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PubMed2004

A method for modeling noise in medical images.

We have developed a method to study the statistical properties of the noise found in various medical images. The method is specifically designed for types of noise with uncorrelated fluctuations. Such signal fluctuations generally originate in the physical processes of imaging rather than in the tissue textures. Various types of noise (e.g., photon, electronics, and quantization) often contribute to degrade medical images; the overall noise is generally assumed to be additive with a zero-mean, constant-variance Gaussian distribution. However, statistical analysis suggests that the noise variance could be better modeled by a nonlinear function of the image intensity depending on external parameters related to the image acquisition protocol. We present a method to extract the relationship between an image intensity and the noise variance and to evaluate the corresponding parameters. The method was applied successfully to magnetic resonance images with different acquisition sequences and to several types of X-ray images.

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PubMed2005

Reduction of noise-induced streak artifacts in X-ray computed tomography through spline-based penalized-likelihood sinogram smoothing.

We present a statistically principled sinogram smoothing approach for X-ray computed tomography (CT) with the intent of reducing noise-induced streak artifacts. These artifacts arise in CT when some subset of the transmission measurements capture relatively few photons because of high attenuation along the measurement lines. Attempts to reduce these artifacts have focused on the use of adaptive filters that strive to tailor the degree of smoothing to the local noise levels in the measurements. While these approaches involve loose consideration of the measurement statistics to determine smoothing levels, they do not explicitly model the statistical distributions of the measurement data. In this paper, we present an explicitly statistical approach to sinogram smoothing in the presence of photon-starved measurements. It is an extension of a nonparametric sinogram smoothing approach using penalized Poisson-likelihood functions that we have previously developed for emission tomography. Because the approach explicitly models the data statistics, it is naturally adaptive--it will smooth more variable measurements more heavily than it does less variable measurements. We find that it significantly reduces streak artifacts and noise levels without comprising image resolution.

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PubMed2006

Local noise weighted filtering for emphysema scoring of low-dose CT images.

Computed tomography (CT) has become the new reference standard for quantification of emphysema. The most popular measure of emphysema derived from CT is the pixel index (PI), which expresses the fraction of the lung volume with abnormally low intensity values. As PI is calculated from a single, fixed threshold on intensity, this measure is strongly influenced by noise. This effect shows up clearly when comparing the PI score of a high-dose scan to the PI score of a low-dose (i.e., noisy) scan of the same subject. In this paper, the noise variance (NOVA) filter is presented: a general framework for (iterative) nonlinear filtering, which uses an estimate of the spatially dependent noise variance in an image. The NOVA filter iteratively estimates the local image noise and filters the image. For the specific purpose of emphysema quantification of low-dose CT images, a dedicated, noniterative NOVA filter is constructed by using prior knowledge of the data to obtain a good estimate of the spatially dependent noise in an image. The performance of the NOVA filter is assessed by comparing characteristics of pairs of high-dose and low-dose scans. The compared characteristics are the PI scores for different thresholds and the size distributions of emphysema bullae. After filtering, the PI scores of high-dose and low-dose images agree to within 2%-3% points. The reproducibility of the high-dose bullae size distribution is also strongly improved. NOVA filtering of a CT image of typically 400 x 512 x 512 voxels takes only a couple of minutes which makes it suitable for routine use in clinical practice.

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PubMed2003

Microarray image enhancement by denoising using stationary wavelet transform.

Microarray imaging is considered an important tool for large scale analysis of gene expression. The accuracy of the gene expression depends on the experiment itself and further image processing. It's well known that the noises introduced during the experiment will greatly affect the accuracy of the gene expression. How to eliminate the effect of the noise constitutes a challenging problem in microarray analysis. Traditionally, statistical methods are used to estimate the noises while the microarray images are being processed. In this paper, we present a new approach to deal with the noise inherent in the microarray image processing procedure. That is, to denoise the image noises before further image processing using stationary wavelet transform (SWT). The time invariant characteristic of SWT is particularly useful in image denoising. The testing result on sample microarray images has shown an enhanced image quality. The results also show that it has a superior performance than conventional discrete wavelet transform and widely used adaptive Wiener filter in this procedure.

