Statistical Signal Model Research Articles

Deep Sparse Representation Based Image Restoration With Denoising Prior

As a powerful statistical signal modeling technique, sparse representation has been widely used in various image restoration (IR) applications. The sparsity-based methods have achieved leading performance in the past few decades. However, in recent years it has been surpassed by other methods, especially the recent deep learning based methods. In this paper, we address the question that whether sparse representation can be competitive again. The way we answer this question is to redesign it with a deep architecture. To be specific, we propose an end-to-end deep architecture that follows the process of the sparse representation based IR. In particular, we learn a sparse convolutional dictionary to replace the traditional dictionary, and a convolutional neural network (CNN) denoising prior to replace the image prior. Through end-to-end training, the parameters in convolutional dictionary and CNN denoiser can be jointly optimized. Experimental results on several representative IR tasks, including image denoising, deblurring and super-resolution, demonstrate that the proposed deep network can achieve superior performance against state-of-the-art model-based and learning-based methods.

Saturating Receiver and Receptor Competition in Synaptic DMC: Deterministic and Statistical Signal Models.

Synaptic communication is based on a biological Molecular Communication (MC) system which may serve as a blueprint for the design of synthetic MC systems. However, the physical modeling of synaptic MC is complicated by the possible saturation of the molecular receiver caused by the competition of neurotransmitters (NTs) for postsynaptic receptors. Receiver saturation renders the system behavior nonlinear in the number of released NTs and is commonly neglected in existing analytical models. Furthermore, due to the ligands' competition for receptors (and vice versa), the individual binding events at the molecular receiver are in general not statistically independent and the commonly used binomial model for the statistics of the received signal does not apply. Hence, in this work, we propose a novel deterministic model for receptor saturation in terms of a state-space description based on an eigenfunction expansion of Fick's diffusion equation. The presented solution is numerically stable and computationally efficient. Employing the proposed deterministic model, we show that saturation at the molecular receiver effectively reduces the peak-value of the expected received signal and accelerates the clearance of NTs as compared to the case when receptor occupancy is neglected. We further derive a statistical model for the received signal in terms of the hypergeometric distribution which accounts for the competition of NTs for receptors and the competition of receptors for NTs. The proposed statistical model reveals how the signal statistics are shaped by the number of released NTs, the number of receptors, and the binding kinetics of the receptors, respectively, in the presence of competition. In particular, we show that the impact of these parameters on the signal variance is qualitatively different depending on the relative numbers of NTs and receptors. Finally, the accuracy of the proposed deterministic and statistical models is verified by particle-based computer simulations.

Statistical Modeling and Bit Error Rate Analysis for Bio-Sensor Receivers in Molecular Communication

The behavior of bio-sensor receivers is studied for molecular communication (MC). Bacteria can be engineered as a bio-sensor receiver to produce an output signal, e.g., produce green fluorescent protein, with respect to an external concentration pulse (MC signal). The signal transduction of bacteria, i.e., bacteria response, can be used to detect the pulse-amplitude modulated MC signals. In this work, a statistical model for the bacteria-based bio-sensor receivers is developed. Statistical signal models are useful to evaluate the reliability of the communication systems. The bacteria response is modeled by approximating a first-order model of signal transduction in the linear ramp-up region. The bacteria response is found to be a function of the response rate (linear ramp-up slope) and the time. Bacterial signal transduction is inherently noisy due to the cascades of biochemical reactions to produce the output signal. Therefore, the first-order model is extended incorporating the noise in both the rate and the timing (random delay) of the bacteria response. The bit error rate performance is studied to reveal the impact of the timing noise against the response rate noise. The developed statistical signal model can aid performance evaluation of bacteria-based bio-sensor receivers in MC and biological sensing.

