Weighted Order Statistic Research Articles

An Energy-Saving Data Statistics-Driven Management Technique for Bio-Powered Indoor Wireless Sensor Nodes

Wireless sensor networks (WSNs) are technologies that play an important role in Internet of Things (IoT) systems. In most applications, sensor nodes are expected to operate for extended periods without maintenance. Therefore, minimizing power consumption and self-sustainability based on energy harvesting (EH) still represent important research challenges. In this article, a power management strategy (PMS) based on the weighted order statistics (WOS) classification technique is proposed to dynamically adapt the duty cycle of the sensor node according to historical data measurements. Unnecessary acquisition and transmission of slow-varying signals are reduced, improving the power consumption of the node. As traditional renewable sources (sunlight, wind, and vibration) are scarce in indoor scenarios, an array of Dypsis Lutescens plants is used as a power bioenergy cell, providing a clean and cost-effective alternative to power indoor sensor nodes. The WOS technique is programmed into an nRF52840 microcontroller, and an ultralow-power BQ25570 harvesting circuit harnesses the energy from the array of plants. Experimental results include the energy performance analysis of the wireless sensor node and the measured power generation capacity of the bioenergy source, showing an energy-autonomous behavior for IoT applications. Average power consumption of 15.6 mW per transmitted data packet of 14 bytes is achieved, which represents the ability to perform at least 693 data transmissions per day considering an 8 F supercapacitor as a storage device.

Intelligent Classification of Large-Scale Remotely Sensed Hyperspectral Images using Multi-GPU Computing

Image classification is one of the most popular tasks used to analyze remote sensing signatures (RSS) of a geographical region from remotely sensed hyperspectral images. However, the high dimensionality of such hyperspectral images raises a series of new challenges. In this paper, a new approach for real-time intelligent classification of large-scale hyperspectral imagery which aggregates Fuzzy logic and the fused weighted order statistic (WOS) with the minimum distance to mean (MDM) techniques using commodity graphics processing units (GPUs) is addressed. Within this context, intelligent image processing methods are algorithmically adapted via parallel computing techniques and efficiently implemented in two NVIDIA Tesla C2075 GPUs. Experimental results demonstrate how such unification reduces drastically the computational load of the real-world hyperspectral classification tasks resulting in efficient numerical algorithms suitable for real-time multi-GPU-adapted implementation.

On extremal behavior of aggregation of largest claims

ABSTRACTIn this paper some dependent risks are considered, and tail asymptotic probabilities for linear combinations of finite number or random number of randomly weighted order statistics are estimated under various assumptions, where the primary random variables have long and dominatedly varying tails. Our findings are highly motivated by the need of the investigation of extremal behavior of aggregation of large claims, which has been shown in Asimit et al. (2012).

Aggregation of randomly weighted large risks

Asymptotic tail probabilities for linear combinations of randomly weighted order statistics are approximated under various assumptions. One key assumption is the asymptotic independence for all risks. Therefore, it is not surprising that the maxima represents the most influential factor when one investigates the tail behaviour of our considered risk aggregation, which, for example, can be found in the reinsurance market. This extreme behaviour confirms the ‘one big jump’ property that has been vastly discussed in the existing literature in various forms whenever asymptotic independence is present. An illustration of our results together with a specific application are explored under the assumption that the underlying risks follow the multivariate log-normal distribution.

Exact Tail Asymptotics of the Total Loss of Largest Claim Reinsurance Treaties

Asymptotic tail probabilities for linear combinations of randomly weighted order statistics are approximated under various assumptions. One key assumption is the asymptotic independence for all risks. Therefore, it is not surprising that the maxima represents the most influential factor when investigates the tail behaviour of our considered risk aggregation, which for example, can be found in the reinsurance market. This extreme behaviour confirms the one big jump property that has been vastly discussed in the existing literature in various forms whenever the asymptotic independence is present. An illustration of our results together with a specific application are explored under the assumption that the underlying risks follow the multivariate Log-normal distribution.