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PubMed2005

Neural network learning algorithms for tracking minor subspace in high-dimensional data stream.

A novel random-gradient-based algorithm is developed for online tracking the minor component (MC) associated with the smallest eigenvalue of the autocorrelation matrix of the input vector sequence. The five available learning algorithms for tracking one MC are extended to those for tracking multiple MCs or the minor subspace (MS). In order to overcome the dynamical divergence properties of some available random-gradient-based algorithms, we propose a modification of the Oja-type algorithms, called OJAm, which can work satisfactorily. The averaging differential equation and the energy function associated with the OJAm are given. It is shown that the averaging differential equation will globally asymptotically converge to an invariance set. The corresponding energy or Lyapunov functions exhibit a unique global minimum attained if and only if its state matrices span the MS of the autocorrelation matrix of a vector data stream. The other stationary points are saddle (unstable) points. The globally convergence of OJAm is also studied. The OJAm provides an efficient online learning for tracking the MS. It can track an orthonormal basis of the MS while the other five available algorithms cannot track any orthonormal basis of the MS. The performances of the relative algorithms are shown via computer simulations.

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PubMed2005

Mutation-based genetic neural network.

Evolving gradient-learning artificial neural networks (ANNs) using an evolutionary algorithm (EA) is a popular approach to address the local optima and design problems of ANN. The typical approach is to combine the strength of backpropagation (BP) in weight learning and EA's capability of searching the architecture space. However, the BP's "gradient descent" approach requires a highly computer-intensive operation that relatively restricts the search coverage of EA by compelling it to use a small population size. To address this problem, we utilized mutation-based genetic neural network (MGNN) to replace BP by using the mutation strategy of local adaptation of evolutionary programming (EP) to effect weight learning. The MGNN's mutation enables the network to dynamically evolve its structure and adapt its weights at the same time. Moreover, MGNN's EP-based encoding scheme allows for a flexible and less restricted formulation of the fitness function and makes fitness computation fast and efficient. This makes it feasible to use larger population sizes and allows MGNN to have a relatively wide search coverage of the architecture space. MGNN implements a stopping criterion where overfitness occurrences are monitored through "sliding-windows" to avoid premature learning and overlearning. Statistical analysis of its performance to some well-known classification problems demonstrate its good generalization capability. It also reveals that locally adapting or scheduling the strategy parameters embedded in each individual network may provide a proper balance between the local and global searching capabilities of MGNN.

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PubMed2005

A performance analysis of two approximate adaptive designs.

The performance of function approximator based adaptive control designs may scale badly with approximator dimension. For a simple system class, both projection based designs and multiresolution approximation based designs have been shown to have good scaling properties with respect to to linear quadratic (LQ) costs. Here we show that by considering a cost functional with penalties on the control rate, the multiresolution approximator based design can outperform the projection based design. Generalizations are briefly discussed.

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PubMed2005

From projection pursuit and CART to adaptive discriminant analysis?

While many efforts have been put into the development of nonlinear approximation theory and its applications to signal and image compression, encoding and denoising, there seems to be very few theoretical developments of adaptive discriminant representations in the area of feature extraction, selection and signal classification. In this paper, we try to advocate the idea that such developments and efforts are worthwhile, based on the theorerical study of a data-driven discriminant analysis method on a simple--yet instructive--example. We consider the problem of classifying a signal drawn from a mixture of two classes, using its projections onto low-dimensional subspaces. Unlike the linear discriminant analysis (LDA) strategy, which selects subspaces that do not depend on the observed signal, we consider an adaptive sequential selection of projections, in the spirit of nonlinear approximation and classification and regression trees (CART): at each step, the subspace is enlarged in a direction that maximizes the mutual information with the unknown class. We derive explicit characterizations of this adaptive discriminant analysis (ADA) strategy in two situations. When the two classes are Gaussian with the same covariance matrix but different means, the adaptive subspaces are actually nonadaptive and can be computed with an algorithm similar to orthonormal matching pursuit. When the classes are centered Gaussians with different covariances, the adaptive subspaces are spanned by eigen-vectors of an operator given by the covariance matrices (just as could be predicted by regular LDA), however we prove that the order of observation of the components along these eigen-vectors actually depends on the observed signal. Numerical experiments on synthetic data illustrate how data-dependent features can be used to outperform LDA on a classification task, and we discuss how our results could be applied in practice.