Wavelet-based Image Modelling for Compression Using Hidden Markov Model

Statistical signal modeling using hidden Markov model is one of the techniques used for image compression. Wavelet based statistical signal models are impractical for most of the real time processing because they usually represent the wavelet coefficients as jointly Gaussian or independent to each other. In this paper, we build up an algorithm that succinctly characterizes the interdependencies of wavelet coefficients and their Non-Gaussian behavior especially for image compression. This is done by extracting the combine feature of hidden Markov model and Wavelet transformation that gives us comparatively better results. To estimate the parameter of wavelet based Hidden Markov model, an efficient expectation maximization algorithm is developed.

Network-Layer Performance Analysis of Multihop Fading Channels

A fundamental problem for the delay and backlog analysis across multihop paths in wireless networks is how to account for the random properties of the wireless channel. Since the usual statistical models for radio signals in a propagation environment do not lend themselves easily to a description of the available service rate, the performance analysis of wireless networks has resorted to higher-layer abstractions, e.g., using Markov chain models. In this paper, we propose a network calculus that can incorporate common statistical models of fading channels and obtain statistical bounds on delay and backlog across multiple nodes. We conduct the analysis in a transfer domain, where the service process at a link is characterized by the instantaneous signal-to-noise ratio at the receiver. We discover that, in the transfer domain, the network model is governed by a dioid algebra, which we refer to as the (min, ×) algebra. Using this algebra, we derive the desired delay and backlog bounds. Using arguments from large deviations theory, we show that the bounds are asymptotically tight. An application of the analysis is demonstrated for a multihop network of Rayleigh fading channels with cross traffic at each hop.

Online Energy Estimation of Relational Operations in Database Systems

Data centers are well known to consume a large amount of energy. As databases are one of the major applications in a data center, building energy-aware database systems has become an active research topic recently. The quantification of the energy cost of database systems is an important task in design. In this paper, we report our recent efforts on this issue, with a focus on the energy cost estimation of query plans during query optimization. We start from building a series of physical models for energy estimation of individual relational operators based on their resource consumption patterns. As the execution of a query plan is a combination of multiple relational operators, we use the physical models as a basis for a comprehensive energy model for the entire query. To address the challenge of maintaining accuracy under system and workload dynamics, we develop an online scheme that dynamically adjusts model parameters based on statistical signal modeling. Our models are implemented in a real database management system and evaluated on a physical test bed. The results show that our solution achieves a high accuracy (worst-case error 13.7 percent) despite noises. Our models also help identify query plans with significantly higher energy efficiency.

Segmentation of B-mode cardiac ultrasound data by Bayesian Probability Maps.

In this paper we present a model for describing the position distribution of the endocardium in the two-chamber apical long-axis view of the heart in clinical B-mode ultrasound cycles. We propose a novel Bayesian formulation, including priors for spatial and temporal smoothness, and preferred shapes and position. The shape model takes into account both endocardium, atrial region and apex. The likelihood is built using a statistical signal model, which attempts to closely model a censored signal. In addition, the use of a censored Gamma mixture model with unknown censoring point, to handle artefacts resulting from left-censoring of the in US clinical B-mode, is to our knowledge novel. The posterior density is sampled by the Gibbs method to estimate the expected latent variable representation of the endocardium, which we call the Bayesian Probability Map; the map describes the probability of pixels being classified as being within the endocardium. The regularization parameters of the model are estimated by cross-validation, and the results are compared against the two-chamber apical model of Chen et al.

A Nonlocal Weighted Joint Sparse Representation Classification Method for Hyperspectral Imagery

As a powerful and promising statistical signal modeling technique, sparse representation has been widely used in various image processing and analysis fields. For hyperspectral image classification, previous studies have shown the effectiveness of the sparsity-based classification methods. In this paper, we propose a nonlocal weighted joint sparse representation classification (NLW-JSRC) method to improve the hyperspectral image classification result. In the joint sparsity model (JSM), different weights are utilized for different neighboring pixels around the central test pixel. The weight of one specific neighboring pixel is determined by the structural similarity between the neighboring pixel and the central test pixel, which is referred to as a nonlocal weighting scheme. In this paper, the simultaneous orthogonal matching pursuit technique is used to solve the nonlocal weighted joint sparsity model (NLW-JSM). The proposed classification algorithm was tested on three hyperspectral images. The experimental results suggest that the proposed algorithm performs better than the other sparsity-based algorithms and the classical support vector machine hyperspectral classifier.