The Generalization of WOSF and Corresponding Outputs

Weighted order statistic filters (WOSF) generate linearly separable Boolean functions. In some cases, 2 different WOSF may generate the same Boolean function. We thus can collect all of the WOSF together, which generate the same Boolean function. In this paper, we construct equivalent classes of WOSF, the BF equivalent class and the global equivalent class. Besides, we use minimum weight vectors as base vectors to build all global classes of same order and characterize WOSF to generalize three properties of global classes. Finally, we propose 3 translated formulas to fast generate corresponding outputs of BF equivalent classes, not perform extra machine training or mathematical computation.

Some aspects of estimating the detection rate of a periodic signal in noisy data and the time position of its components

Processing and analysis of periodic signals (including noisy ones) are considered to estimate the time position of the corresponding components including the case of frequency modulation. It is proposed to employ four steps of signal processing and analysis: weighted order statistic (WOS) filters in order to enhance the quality of both the signal itself and its components of special interest; dispersion estimation on a certain sliding basis; analysis of such an estimate as a two-dimensional black-and-white image in order to list the connected sets of nonempty clusters; and, finally, behavior analysis of cluster families in order to calculate the necessary estimates. A method is considered for the recognition of characteristic features of cluster families, and on its basis a technique is suggested for estimating the initial time for a signal to come into existence (the moment of the arrival of a wave). We give the results of processing and analysis of practical data obtained during a field trip as a part of active geophysical monitoring.

Extractive Support Vector Algorithm on Support Vector Machines for Image Restoration

The major problem of SVMs is the dependence of the nonlinear separating surface on the entire dataset which creates unwieldy storage problems. This paper proposes a novel design algorithm, called the extractive support vector algorithm, which provides improved learning speed and a vastly improved performance. Instead of learning and training with all input patterns, the proposed algorithm selects support vectors from the input patterns and uses these support vectors as the training patterns. Experimental results reveal that our proposed algorithmprovides near optimal solutions and outperforms the existing design algorithms. In addition, a significant framework which is based on extractive support vector algorithm is proposed for image restoration. In the framework, input patterns are classified by three filters: weighted order statistics filter, alpha-trimmed mean filter and identity filter. Our proposed filter can achieve three objectives: noise attenuation, chromaticity retention, and preservation of edges and details. Extensive simulation results illustrate that our proposed filter not only achieves these three objectives but also possesses robust and adaptive capabilities, and outperforms other proposed filtering techniques.

Some issues in improving quality of noisy periodic signals and estimating their parameters and characteristics numerically by using a cluster approach: Problem statement

In this paper, a technique is proposed to process and analyze noisy periodic signals recorded at discrete moments of time. The technique includes two stages: (a) signal quality improvement (processing) with the use of weighted order statistics filters, and (b) cluster analysis of processing results. Basic definitions and specific features of this type of filtration are given, as well as formulations and definitions of cluster analysis, which enable problems to be stated for periodic signal analysis. The efficiency of cluster analysis with weighted order statistics filters is proved based on results of numerical modeling of a noisy frequency-modulated signal.

Dichotomous Learning Algorithm for the Optimal Design of Weighted Order Statistics Filters

Weighted order statistics (WOS) filters are highly effective, in processing digital signals, due to their simple window structure. This paper proposes a fast and efficient learning algorithm that both improves learning speed and reduces the complexity of designing WOS filters. The algorithm uses a dichotomous approach to reduce the Boolean functions from 255 levels to two levels which are separated by an optimal hyperplane. The design concept of this algorithm is similar to that of support vector machines (SVMs), which use two separate sets of data to determine the optimal hyperplane. A conjugate gradient algorithm is adopted, to solve the orthant-constrained optimum problem, in order to improve memory storage for the large amounts of data required in the design process. Prior literature includes three different schemes for learning: one approach updates the parameters via pattern-mode learning, while the others involve batch-mode learning and semi-batch mode learning. Our proposed method approximates the optimal weighted order statistics filters far more rapidly than either Yoo's algorithm or adaptive neural filters.

