not only considers local phase features by using a quadrature filter to distinguish between lines and edges, but also uses the weighted geometric mean of the blurred and shifted responses of the quadrature filter, which allows more tolerance of vessels with irregular appearance. As a result, this filter shows a strong response to the vascular features under typical imaging conditions. Results based on eight publicly available datasets (six 2-D data sets, one 3-D data set, and one 3-D synthetic data set) demonstrate its superior performance to other state-of-the-art methods.

The paper proposes an extension of the conventional cubature quadrature Kalman filter (CQKF), in order to enable it for dealing with randomly delayed measurement problems for nonlinear systems. The proposed extension is bounded with an assumption that the maximum delay does not exceed unit sampling time which is alternatively called as one step delayed measurements in this paper. The proposed method which uses third-degree spherical cubature rule and arbitrary order Gauss-Laguerre quadrature rule to solve the intractable integrals is more accurate compared to its existing cubature Kalman filter (CKF) based counterpart. The efficacy of the proposed algorithm has been demonstrated for a maneuvering target tracking problem.

A new, efficient switching median–mean filter is proposed to remove high density impulse noise from digital images. The proposed method consists of detection and filtering stages. The pixels that are labeled noise-free in the detection stage remain unchanged and the noisy-pixels are replaced by the reference image based the proposed filter with 3 × 3 window. The simulation results show that the proposed filter outperforms some existing methods, both in vision and quantitative measurements. Moreover, our method is not only efficient to remove high density impulse noise and preserve the details in the image, but also possess a short processing time.

Quadrature demodulation is used in medical ultrasound imaging to derive the envelope and instantaneous phase of the received radio-frequency (RF) signal. In quadrature demodulation, RF signal is multiplied with the sine and cosine wave reference signal and then low-pass filtered to produce the base-band complex signal, which has high computational complexity. In this paper, we propose an efficient quadrature demodulation method for B-mode and color flow imaging, in which the RF signal is demodulated by a pair of finite impulse response filters without mixing with the reference signal, to reduce the computational complexity. The proposed method was evaluated with simulation and in vivo experiments. From the simulation results, the proposed quadrature demodulation method produced similar normalized residual sum of squares (NRSS) and velocity profile compared with the conventional quadrature demodulation method. In the in vivo color flow imaging experiments, the time of the demodulation process was 5.66 ms and 3.36 ms, for the conventional method and the proposed method, respectively. These results indicated that the proposed method can maintain the performance of quadrature demodulation while reducing computational complexity.

The recently emerging cubature Kalman filter and the sparse-grid quadrature filter approximate the numerical integrations for the mean and covariance in Gaussian filters using the spherical-radial cubature rule and the sparse-grid quadrature rule, respectively. This technical note reveals that 1) spherical rules can be obtained by the projection of sparse-grid quadrature rules; 2) the third- and some of the fifth-degree spherical-radial cubature rules can be directly constructed from sparse-grid quadrature rules.

The design of two-channel quadrature mirror filter banks can be constructed based on real infinite impulse response (IIR) all-pass digital filters without yielding magnitude distortion. The design problem is first formulated as a phase optimization using IIR all-pass filters in the least-squares sense. Then the nonlinear phase optimization is further converted into solving an eigenproblem of an appropriate real, symmetric, and positive-definite matrix. In this paper, the minor component analysis algorithm based on the neural learning rule is exploited to the design of eigenfilter. When the learning algorithm achieves convergence, the weights of the neural system approximate the smallest eigenvector, which are the optimal filter coefficients of the IIR all-pass filters. The simulation results confirm that the proposed neural-based method can achieve accurate performance by incorporating the simple neural model.

In this study, Cosine Modulated Filter Bank design and Quadrature Mirror Filter Bank design are performed using prototype filter designed with Artificial Bee Colony Algorithm. The same design example parameters were used for both filter banks; the performances of the filter banks designed at different orders are compared in terms of stopband attenuation, mean square error, peak reconstruction error and computational time.

The automated detection of cerebral vessels is of great importance in understanding of the diagnosis, treatment and mechanism of many brain vascular pathologies. However, automatic vessel detection from 3D angiography continues to be an open issue. In this paper we introduce a novel 3D symmetry filter that has excellent performance on enhancing vessels in magnetic resonance angiography (MRA). The proposed filter not only takes into account of local phase features estimated by using a quadrature filter so as to distinguish between lines and the edges, but also uses the weighted geometric mean of the blurred and shifted responses of the quadrature filter, which allows more tolerance in the position of the respective contours. As a result this filter can produce a strong response to the vascular features despite variations in scale, contrast, and bifurcations in images. Our results demonstrate its superior performance to other state-of-the-art methods.

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous variable systems., Comment: 6 pages, 2 figures