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PubMed2005

Adaptive neural control for a class of nonlinearly parametric time-delay systems.

In this paper, an adaptive neural controller for a class of time-delay nonlinear systems with unknown nonlinearities is proposed. Based on a wavelet neural network (WNN) online approximation model, a state feedback adaptive controller is obtained by constructing a novel integral-type Lyapunov-Krasovskii functional, which also efficiently overcomes the controller singularity problem. It is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed-loop systems. An example is provided to illustrate the application of the approach.

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PubMed2005

Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays.

This paper presents a sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with distributed time delays. The results impose constraint conditions on the network parameters of neural system independently of the delay parameter, and they are applicable to all continuous nonmonotonic neuron activation functions. It is shown that in some special cases of the results, the stability criteria can be easily checked. Some examples are also given to compare the results with the previous results derived in the literature.

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PubMed2005

Zeroing polynomials using modified constrained neural network approach.

This paper proposes new modified constrained learning neural root finders (NRFs) of polynomial constructed by backpropagation network (BPN). The technique is based on the relationships between the roots and the coefficients of polynomial as well as between the root moments and the coefficients of the polynomial. We investigated different resulting constrained learning algorithms (CLAs) based on the variants of the error cost functions (ECFs) in the constrained BPN and derived a new modified CLA (MCLA), and found that the computational complexities of the CLA and the MCLA based on the root-moment method (RMM) are the order of polynomial, and that the MCLA is simpler than the CLA. Further, we also discussed the effects of the different parameters with the CLA and the MCLA on the NRFs. In particular, considering the coefficients of the polynomials involved in practice to possibly be perturbed by noisy sources, thus, we also evaluated and discussed the effects of noises on the two NRFs. Finally, to demonstrate the advantage of our neural approaches over the nonneural ones, a series of simulating experiments are conducted.

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PubMed2005

Survey of clustering algorithms.

Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.

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PubMed2005

Decision feedback recurrent neural equalization with fast convergence rate.

Real-time recurrent learning (RTRL), commonly employed for training a fully connected recurrent neural network (RNN), has a drawback of slow convergence rate. In the light of this deficiency, a decision feedback recurrent neural equalizer (DFRNE) using the RTRL requires long training sequences to achieve good performance. In this paper, extended Kalman filter (EKF) algorithms based on the RTRL for the DFRNE are presented in state-space formulation of the system, in particular for complex-valued signal processing. The main features of global EKF and decoupled EKF algorithms are fast convergence and good tracking performance. Through nonlinear channel equalization, performance of the DFRNE with the EKF algorithms is evaluated and compared with that of the DFRNE with the RTRL.

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PubMed2005

Efficient training algorithms for a class of shunting inhibitory convolutional neural networks.

This article presents some efficient training algorithms, based on first-order, second-order, and conjugate gradient optimization methods, for a class of convolutional neural networks (CoNNs), known as shunting inhibitory convolution neural networks. Furthermore, a new hybrid method is proposed, which is derived from the principles of Quickprop, Rprop, SuperSAB, and least squares (LS). Experimental results show that the new hybrid method can perform as well as the Levenberg-Marquardt (LM) algorithm, but at a much lower computational cost and less memory storage. For comparison sake, the visual pattern recognition task of face/nonface discrimination is chosen as a classification problem to evaluate the performance of the training algorithms. Sixteen training algorithms are implemented for the three different variants of the proposed CoNN architecture: binary-, Toeplitz- and fully connected architectures. All implemented algorithms can train the three network architectures successfully, but their convergence speed vary markedly. In particular, the combination of LS with the new hybrid method and LS with the LM method achieve the best convergence rates in terms of number of training epochs. In addition, the classification accuracies of all three architectures are assessed using ten-fold cross validation. The results show that the binary- and Toeplitz-connected architectures outperform slightly the fully connected architecture: the lowest error rates across all training algorithms are 1.95% for Toeplitz-connected, 2.10% for the binary-connected, and 2.20% for the fully connected network. In general, the modified Broyden-Fletcher-Goldfarb-Shanno (BFGS) methods, the three variants of LM algorithm, and the new hybrid/LS method perform consistently well, achieving error rates of less than 3% averaged across all three architectures.