Weighted order statistic and fuzzy rules CFAR detector for Weibull clutter

Order statistic (OS) CFAR processor is a powerful detector, but similar to many other CFAR detectors, suffers from clutter edge as well as interfering targets. To overcome these problems, two derivations of this detector have been developed. These are order statistic greatest of (OSGO) and order statistic smallest of (OSSO) CFAR processors. The cost, paid for this improvement, is a considerable decrease in detection probability for homogenous Weibull clutter. Furthermore, a substantial performance degradation of OSGO in interfering target (high target masking effect) and an excessive false alarm of OSSO in clutter edge, also, occur. This behavior is a result of non-soft rules used in these two detectors. This paper proposes a weighted order statistic and fuzzy rules-CFAR detector, which employs some soft rules based on fuzzy logic to cure the mentioned problems. Our simulation results demonstrate that considering realistic Weibull clutter, the proposed detector gives better detection probability than that of OSGO and OSSO detectors. Moreover, considering the problems of clutter edge and interfering target, the performance of the method is comparable to the best performance of the OSGO and OSSO detectors in different conditions.

Optimal Distributed Detection in Clustered Wireless Sensor Networks

In a clustered, multihop sensor network, a large number of inexpensive, geographically-distributed sensor nodes each use their observations of the environment to make local hard decisions about whether an event has occurred. Each node then transmits its local decision over one or more wireless hops to the clusterhead (CH). When all local decisions have been gathered by the CH, it fuses them into a final hard decision about the event. Two sources of error affect the CH's final decision: 1) local decision errors made by the sensor nodes because of noisy measurements or unreliable sensors and 2) bit errors affecting each hop on the wireless communication channel. We show that if both of these sources of error are considered, then the optimal decision at the CH is obtained by thresholding a weighted sum of the nodes' local decisions or, equivalently, computing a weighted order statistic of these decisions. The optimal weights are shown to be functions of the bit error probability of the channel and the ring from which the local decision originated. We determine the error probability of this optimal fusion algorithm, the effect of adding more nodes or rings to the cluster, and the tradeoffs involving the energy consumed in the network, the decision error probability, and the time to reach a decision. This paper thus provides tools to determine the effect of measurement and communication errors on other tradeoffs in the design of clustered sensor networks.

The Optimal Design of Weighted Order Statistics Filters by Using Support Vector Machines

Support vector machines (SVMs), a classification algorithm for the machine learning community, have been shown to provide higher performance than traditional learning machines. In this paper, the technique of SVMs is introduced into the design of weighted order statistics (WOS) filters. WOS filters are highly effective, in processing digital signals, because they have a simple window structure. However, due to threshold decomposition and stacking property, the development of WOS filters cannot significantly improve both the design complexity and estimation error. This paper proposes a new designing technique which can improve the learning speed and reduce the complexity of designing WOS filters. This technique uses a dichotomous approach to reduce the Boolean functions from 255 levels to two levels, which are separated by an optimal hyperplane, Furthermore, the optimal hyperplane is gotten by using the technique of SVMs. our proposed method approximates the optimal weighted order statistics filters more rapidly than the adaptive neural filters.

Co-Phased Median Filters, Some Peculiarities of Sweep Signal Processing

Median filters are nonlinear and a theoretical analysis of their behavior is very difficult and so are rarely used for the processing of seismic data. However, they are able to preserve steps, sharp discontinuities and edges that are lost using most other standard filters. As seismic data are mostly harmonic or frequency modulated signals in the frequency range 1 to 10 Hz, the median filter must be adapted so as to suppress noise but not unduly distort the signal. This can be accomplished by using a median filter whose length is n times that of signal period where n is even. By use of weighted-order statistics, samples of the signals closest in phase can be obtained. To illustrate the method, a signal from a frequency band of 6.3–7.5 Hz was processed and the quality of the signal enhanced two fold over the quality of the signal without processing.