Genetic algorithm optimized distribution sampling test for M-QAM modulation classification

With the classification performance and computational complexity in mind, we propose a new optimized distribution sampling test (ODST) classifier for automatic classification of M-QAM signals. In ODST, signal cumulative distributions are sampled at pre-established locations. The actual sampling process is transformed into simple counting task for reduced computational complexity. The optimization of sampling locations is based on theoretical signal models derived under various channel conditions. Genetic Algorithm (GA) is employed to optimize distance metrics using sampled distribution parameters for distribution test between signals. The final decision is made based on distances between tested signal and candidate modulations. By using multiple sampling locations on signal cumulative distributions, the classifier's robustness is enhanced for possible signal statistical variance or signal model mismatching. AWGN channel, phase offset, and frequency offset are considered to evaluate the performance of the proposed algorithm. Experimental results show that the proposed method has advantages in both classification accuracy and computational complexity over most existing classifiers.

Random Signals and Systems (Pincibono, B.; 2003) [Book reviews

This excellent book answers the need for proper modeling methodologies in order to advance our structural knowledge of the human brain. Some of the topics covered include: random signals and probability; multidimensional random variables; spectral properties of random signals; statistical models for random signals; Poisson processes and affiliated signals; random signals and dynamic systems; mean square estimation for stationary signals; prediction for stationary signals; time recursive methods; and matched filters. Suitable problems are set out at the end of each chapters. The audience of this volume should consist of researchers in computational intelligence, biomedical signal processing, and artificial neural networks, engineers, professionals, and academics.

An Approach for Solving the Permutation Problem of Convolutive Blind Source Separation Based on Statistical Signal Models

In this paper, we present a new algorithm for solving the permutation ambiguity in convolutive blind source separation. Transformed to the frequency domain, existing algorithms can efficiently solve the reduction of the source separation problem into independent instantaneous separation in each frequency bin. However, this independency leads to the problem of correctly aligning these single bins. The new algorithm models the frequency-domain separated signals by means of the generalized Gaussian distribution and employs the small deviation of the parameters between neighboring bins for the detection of correct permutations. The performance of the algorithm will be demonstrated on synthetic and real-world data.

Parametric Velocity Synthetic Aperture Radar: Multilook Processing and Its Applications

Based on a parametric model and some optimum methods, it has been previously proved that parametric velocity synthetic aperture radar (VSAR) may improve the performances of moving target detection and parameter estimation simultaneously. In this paper, multilook processing is studied for parametric VSAR. At first, statistical signal models are established for azimuth multilook processing (AMLP) and range multilook processing (RMLP), respectively. By combining the multiple AMLP sublook pixel vectors, it is shown that the clutter parameter estimation accuracy can be further improved via the maximum-likelihood estimation methods. Meanwhile, based on the adaptive implementation for the optimum processing of VSAR, RMLP can be used to improve slowly moving target detection performance via the noncoherent integration of multiple range sublooks. Furthermore, it is shown that the Doppler frequencies of moving targets vary linearly with different range sublooks due to the different carrier frequencies of sublooks. Therefore, based on a proposed novel two-step multilook diversity (TS-MLD) estimator for RMLP, the "azimuth location ambiguity" of VSAR can be well resolved via least squares linear regression, without configuration change of the conventional VSAR. Also, the estimation accuracy of target's unambiguous Doppler frequency, as well as target's azimuth location, is derived for the proposed TS-MLD method. Finally, numerical experiments and scene simulations are provided to demonstrate the effectiveness of the proposed multilook-based methods.

