On three intelligent systems: dynamic neural,fuzzy, and wavelet networks for training trajectory

Intelligent systems cover a wide range of technologies related to hard sciences, such as modeling and control theory, and soft sciences, such as the artificial intelligence (AI). Intelligent systems, including neural networks (NNs), fuzzy logic (FL), and wavelet techniques, utilize the concepts of biological systems and human cognitive capabilities. These three systems have been recognized as a robust and attractive alternative to the some of the classical modeling and control methods. The application of classical NNs, FL, and wavelet technology to dynamic system modeling and control has been constrained by the non-dynamic nature of their popular architectures. The major drawbacks of these architectures are the curse of dimensionality, such as the requirement of too many parameters in NNs, the use of large rule bases in FL, the large number of wavelets, and the long training times, etc. These problems can be overcome with dynamic network structures, referred to as dynamic neural networks (DNNs), dynamic fuzzy networks (DFNs), and dynamic wavelet networks (DWNs), which have unconstrained connectivity and dynamic neural, fuzzy, and wavelet processing units, called neurons, feurons, and wavelons, respectively. The structure of dynamic networks are based on Hopfield networks. Here, we present a comparative study of DNNs, DFNs, and DWNs for non-linear dynamical system modeling. All three dynamic networks have a lag dynamic, an activation function, and interconnection weights. The network weights are adjusted using fast training (optimization) algorithms (quasi-Newton methods). Also, it has been shown that all dynamic networks can be effectively used in non-linear system modeling, and that DWNs result in the best capacity. But all networks have non-linearity properties in non-linear systems. In this study, all dynamic networks are considered as a non-linear optimization with dynamic equality constraints for non-linear system modeling. They encapsulate and generalize the target trajectories. The adjoint theory, whose computational complexity is significantly less than the direct method, has been used in the training of the networks. The updating of weights (identification of network parameters) is based on Broyden–Fletcher–Goldfarb–Shanno method. First, phase portrait examples are given. From this, it has been shown that they have oscillatory and chaotic properties. A dynamical system with discrete events is modeled using the above network structure. There is a localization property at discrete event instants for time and frequency in this example.     

A novel algorithm for wavelet based ECG signal coding

Wavelets have emerged as powerful tools for signal coding especially bio-signal processing. Wavelet transform is used to represent the signal to some other time-frequency representation better suited for detecting and removing redundancies. A novel algorithm for wavelet based ECG signal coding is proposed in this paper. Experimental results show that this algorithm outperforms than other coders such as Djohn, EZW, SPIHT, etc., exits in the literature in terms of simplicity and coding efficiency by successive partition the wavelet coefficients in the space frequency domain and send them using adaptive decimal to binary conversion. Proposed algorithm is significantly more efficient in compression, simple in implementation and in computation than the previously proposed coders. This algorithm is tested for 26 different records from MIT-BIH arrhythmia database and obtained an average percent root mean square difference as around 0.01-4.8% for an average compression ratio of 2:1 to 35:1. A compression ratio of 8.5108:1 is achieved for MIT-BIH arrhythmia database record 117 with a percent mean square difference as 1.29%.     

Wavelet-based procedures for proteomic mass spectrometry data processing

Proteomics aims at determining the structure, function and expression of proteins. High-throughput mass spectrometry (MS) is emerging as a leading technique in the proteomics revolution. Though it can be used to find disease-related protein patterns in mixtures of proteins derived from easily obtained samples, key challenges remain in the processing of proteomic MS data. Multiscale mathematical tools such as wavelets play an important role in signal processing and statistical data analysis. A wavelet-based algorithm for proteomic data processing is developed. A MATLAB implementation of the software package, called WaveSpect0, is presented including processing procedures of step-interval unification, adaptive stationary discrete wavelet denoising, baseline correction using splines, normalization, peak detection, and a newly designed peak alignment method using clustering techniques. Applications to real MS data sets for different cancer research projects in Vanderbilt Ingram Cancer Center show that the algorithm is efficient and satisfactory in MS data mining.     

Improved Bayesian image denoising based on wavelets with applications to electron microscopy

In this work we discuss an improvement of the image-denoising wavelet-based method presented by Bijaoui [Wavelets, Gaussian mixtures and Wiener filtering, Signal Process. 82 (2002) 709-712]. We show that the parameter estimation step can be replaced by a constrained nonlinear optimization. We propose three different methods to estimate the parameters. As in Bijaoui's original article, two of them deal with white noise. We show that the resulting algorithms improve the one originally proposed. Our third method extends the applicability of the denoising algorithm to colored noise. We test our algorithms with images simulating electron microscopy (EM) conditions as well as experimental EM images.     

Wavelet-based noise reduction for improved deconvolution of time-series data in dynamic susceptibility-contrast MRI

Dynamic susceptibility-contrast (DSC) MRI requires deconvolution to retrieve the tissue residue function R(t) and the cerebral blood flow (CBF). In this study, deconvolution of time-series data was performed by wavelet-transform-based denoising combined with the Fourier transform (FT). Traditional FT-based deconvolution of noisy data requires frequency-domain filtering, often leading to excessive smoothing of the recovered signal. In the present approach, only a low degree of regularisation was employed while the major noise reduction was accomplished by wavelet transformation of data and Wiener-like filtering in the wavelet space. After inverse wavelet transform, the estimate of CBF·R(t) was obtained. DSC-MRI signal-versus-time curves (signal-to-noise ratios 40 and 100) were simulated, corresponding to CBF values in the range 10–60 ml/(min 100 g). Three shapes of the tissue residue function were investigated. The technique was also applied to six volunteers. Simulations showed CBF estimates with acceptable accuracy and precision, as well as independence of any time shift between the arterial input function and the tissue concentration curve. The grey-matter to white-matter CBF ratio in volunteers was 2.4±0.2. The proposed wavelet/FT deconvolution is robust and can be implemented into existing perfusion software. CBF maps from healthy volunteers showed high quality.     

