Discrete-time cellular neural networks in FPGA

This paper describes a novel architecture for the hardware implementation of non-linear multi-layer cellular neural networks. This makes it feasible to design CNNs with millions of neurons accommodated in low price FPGA devices, being able to process standard video in real time.This research has been funded by MTyAS of Spain, IMSERSO RETVIS 150/06

Convergence of Discrete-Time Cellular Neural Networks with Application to Image Processing

The paper considers a class of discrete-time cellular neural networks (DT-CNNs) obtained by applying Euler's discretization scheme to standard CNNs. Let T be the DT-CNN interconnection matrix which is defined by the feedback cloning template. The paper shows that a DT-CNN is convergent, i.e. each solution tends to an equilibrium point, when T is symmetric and, in the case where T + En is not positive-semidefinite, the step size of Euler's discretization scheme does not exceed a given bound (En is the n × n unit matrix). It is shown that two relevant properties hold as a consequence of the local and space-invariant interconnecting structure of a DT-CNN, namely: (1) the bound on the step size can be easily estimated via the elements of the DT-CNN feedback cloning template only; (2) the bound is independent of the DT-CNN dimension. These two properties make DT-CNNs very effective in view of computer simulations and for the practical applications to high-dimensional processing tasks. The obtained results are proved via Lyapunov approach and LaSalle's Invariance Principle in combination with some fundamental inequalities enjoyed by the projection operator on a convex set. The results are compared with previous ones in the literature on the convergence of DT-CNNs and also with those obtained for different neural network models as the Brain-State-in-a-Box model. Finally, the results on convergence are illustrated via the application to some relevant 2D and 1D DT-CNNs for image processing tasks

p-adic Cellular Neural Networks

In this article we introduce the p-adic cellular neural networks which are mathematical generalizations of the classical cellular neural networks (CNNs) introduced by Chua and Yang. The new networks have infinitely many cells which are organized hierarchically in rooted trees, and also they have infinitely many hidden layers. Intuitively, the p-adic CNNs occur as limits of large hierarchical discrete CNNs. More precisely, the new networks can be very well approximated by hierarchical discrete CNNs. Mathematically speaking, each of the new networks is modeled by one integro-differential equation depending on several p-adic spatial variables and the time. We study the Cauchy problem associated to these integro-differential equations and also provide numerical methods for solving them

Behavioral models of nonlinear filters based on discrete time cellular neural networks

The nonlinear dynamic system modeling based on the input/output relationship results from solving the approximation problem. One can distinguish two large classes: polynomials and neural networks. The different types of neural networks draw attention. The discrete time feedforward cellular neural network is suggested for filtering non-Gaussian noise, as well as the example of nonlinear filters modeling to cancel the impulse noise is represented

Discrete Dynamical Systems Embedded in Cantor Sets

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $N$ variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit $N\to\infty$. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological entropy and Lyapunov exponents through the concept of error-profile. We made explicit calculations both numerical and analytic for well known discrete dynamical models.Comment: 36 pages, 13 figures: minor text amendments in places, time running top to bottom in figures, to appear in J. Math. Phy

Current-Mode Techniques for the Implementation of Continuous- and Discrete-Time Cellular Neural Networks

This paper presents a unified, comprehensive approach to the design of continuous-time (CT) and discrete-time (DT) cellular neural networks (CNN) using CMOS current-mode analog techniques. The net input signals are currents instead of voltages as presented in previous approaches, thus avoiding the need for current-to-voltage dedicated interfaces in image processing tasks with photosensor devices. Outputs may be either currents or voltages. Cell design relies on exploitation of current mirror properties for the efficient implementation of both linear and nonlinear analog operators. These cells are simpler and easier to design than those found in previously reported CT and DT-CNN devices. Basic design issues are covered, together with discussions on the influence of nonidealities and advanced circuit design issues as well as design for manufacturability considerations associated with statistical analysis. Three prototypes have been designed for l.6-pm n-well CMOS technologies. One is discrete-time and can be reconfigured via local logic for noise removal, feature extraction (borders and edges), shadow detection, hole filling, and connected component detection (CCD) on a rectangular grid with unity neighborhood radius. The other two prototypes are continuous-time and fixed template: one for CCD and other for noise removal. Experimental results are given illustrating performance of these prototypes

State Estimation for Discrete-Time Fuzzy Cellular Neural Networks with Mixed Time Delays

This paper is concerned with the exponential state estimation problem for a class of discrete-time fuzzy cellular neural networks with mixed time delays. The main purpose is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. By constructing a novel Lyapunov-Krasovskii functional which contains a triple summation term, some sufficient conditions are derived to guarantee the existence of the state estimator. The linear matrix inequality approach is employed for the first time to deal with the fuzzy cellular neural networks in the discrete-time case. Compared with the present conditions in the form of M-matrix, the results obtained in this paper are less conservative and can be checked readily by the MATLAB toolbox. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed results