Permutation weighted order statistic filter lattices

We introduce and analyze a new class of nonlinear filters called permutation weighted order statistic (PWOS) filters. These filters extend the concept of weighted order statistic (WOS) filters, in which filter weights associated with the input samples are used to replicate the corresponding samples, and an order statistic is chosen as the filter output. PWOS filters replicate each input sample according to weights determined by the temporal-order and rank-order of samples within a window. Hence, PWOS filters are in essence time-varying WOS filters. By varying the amount of temporal-rank order information used in selecting the output for a given observation window size, we obtain a wide range of filters that are shown to comprise a complete lattice structure. At the simplest level in the lattice, PWOS filters reduce to the well-known WOS filter, but for higher levels in the lattice, the obtained selection filters can model complex nonlinear systems and signal distortions. It is shown that PWOS filters are realizable by a N! piecewise linear threshold logic gate where the coefficients within each partition can be easily optimized using stack filter theory. Simulations are included to show the advantages of PWOS filters for the processing of image and video signals.     

A class of order statistic LMS algorithms

Conventional gradient-based adaptive filters, as typified by the well-known LMS algorithm, use an instantaneous estimate of the error-surface gradient to update the filter coefficients. Such a strategy leaves the algorithm extremely vulnerable to impulsive interference. A class of adaptive algorithms employing order statistic filtering of the sampled gradient estimates is presented. These algorithms, dubbed order statistic least mean squares (OSLMS), are designed to facilitate adaptive filter performance close to the least squares optimum across a wide range of input environments from Gaussian to highly impulsive. Three specific OSLMS filters are defined: the median LMS, the average LMS, and the trimmed-mean LMS. The properties of these algorithms are investigated and the potential for improvement demonstrated. Finally, a general adaptive OSLMS scheme in which the nature of the order-statistic operator is also adapted in response to the statistics of the input signal is presented. It is shown that this can facilitate performance gains over a wide range of input data types     

A new algorithm for order statistic and sorting

An algorithm for rank filtering and stack filtering is presented. This algorithm is simple and results in fast and easy implementations. Various implementations of the algorithm are described, and the H-tree design is shown to be most area efficient. Also introduced is a modification of the filtering algorithm that results in better implement sorting     

Multistage order statistic filters for image sequence processing

The application of multistage order statistic filters (MOS) to the task of noise suppression in time-varying imagery is studied. It is shown that MOS filters efficiently preserve image structures under motion without motion compensation preprocessing. In particular, the families of multistage median and weighted median filters are considered. Motion preservation and statistical smoothing measures are derived. It is shown that spatiotemporal filtering allows for a significant improvement over both spatial and temporal filtering in terms of output image resolution and noise suppression     

New direct design method for weighted order statistic filters

The paper describes a new method for the design of optimum weighted order statistic (WOS) filters. WOS filters form a general class of increasing filters which generate an output based on the weighted rank ordering of the samples within the filter window. They include the median, weighted median, stack filters and morphological filters with flat structuring elements. This new design method is applicable to all of these operators. It has the advantage over existing techniques in that the filter weights are calculated directly from the training set observations and require no iteration. The method makes an assumption about the training set observations known as the weight monotonic property. It tests if the training set corruption is suitable for correction with an increasing filter. Where the assumption does not hold then a WOS filter should not be used for that training set. The paper includes two examples to demonstrate the design method and a justification for a training set approach to image restoration problems. Other benefits arising from the new design method are outlined in the paper. These include a method to determine the minimum MAE possible for a given training set and filter window.     