Multiscale characterization of materials with distributed pores and inclusions and application to crack formation in an aluminum alloy

The paper reports a study on the mechanical behavior of materials containing pores and inclusions distributed over a wide range of length scales. Utilizing a wavelet-based multiscale process such microstructures are characterized and their effects on material properties is studied. In order to present the process in a semi-analytical fashion, the variance of the strain field for an approximated one-dimensional deformation problem is examined in detail. It is shown that with respect to crack initiation, there is a strong interplay between the distribution of pores and inclusions. Furthermore, their interaction with boundaries proves to be paramount. The process is applied to a particular cast aluminum alloy where pores are, in general, about two orders of magnitude larger than the silicon particles (inclusions). Results agree well with recent experimental reports on crack initiation where the interplay of pores, inclusions, and boundaries is observed, yet not explained on a fundamental basis. The present work extends recent efforts on porous materials [Frantziskonis G. Wavelet-based analysis of multiscale phenomena—application to material porosity and identification of dominant scales. Prob Eng Mech (this issue). PII: S0266-8920(2)00032-2] to include the interaction of pores at certain scales with inclusions at other scales as well as the interaction of both with boundaries.     

Locally constrained synthetic LoDs generation for natural terrain meshes

Terrain representation is a basic topic in the field of interactive graphics. The amount of data required for a good quality of the terrain offers an important challenge to developers of such systems. For users of these applications, the accuracy of geographical data is generally less important than its natural visual appearance. This makes it possible to maintain a limited geographical database for the system and to extend it generating synthetic data. The evaluation of the intrinsic properties of the terrain (i.e. fractal dimension, roughness, etc.) may be used as the basis for generating extra data accomplishing the same patterns discovered in the actual information. However, it is also interesting to point out that in most natural landscapes, it is usual to have human or natural changes in the basic properties of some areas, i.e. a road or a river. This fact can make it more difficult for synthetic data generation to be free of visual artifacts within these areas. In this paper, we combine fractal and wavelet theories to provide extra data which keeps the natural properties of actual information available. New levels of detail for the terrain are obtained by applying an inverse Wavelet Transform to a set of values randomly generated, thus maintaining the coherence of statistical properties with the original geographical data. Combined with this approach, the use of energy reduction masks has been added in order to avoid undesired visual artifacts in those special areas for which the general terrain properties are no longer valid.     

A multiscale edge detection algorithm based on wavelet domain vector hidden Markov tree model

The wavelet analysis is an efficient tool for the detection of image edges. Based on the wavelet analysis, we present an unsupervised learning algorithm to detect image edges in this paper. A wavelet domain vector hidden Markov tree (WD-VHMT) is employed in our algorithm to model the statistical properties of multiscale and multidirectional (subband) wavelet coefficients of an image. With this model, each wavelet coefficient is viewed as an observation of its hidden state and the hidden state indicates if the wavelet coefficient belongs to an edge. The WD-VHMT model can be learned by an expectation-maximization algorithm. After the model is learned, we employ an extended Viterbi algorithm to uncover the hidden state sequences according to the maximum a posterior estimation. The experiment results of the edge detection for several images are provided to evaluate our algorithm.     

Generating Reflected Directions from BRDF Data

Monte-Carlo path tracing algorithms for computer graphics require that given an incident light ray at a surface an outgoing direction can be computed with a distribution given by the magnitude of the bidirectional reflectance distribution function (BRDF). For analytic reflectance functions this can be done using various techniques including inverting the function, or tabulating some representation of the inverse. However, measured BRDF data sets are too large for this to be practical. We present a method to generate reflection rays distributed according to the magnitude of the BRDF. The method relies on a wavelet-based representation of the BRDF. This representation is efficient and compact, allowing large, anisotropic measured BRDF data sets to be represented with a few thousand coefficients. In particular, we exploit the wavelet representation to quickly compute integrals over ranges of the BRDF.     

Content-based image indexing and searching using Daubechies' wavelets

This paper describes WBIIS (Wavelet-Based Image Indexing and Searching), a new image indexing and retrieval algorithm with partial sketch image searching capability for large image databases. The algorithm characterizes the color variations over the spatial extent of the image in a manner that provides semantically meaningful image comparisons. The indexing algorithm applies a Daubechies' wavelet transform for each of the three opponent color components. The wavelet coefficients in the lowest few frequency bands, and their variances, are stored as feature vectors. To speed up retrieval, a two-step procedure is used that first does a crude selection based on the variances, and then refines the search by performing a feature vector match between the selected images and the query. For better accuracy in searching, two-level multiresolution matching may also be used. Masks are used for partial-sketch queries. This technique performs much better in capturing coherence of image, object granularity, local color/texture, and bias avoidance than traditional color layout algorithms. WBIIS is much faster and more accurate than traditional algorithms. When tested on a database of more than 10 000 general-purpose images, the best 100 matches were found in 3.3 seconds.