The wavelet-NARMAX representation : a hybrid model structure combining polynomial models with multiresolution wavelet decompositions

A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory, and have been extensively used in linear and nonlinear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilise the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input-output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input-output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model

Information Surfaces in Systems Biology and Applications to Engineering Sustainable Agriculture

Systems biology of plants offers myriad opportunities and many challenges in modeling. A number of technical challenges stem from paucity of computational methods for discovery of the most fundamental properties of complex dynamical systems. In systems engineering, eigen-mode analysis have proved to be a powerful approach. Following this philosophy, we introduce a new theory that has the benefits of eigen-mode analysis, while it allows investigation of complex dynamics prior to estimation of optimal scales and resolutions. Information Surfaces organizes the many intricate relationships among "eigen-modes" of gene networks at multiple scales and via an adaptable multi-resolution analytic approach that permits discovery of the appropriate scale and resolution for discovery of functions of genes in the model plant Arabidopsis. Applications are many, and some pertain developments of crops that sustainable agriculture requires.Comment: 24 Pages, DoCEIS 1

A black-box model for neurons

We explore the identification of neuronal voltage traces by artificial neural networks based on wavelets (Wavenet). More precisely, we apply a modification in the representation of dynamical systems by Wavenet which decreases the number of used functions; this approach combines localized and global scope functions (unlike Wavenet, which uses localized functions only). As a proof-of-concept, we focus on the identification of voltage traces obtained by simulation of a paradigmatic neuron model, the Morris-Lecar model. We show that, after training our artificial network with biologically plausible input currents, the network is able to identify the neuron's behaviour with high accuracy, thus obtaining a black box that can be then used for predictive goals. Interestingly, the interval of input currents used for training, ranging from stimuli for which the neuron is quiescent to stimuli that elicit spikes, shows the ability of our network to identify abrupt changes in the bifurcation diagram, from almost linear input-output relationships to highly nonlinear ones. These findings open new avenues to investigate the identification of other neuron models and to provide heuristic models for real neurons by stimulating them in closed-loop experiments, that is, using the dynamic-clamp, a well-known electrophysiology technique.Peer ReviewedPostprint (author's final draft

Neural Pattern Recognition on Multichannel Input Representation

This article presents a new neural pattern recognition architecture on multichannel data representation. The architecture emploies generalized ART modules as building blocks to construct a supervised learning system generating recognition codes on channels dynamically selected in context using serial and parallel match trackings led by inter-ART vigilance signals.Sharp Corporation, Information Techology Research Laboratories, Nara, Japa

Combined wavelet domain and motion compensated filtering compliant with video codecs

In this paper, we introduce the idea of using motion estimation resources from a video codec for video denoising. This is not straightforward because the motion estimators aimed for video compression and coding, tolerate errors in the estimated motion field and hence are not directly applicable to video denoising. To solve this problem, we propose a novel motion field filtering step that refines the accuracy of the motion estimates to a degree that is required for denoising. We illustrate the use of the proposed motion estimation method within a wavelet-based video denoising scheme. The resulting video denoising method is of low-complexity and receives comparable results with respect to the latest video denoising methods

Denoising Techniques Based on the Multiresolution Representation

So far, considerable research efforts have been invested in the are of using statistical methods for image processing purposes yielding to a significant amount of models that aim to improve as much as possible the still existing and currently used processing techniques, some of them being based on using wavelet representation of images. Among them the simplest and the most attractive one use the Gaussian assumption about the distribution of the wavelet coefficients. This model has been successfully used in image denoising and restoration. The limitation comes from the fact that only the first-order statistics of wavelet coefficients are taking into account and the higher-order ones are ignored. The dependencies between wavelet coefficients can be formulated explicitly, or implicitly. The multiresolution representation is used to develop a class of algorithms for noise removal in case of normal models. The multiresolution algorithms perform the restoration tasks by combining, at each resolution level, according to a certain rule, the pixels of a binary support image. The values of the support image pixels are either 1 or 0 depending on their significance degree. At each resolution level, the contiguous areas of the support image corresponding to 1-value pixels are taken as possible objects of the image. Our work reports two attempts in using the multiresolution based algorithms for restoration purposes in case of normally distributed noise. Several results obtained using our new restoration algorithm are presented in the final sections of the paper.multiresolution support, wavelet transform, filtering techniques, statistically significant wavelet coefficients

A Fully Unsupervised Texture Segmentation Algorithm

This paper presents a fully unsupervised texture segmentation algorithm by using a modified discrete wavelet frames decomposition and a mean shift algorithm. By fully unsupervised, we mean the algorithm does not require any knowledge of the type of texture present nor the number of textures in the image to be segmented. The basic idea of the proposed method is to use the modified discrete wavelet frames to extract useful information from the image. Then, starting from the lowest level, the mean shift algorithm is used together with the fuzzy c-means clustering to divide the data into an appropriate number of clusters. The data clustering process is then refined at every level by taking into account the data at that particular level. The final crispy segmentation is obtained at the root level. This approach is applied to segment a variety of composite texture images into homogeneous texture areas and very good segmentation results are reported