A Practical Parallel Architecture for Stacks Filters

Stack filters belong to the class of non-linear filters and include the well-known median filter, weighted median filters, order statistic filters and weighted order statistic filters. Any stack filter can be implemented by using the parallel threshold decomposition architecture which allows implementing their non-linear processing by means of a collection of identical binary filters (Boolean logic circuits). Although it is conceptually simple and useful to study the filter properties, this architecture is not practical for direct hardware implementation because as many as (M ? 1) binary filters are required for a M-valued input signal and M is large in many applications. In this paper we introduce a new parallel architecture for stack filter implementations. The complexity is now proportional to the window width L of the filter, instead of to M. In most applications L is much smaller than M which translates into efficient hardware implementations. The attractive characteristic of ease of design exhibited by the threshold decomposition architecture is kept. In fact, for a given stack filter both in the conventional implementation and in the proposed one, the same binary filter is required. The key concept supporting the new architecture is a modified decomposition scheme which generates L binary signals for a multi-valued input. As an application example, a complex WOS filter is designed and prototyped in an FPGA.

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.

Weighted order statistics filter for real-time signal processing applications based on pass transistor logic

The authors describe the rationale of the design of complex weighted order statistics filters (WOS filters) suitable for real-time signal processing applications. It is based on a simple stack-like architecture that decomposes the M-valued signals into a reduced number of binary signals which are filtered by identical boolean logic circuits (binary filters). The main distinguishing feature of the proposed procedure is the efficient implementation of both the decomposition stage and the binary filters. The former is achieved on the basis of introducing a new decomposition scheme which can be economically translated to hardware. The latter comes from realising that the binary filters required for WOS filtering are threshold functions and from the development of a systematic methodology for building pass-transistor networks that implement them. Results for a complex example filter show a sample frequency of over 175 MHz in a 0.35 μm MOS technology at 3.3 V.

0.8 μm cmos implementation of weighted-order statistic image filter based on cellular neural network architecture

In this paper, a very large scale integration chip of an analog image weighted-order statistic (WOS) filter based on cellular neural network (CNN) architecture for real-time applications is described. The chip has been implemented in CMOS AMS 0.8 /spl mu/m technology. CNN-based filter consists of feedforward nonlinear template B operating within the window of 3 /spl times/ 3 pixels around the central pixel being filtered. The feedforward nonlinear CNN coefficients have been realized using programmable nonlinear coupler circuits. The WOS filter chip allows for processing of images with 300 pixels horizontal resolution. The resolution can be increased by cascading of the chips. Experimental results of basic circuit building blocks measurements are presented. Functional tests of the chip have been performed using a special test setup for PAL composite video signal processing. Using the setup real images have been filtered by WOS filter chip under test.

An examination of decomposition sparsity

Sparsity of transform domain coefficients is a critical requirement for algorithms employing wavelet transforms to pre-process signals or images. This paper examines a measure of transform domain sparsity which provides a means of comparing wavelet and subband decomposition performance. The transforms of one-dimensional signals and two-dimensional images are considered using 110 different wavelets and nonlinear subband decomposition filters, including weighted order statistics and functions of weighted order statistics. These measurements indicate that nonlinear subband decompositions employing median filters or central order statistics can produce sparser decompositions than wavelets for certain classes of signals and images.

A neural learning approach for adaptive image restoration using a fuzzy model-based network architecture

We address the problem of adaptive regularization in image restoration by adopting a neural-network learning approach. Instead of explicitly specifying the local regularization parameter values, they are regarded as network weights which are then modified through the supply of appropriate training examples. The desired response of the network is in the form of a gray level value estimate of the current pixel using weighted order statistic (WOS) filter. However, instead of replacing the previous value with this estimate, this is used to modify the network weights, or equivalently, the regularization parameters such that the restored gray level value produced by the network is closer to this desired response. In this way, the single WOS estimation scheme can allow appropriate parameter values to emerge under different noise conditions, rather than requiring their explicit selection in each occasion. In addition, we also consider the separate regularization of edges and textures due to their different noise masking capabilities. This in turn requires discriminating between these two feature types. Due to the inability of conventional local variance measures to distinguish these two high variance features, we propose the new edge-texture characterization (ETC) measure which performs this discrimination based on a scalar value only. This is then incorporated into a fuzzified form of the previous neural network which determines the degree of membership of each high variance pixel in two fuzzy sets, the EDGE and TEXTURE fuzzy sets, from the local ETC value, and then evaluates the appropriate regularization parameter by appropriately combining these two membership function values.