Likelihood ratios for signals in additive white noise

We present a formula for likelihood functionals for signals in which the corrupting noise is modelled as white noise rather than the usual Wiener process. The main difference is the appearance of an additional term corresponding to the conditional mean square error. By way of one application we consider the order-disorder problem of Shiryayev.Research supported in part under Grant No. 73-2492, Applied Math. Divn., AFOSR, USAF.     

Tracking almost periodic signals under white noise perturbations

A result of the "law of large numbers" type is obtained for the cost of tracking almost periodic signals if the deterministic optimal feedback law is used in the presence of white noise perturbations     

A cryptographic watermarking technique for multimedia signals

Digital watermarking has been widely used in digital rights management and copyright protection. In this paper, new cryptographic watermark schemes are proposed. Compare to the existing watermarking techniques, our proposed watermark schemes combine both security and efficiency that none of the existing schemes can do. We first develop an algorithm to randomly generate the watermark indices based on the discrete logarithm problem (DLP) and the Fermat’s little theorem. Then we embed watermark signal into the host image in both time domain and frequency domain at the indices. Our security analysis and simulation demonstrate that our proposed schemes can achieve excellent transparency and robustness under the major security attacks and common signal degradations. The novel approaches provided in this paper are ideal for general purpose commercial digital media copyright protection.     

On detection of the number of signals in presence of white noise

In this paper, the authors propose procedures for detection of the number of signals in presence of Gaussian white noise under an additive model. This problem is related to the problem of finding the multiplicity of the smallest eigenvalue of the covariance matrix of the observation vector. The methods used in this paper fall within the framework of the model selection procedures using information theoretic criteria. The strong consistency of the estimates of the number of signals, under different situations, is established. Extensions of the results are also discussed when the noise is not necessarily Gaussian. Also, certain information-theoretic criteria are investigated for determination of the multiplicities of various eigenvalues.     

A delta white noise functional

The additive renormalization% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabs7adaWgaaWcbaGaaeySdiaab6cacaqG0bqefeKCPfgBaGqb% diaa-bcaaeqaaOGaeyypa0Jaa8hiaiaacIcacaaIYaGaeqiWdaNaai% ykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIYaaaaGqadOGa% a4hiaiGacwgacaGG4bGaaiiCaiaacIcacqGHsislcaqGXoWaaWbaaS% qabeaacaqGYaaaaOGaai4laiaaikdacaGGPaGaa4hiaiaacQdaciGG% LbGaaiiEaiaacchacqGHXcqSdaWadiqaaiabgkHiTiaadkeacaGGNa% GaaiikaiaadshacaGGPaWaaWbaaSqabeaacaaIYaaaaOGaai4laiaa% ikdacaGFGaGaey4kaSIaa4hiaiaabg7acaWGcbGaai4jaiaacIcaca% WG0bGaaiykaaGaay5waiaaw2faaiaacQdaaaa!6C5C!\[{\rm{\delta }}_{{\rm{\alpha }}{\rm{.t}} } = (2\pi )^{ - 1/2} \exp ( - {\rm{\alpha }}^{\rm{2}} /2) :\exp \pm \left[ { - B'(t)^2 /2 + {\rm{\alpha }}B'(t)} \right]:\]is shown to be a generalized Brownian functional. Some of its properties are derived. is shown to be a generalized Brownian functional. Some of its properties are derived.On leave from Universidade do Minho, Area de Matematica, Largo Carlos Amarante, P-4700 Braga, Portugal.     

A robust chaotic algorithm for digital image steganography

This paper proposes a new robust chaotic algorithm for digital image steganography based on a 3-dimensional chaotic cat map and lifted discrete wavelet transforms. The irregular outputs of the cat map are used to embed a secret message in a digital cover image. Discrete wavelet transforms are used to provide robustness. Sweldens’ lifting scheme is applied to ensure integer-to-integer transforms, thus improving the robustness of the algorithm. The suggested scheme is fast, efficient and flexible. Empirical results are presented to showcase the satisfactory performance of our proposed steganographic scheme in terms of its effectiveness (imperceptibility and security) and feasibility. Comparison with some existing transform domain steganographic schemes is also presented.     

Robust digital controllers for uncertain chaotic systems: A digital redesign approach

In this paper, a new and systematic method for designing robust digital controllers for uncertain nonlinear systems with structured uncertainties is presented. In the proposed method, a controller is designed in terms of the optimal linear model representation of the nominal system around each operating point of the trajectory, while the uncertainties are decomposed such that the uncertain nonlinear system can be rewritten as a set of local linear models with disturbed inputs. Applying conventional robust control techniques, continuous-time robust controllers are first designed to eliminate the effects of the uncertainties on the underlying system. Then, a robust digital controller is obtained as the result of a digital redesign of the designed continuous-time robust controller using the state-matching technique. The effectiveness of the proposed controller design method is illustrated through some numerical examples on complex nonlinear systems––chaotic systems.     