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PubMed2005

Blind equalization using a predictive radial basis function neural network.

In this paper, we propose a novel blind equalization approach based on radial basis function (RBF) neural networks. By exploiting the short-term predictability of the system input, a RBF neural net is used to predict the inverse filter output. It is shown here that when the prediction error of the RBF neural net is minimized, the coefficients of the inverse system are identical to those of the unknown system. To enhance the identification performance in noisy environments, the improved least square (ILS) method based on the concept of orthogonal distance to red the estimation bias caused by additive measurement noise is proposed here to perform the training. The convergence rate of the ILS learning is analyzed, and the asymptotic mean square error (MSE) of the proposed predictive RBF identification method is derived theoretically. Monte Carlo simulations show that the proposed method is effective for blind system identification. The new blind technique is then applied to two practical applications: equalization of real-life radar sea clutter collected at the east coast of Canada and deconvolution of real speech signals. In both cases, the proposed blind equalization technique is found to perform satisfactory even when the channel effects and measurement noise are strong.

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PubMed2005

Enhanced FMAM based on empirical kernel map.

The existing morphological auto-associative memory models based on the morphological operations, typically including morphological auto-associative memories (auto-MAM) proposed by Ritter et al. and our fuzzy morphological auto-associative memories (auto-FMAM), have many attractive advantages such as unlimited storage capacity, one-shot recall speed and good noise-tolerance to single erosive or dilative noise. However, they suffer from the extreme vulnerability to noise of mixing erosion and dilation, resulting in great degradation on recall performance. To overcome this shortcoming, we focus on FMAM and propose an enhanced FMAM (EFMAM) based on the empirical kernel map. Although it is simple, EFMAM can significantly improve the auto-FMAM with respect to the recognition accuracy under hybrid-noise and computational effort. Experiments conducted on the thumbnail-sized faces (28 x 23 and 14 x 11) scaled from the ORL database show the average accuracies of 92%, 90%, and 88% with 40 classes under 10%, 20%, and 30% randomly generated hybrid-noises, respectively, which are far higher than the auto-FMAM (67%, 46%, 31%) under the same noise levels.

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PubMed2005

A new class of wavelet networks for nonlinear system identification.

A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions.

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PubMed2005

Randomized algorithms for stability and robustness analysis of high-speed communication networks.

This paper initiates a study toward developing and applying randomized algorithms for stability of high-speed communication networks. The focus is on congestion and delay-based flow controllers for sources, which are "utility maximizers" for individual users. First, we introduce a nonlinear algorithm for such source flow controllers, which uses as feedback aggregate congestion and delay information from bottleneck nodes of the network, and depends on a number of parameters, among which are link capacities, user preference for utility, and pricing. We then linearize this nonlinear model around its unique equilibrium point and perform a robustness analysis for a special symmetric case with a single bottleneck node. The "symmetry" here captures the scenario when certain utility and pricing parameters are the same across all active users, for which we derive closed-form necessary and sufficient conditions for stability and robustness under parameter variations. In addition, the ranges of values for the utility and pricing parameters for which stability is guaranteed are computed exactly. These results also admit counterparts for the case when the pricing parameters vary across users, but the utility parameter values are still the same. In the general nonsymmetric case, when closed-form derivation is not possible, we construct specific randomized algorithms which provide a probabilistic estimate of the local stability of the network. In particular, we use Monte Carlo as well as quasi-Monte Carlo techniques for the linearized model. The results obtained provide a complete analysis of congestion control algorithms for internet style networks with a single bottleneck node as well as for networks with general random topologies.

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