Stimulus design for auditory neuroethology using state space modeling and the extended Kalman smoother

A new method for designing vocalization based stimuli for experiments in auditory neurophysiology is described. This analysis-synthesis technique leverages a state space statistical signal model and the extended Kalman smoother for tracking the frequency, amplitude, and phase information of harmonically related components in recorded vocalizations. Using the same state space model, these parameters can then be used to synthesize the vocalizations and random or deterministic variants of the vocalizations. This method is shown to outperform short-time Fourier transform based frequency tracking methods in both noisy and noise-free synthetic test signals. It is further shown to accurately track recorded hummingbird, human, and bat vocalizations while removing recording artifacts such as noise, echo, and digital aliasing in the synthesis phase.

Collaborative Localization With Received-Signal Strength in Wireless Sensor Networks

In this paper, we present an in-depth study of two collaborative-localization methods, called the multidimensional scaling (MDS) and maximum-likelihood estimator (MLE), for wireless sensor networks. From theoretical analysis, it is shown that MLE is more appropriate than MDS, given the underlying assumption of statistical signal models of the received-signal-strength-based localization problem. We also show that MDS can approximately achieve asymptotic efficiency with appropriate weighting schemes in some scenarios. From extensive simulation results, it is noted that the nonlinear least square algorithms that are commonly used to determine MLE are not as efficient as the iterative MDS algorithms. Thus, we propose a new integrated method MDS-MLE to effectively benefit from the strength of both methods. In the new method, MDS is used as an initialization method for MLE. With the solution of MDS as an initial value, MLE converges much faster and achieves significantly better performance than with random initial values. Superior performance of the new method is clearly demonstrated through simulation results. The effects of the deployment density of sensor nodes and reference nodes (RNs), as well as the deployment structure of RNs, are also studied through various simulations.

Adaptive regularization network based neural modeling paradigm for nonlinear adaptive estimation of cerebral evoked potentials

In this paper we report an adaptive regularization network (ARN) approach to realizing fast blind separation of cerebral evoked potentials (EPs) from background electroencephalogram (EEG) activity with no need to make any explicit assumption on the statistical (or deterministic) signal model. The ARNs are proposed to construct nonlinear EEG and EP signal models. A novel adaptive regularization training (ART) algorithm is proposed to improve the generalization performance of the ARN. Two adaptive neural modeling methods based on the ARN are developed and their implementation and performance analysis are also presented. The computer experiments using simulated and measured visual evoked potential (VEP) data have shown that the proposed ARN modeling paradigm yields computationally efficient and more accurate VEP signal estimation owing to its intrinsic model-free and nonlinear processing characteristics.

On‐line reliability estimation for individual components using statistical degradation signal models

AbstractWith very few exceptions, most contemporary reliability engineering methods are geared towards estimating a population characteristic(s) of a system, subsystem or component. The information so extracted is extremely valuable for manufacturers and others that deal with product in relatively large volumes. In contrast, end users are typically more interested in the behavior of a ‘particular’ component used in their system to arrive at optimal component replacement or maintenance strategies leading to improved system utilization, while reducing risk and maintenance costs. The traditional approach to addressing this need is to monitor the component through degradation signals and ‘classifying’ the state of a component into discrete classes, say ‘good’, ‘bad’ and ‘in‐between’ categories. In the event, one can develop effective degradation signal forecasting models and precisely define component failure in the degradation signal space, then, one can move beyond the classification approach to a more vigorous reliability estimation and forecasting scheme for the individual unit. This paper demonstrates the feasibility of such an approach using ‘general’ polynomial regression models for degradation signal modeling. The proposed methods allow first‐order autocorrelation in the residuals as well as weighted regression. Parametric bootstrap techniques are used for calculating confidence intervals for the estimated reliability. The proposed method is evaluated on a cutting tool monitoring problem. In particular, the method is used to monitor high‐speed steel drill‐bits used for drilling holes in stainless‐steel metal plates. A second study involves modeling and forecasting fatigue‐crack‐growth data from the literature. The task involved estimating and forecasting the reliability of plates expected to fail due to fatigue‐crack‐growth. Both studies reveal very promising results. Copyright © 2002 John Wiley & Sons, Ltd.