On the VLSI implementation of real-time order statistic filters

Real-time implementation of an order-statistic filter (OSF) or ranked order filter requires the computation of the order statistic (ranked order) of the samples in a window which gets periodically updated with the arrival of a new sample(s). The authors give an algorithm for the computation of the running order statistic. A highly parallel architecture suitable for VLSI implementation is presented. The architecture is very versatile, with programmable window size and rank order. An expansion algorithm and its VLSI architecture, which permit the usage of two r-bit OSFs to implement an (r+1)-bit OSF, where r is the resolution of the input signal samples, are given. In a special case where one is satisfied with at most one LSB error, the hardware complexity of the proposed architecture can be reduced by almost one half. It is further shown how a VLSI chip incorporating the proposed architecture can be used as the basic building block in the real-time implementation of other forms of nonlinear filters     

Robust methods for model order estimation

Model order estimation is a subject in time series analysis that deals with fitting a parametric model to a vector of observations. This paper focuses on several model order estimators known in the literature and examines their performance under small deviations of the probability distribution of the noise with respect to a nominal distribution assumed in the model. It is demonstrated that the standard estimators suffer from high sensitivity to deviations from the nominal distribution, and a drastic performance degradation is experienced. To overcome this problem, robust estimators that are insensitive to small deviations from the nominal distribution are developed. These estimators are based on a composition between model order estimation methods and robust statistical inference techniques known in the literature. In addition, a new estimator based on a locally best test for weak signals is presented both in nonrobust and robust versions. The proposed robust model order estimators are developed on a heuristic basis, and there is no claim of optimality, but experimental results indicate that they provide significant improvement over the standard estimators     

A new implementation of generalized order statistic filter bythreshold decomposition

The order statistic (OS) filter of M-level signals has three stages: thresholding, binary filtering, and reconstruction. For binary filtering, the authors use a pipelined sorting network instead of positive Boolean functions, which are very complex for a generalized OS filter. They also develop a fast reconstructor with (2M-2-log ₂M) half adders. Both the computation time and latency time are just four times that of one gate delay. The design is also suitable for VLSI cellular array implementation     

Adaptive multistage weighted order statistic filters based on thebackpropagation algorithm

As a concise representation of stack filters, multistage weighted-order statistic (MWOS) filters are introduced, which correspond to multistage threshold logic gates or multilayer perceptrons in the binary domain. Two adaptive algorithms are derived for finding optimal MWOS filters under the mean absolute error criterion and the mean square error criterion, respectively. Experimental results from image enhancement are provided to compare the performance of adaptive MWOS filters and adaptive stack filters     

基于高阶累积量的盲自适应解相关检测器

基于高阶累积量,本文提出一种新的无约束优化准则,并且证明该优化准则有全局最小值,其及值点满足解相关条件,得到一种新的盲自适应解相关检测器。仿真结果表明,该检测器具有较强的干扰抑制能力。     

Trimmed geometric mean order statistic CFAR detector for Pareto distributed clutter

Recent investigations have validated the Pareto class of models for radar backscattering from the sea surface for X-band maritime surveillance radar. As such, there has been much interest in the derivation of sliding window detectors, for operation in such clutter, with the constant false alarm rate property. A general expression is derived, allowing the determination of the probability of false alarm for such detectors, based upon a recently introduced invariant statistic. For a specific example of its application, a trimmed geometric mean order statistic constant false alarm rate detector is developed and compared with some recently derived detectors. It will be shown that this new detector can be designed to not only manage interference in the clutter range profile but can be very effective at managing range spread targets.     

Robust MMSE receiver employing Hampel-type nonlinear preprocessing for DS-CDMA communication in impulsive noise

A robust minimum mean square error receiver using Hampel-type nonlinear preprocessing is proposed for mitigating both unknown multiple-access interference and impulsive noise. Simulation results are presented to demonstrate the performance of the proposed receiver structure for three distinct nonlinearities in the presence of additive impulsive Gaussian noise.     

Nth order voltage-mode universal filter employing only plus type differential difference current conveyor

Analog Integrated Circuits and Signal Processing - A general topology for realizing nth order voltage-mode universal filter responses with multiple-input and single-output using only plus type...     

A multisensor employing an ultrasonic Lamb-wave oscillator

Initial experimental, analytical, and numerical evaluations of a microsensor that uses ultrasonic Lamb waves propagating in a thin plate supported by a silicon die are presented. Changes of oscillator frequency indicate magnitudes of the variables sensed. Because it is sensitive to many measurands, the device could operate as a microphone, biosensor, chemical vapor or gas detector, scale, pressure sensor, densitometer, radiometer, or thermometer. Because it is based on the use of Lamb waves, the sensor has selective response and sensitive operation in the low-megahertz frequency range in vacuum, in a gas, or while immersed in a liquid     

FDM-channel selection filter employing an arrayed-waveguide gratingmultiplexer

A novel channel selection filter based on an arrayed-waveguide grating multiplexer is reported for optical frequency-division-multiplexer (FDM) networks. The filter employs fold-back optical paths and optical switches, and can be operated digitally with multiple switches. A 16 channel selection filter employing a silica-based 16×16 multiplexer achieves a 20 GHz bandwidth and a crosstalk of less than 27 dB     

A reduced order extended Kalman filter for sequential imagescontaining a moving object

The extended Kalman filter (EKF) is applied to the reduction of noise in sequential images containing a moving object and to the estimation of the object's velocity. A computationally tractable approximation of the EKF, called the parallel extended Kalman filter (PEKF), is generated. The PEKF consists of a parallel bank of third-order EKFs, operating on the Fourier coefficients of the image, followed by a finite impulse response filter. The PEKF is shown to converge to the optimal (in the mean square sense) algorithm in the limit as the velocity estimation errors approach zero. The performance of the PEKF is demonstrated for very low signal-to-noise ratio (SNR) images. The PEKF also provides a natural setting for tracking slow changes in the object (real or apparent) and its velocity, since these variations are included in the model. The relation of the PEKF to another frequency domain algorithm for velocity estimation is discussed. The algorithm is illustrated by application to an example and its performance is demonstrated in the presence of velocity estimation errors.     

基于零阶统计量的韧性归一化自适应时间延迟估计

依据零阶统计量理论,给出对数矩过程、对数宽平稳及对数各态遍历的定义,提出一种韧性的归一化自适应时间延迟估计方法(简称NZOSTDE).该算法用FIR滤波器对两个含有脉冲噪声的观测信号建模,利用不存在有限方差的脉冲信号经过对数变换后其各阶矩的存在性和几何功率的概念,在对数域基于最小均方误差(LMS)准则归一化自适应得到FIR滤波器的系数,该系数最大值对应的序号就是时间延迟的估计值.本文提出的新算法克服了基于分数低阶统计量(FLOS)算法的局限性.计算机仿真实验表明,NZOSTDE算法在强脉冲噪声环境下比归一化最小平均P范数时间延迟估计方法(简称NLMPTDE)算法更具有韧性.     

Bayesian prediction of the jth order statistic with burr distribution and a random sample size

This work is concerned with the Bayesian prediction problem of the j order statistic when the size of the future sample is a random variable and the samples are drawn from a generalized Burr distribution (GBD). A numerical illustration is also given.     

Robust velocity estimates, stream functions, and simulatedLagrangian drifters from sequential spacecraft data

The maximum cross-correlation (MCC) method has been used to compute both oceanic and cloud velocity vectors from sequences of satellite data [e.g., advanced very high resolution radiometer (AVHRR), coastal zone color scanner (CZCS), geostationary observing earth satellite (GOES)]. Unfortunately, the two-dimensional cross-correlation functions used in the computation often contain saddlepoints, which can give rise to large magnitude and direction uncertainties in the derived velocity estimates. This paper develops a numerical iterative procedure that combines image analysis methods and dynamical constraints to minimize these difficulties. The resultant velocities are both physically realistic and numerically stable. Thus, it is also possible to compute stream functions and simulated Lagrangian drifters. The validity of these results are confirmed with independent oceanic observations. Finally, the advective-diffusive equation is solved for a few oceanic applications (e.g., prediction of sea-surface temperature, dispersal of anchovy eggs and larvae) using the derived velocities