Information-theoretic comparisons of cellular multiple-access systems with bandwidth-dependent fading considerations

The coding performances of generic DS-CDMA, FDMA and hybrid F/TDMA systems with equivalent operating conditions are analysed and compared based on two information-theoretic performance measures, namely, channel capacity and probability of codeword decoding error. Statistical signal models for the different systems are developed, which, among other practical considerations, incorporate the effects of multicell operation, raised-cosine bandlimiting and multipath fading statistics which vary with the signalling bandwidth used. The results obtained provide insights into some fundamental mechanisms which contribute to the relative spectral efficiency among different multiple-access systems.

Seismic threshold monitoring for continuous assessment of global detection capability

AbstractContinuous seismic threshold monitoring is a technique that has been developed over the past several years to assess the upper magnitude limit of possible seismic events that might have occurred in a geographical target area. The method provides continuous time monitoring at a given confidence level. In this article we expand upon previous work to apply the method to a global network of seismic stations and give examples of applications from a prototype system that will be installed at the International Data Center for monitoring the Comprehensive Nuclear Test Ban Treaty.Using a global grid of 2562 geographical aiming points, we computed site-specific threshold traces for each grid point and applied spatial interpolation to obtain full global coverage. For each grid point, the procedure is in principle to “focus” the network by tuning the frequency filters and array beams using available information on signal and noise characteristics at each station-site combination. Standard global P-phase attenuation relationships and travel-time tables (IASP91) are used in this initial implementation, but the system lends itself easily to applying station-site-specific corrections (magnitudes, travel times, etc.) to each seismic phase.We give examples of two main types of applications based on data from a worldwide seismic network: (a) an estimated continuous global threshold level and (b) an estimated continuous global detection capability. The first application provides a continuous view of the global seismic “background field” as calculated from the station data, with the purpose of assessing the upper magnitude limit of any seismic event that might have occurred anywhere on Earth. The second application introduces detection thresholds for each station and provides a simplified estimate, continuously in time, of the n-station detection capability of the network. The latter approach naturally produces higher threshold values, with the difference typically being 0.5-1 magnitude unit. We show that both these approaches are useful especially during large earthquakes, where conventional capability maps based on statistical noise and signal models cannot be applied.In order to illustrate the usefulness of combining global monitoring with site-specific monitoring for areas of special interest, we consider a large earthquake aftershock sequence in Kamchatka and its effect on the threshold trace in a very different region (the Novaya Zemlya nuclear test site). We demonstrate that the effects of the aftershock signals on the thresholds calculated for Novaya Zemlya are modest, partly because of the emphasis on high-frequency signals. This indicates that threshold monitoring could provide significantly improved seismic monitoring during aftershock sequences compared with conventional methods, for which the large number of detected phases tends to saturate the phase association process.

Vectorcardiographic loop alignment and morphologic beat-to-beat variability.

The measurement of subtle morphologic beat-to-beat variations in the electrocardiogram is complicated by the presence of respiration-induced movements of the heart. A statistical signal model is developed which accounts for such movements by means of scaling, rotation, and time synchronization of vectorcardiographic loops. The maximum-likelihood estimator of the parameters describing these three transformations is presented and is extended to the case of multiple loop alignment. The performance of the method is assessed by measuring morphologic variability before and after loop alignment. It is shown that the effects of respiration on morphologic variability can be considerably reduced by the new method. Measurements on morphologic variability were typically reduced by a factor of 0.53 after loop alignment. The results show also that beat-to-beat measurements are strongly dependent on the selected sampling rate and that a rate of 1 kHz is too low.

Multichannel blind identification: from subspace to maximum likelihood methods

A review of blind channel estimation algorithms is presented. From the (second-order) moment-based methods to the maximum likelihood approaches, under both statistical and deterministic signal models. We outline basic ideas behind several new developments, the assumptions and identifiability conditions required by these approaches, and the algorithm characteristics and their performance. This review serves as an introductory reference for this currently active research area.