Wiener distributions and white noise analysis

The paper describes the structure of a new space of generalized Wiener functionals, , called the Wiener algebra, or space of Wiener distributions, and demonstrates its use in the white noise analysis. The concepts of derivatives and integrals for multi-time parameter generalized stochastic process:^N are introduced, and a derivative version of Itô's lemma is proved. The algebraic structure of and its lattice of subspaces is elaborated, and within this framework a generalized version of the Malliavin calculus is presented.     

A finitely additive white noise approach to nonlinear filtering

An approach to nonlinear filtering theory is developed in which finitely additive white noise replaces the Wiener process in the observation process model. The important case when the signal is a Markov process independent of the noise is investigated in detail. The theory turns out to be simpler than the current theory based on the stochastic calculus. Stochastic partial differential equations are replaced by partial differential equations in which the observation (in the finitely additive set up) occurs as a parameter. Theorems on existence and uniqueness of solutions are obtained. The white noise approach has the advantage that it provides a robust solution to the filtering problem. Furthermore, the robust theory based on the Ito calculus can be recovered from the results of this paper.     

An image adaptive, wavelet-based watermarking of digital images

In digital management, multimedia content and data can easily be used in an illegal way—being copied, modified and distributed again. Copyright protection, intellectual and material rights protection for authors, owners, buyers, distributors and the authenticity of content are crucial factors in solving an urgent and real problem. In such scenario digital watermark techniques are emerging as a valid solution. In this paper, we describe an algorithm—called WM2.0—for an invisible watermark: private, strong, wavelet-based and developed for digital images protection and authenticity. Using discrete wavelet transform (DWT) is motivated by good time-frequency features and well-matching with human visual system directives. These two combined elements are important in building an invisible and robust watermark. WM2.0 works on a dual scheme: watermark embedding and watermark detection. The watermark is embedded into high frequency DWT components of a specific sub-image and it is calculated in correlation with the image features and statistic properties. Watermark detection applies a re-synchronization between the original and watermarked image. The correlation between the watermarked DWT coefficients and the watermark signal is calculated according to the Neyman–Pearson statistic criterion. Experimentation on a large set of different images has shown to be resistant against geometric, filtering and StirMark attacks with a low rate of false alarm.     

The influence of noise on a classical chaotic scatterer

A classical, chaotic scatterer consisting of three, equal-sized, equidistant hard discs, also known as the Gaspard–Rice system [Gaspard P, Rice SA. Scattering from a classically chaotic repellor. J Chem Phys 1989;90(4):2225–2241] is studied in the presence of white noise. The fractal dimension of the stable manifold is measured using the uncertainty fraction. The volume of the manifold, and thus of the invariant set, when considered in a possibilistic sense, is found to scale with the magnitude of the noise, thus extending the results of Ott et al. [Ott E, York ED, Yorke JA. A scaling law: How an attractors volume depends on noise level. Physica D 1985;16:62–78] from attracting to non-attracting sets.     

Design and FPGA-realization of a self-synchronizing chaotic decoder in the presence of noise

This paper describes requirement for wireless transmission of Chaotic Code Division Multiplexed Access (Chaotic CDMA) and it focuses on real-time synchronization algorithm embedded into electronic programmable device. CDMA with quasi-orthogonal codes is used to allow multi-users to transmit simultaneously in the same channel. Since the channel is shared between all users, the receiver system has to cope with channel noise and overall with interference from other users. As a result, one of the main problems of communication with quasi-orthogonal chaotic codes is to implement a real time decoder in presence of noise. Even if set-membership algorithm are efficient in real time synchronization of chaotic discrete generators in the presence of noise, these algorithms require a large memory resource. In this paper, we propose an evolution of set-membership algorithm toward genetic algorithm to be implemented into electronic programmable device. The advantage of genetic algorithm compared with set-membership algorithm is that they require a fixed size of memory.     

First order differential operators in white noise analysis

Let be the space of test white noise functionals. We first introduce a family of products on including Wiener and Wick products, and then show that with each product , we can associate a first order differential operator, called a first order -differential operator. We next show that a first order -differential operator is indeed a continuous derivation under the product . We finally characterize by means of rotation-invariance and continuous derivation under the product . Here and are the Gross Laplacian and the number operator on , respectively.

     

A white noise approach to infinitely divisible distributions on Gel'fand triple

In this note, we apply white noise analysis to infinitely divisible distributions on a real Gel'fand triple E⊂H⊂E^∗. We first introduce an index, called Hida index, for a measure on E⊂H⊂E^∗. And then, under some mild conditions, we obtain a general inequality which indicates a connection between the Hida index of an infinitely divisible distribution on E⊂H⊂E^∗ and that of its Lévy measure. Finally we prove that the Hida index of the standard compound Poisson distribution on E⊂H⊂E^∗ is exactly 1.     

Bifurcation structure of chaotic attractor in switched dynamical systems with spike noise

High-frequency ripple (spike noise) effects in the qualitative properties of DC/DC converter circuits. This study investigates the bifurcation structure of a chaotic attractor in a switched dynamical system with spike noise. First, we introduce the system dynamics and derive the associated Poincaré map. Next, we show the bifurcation structure of the chaotic attractor in a system with spike noise. Finally, we investigate the dynamical effect of spike noise in the existence region of the chaotic attractor compare with that of a chaotic attractor in a system with ideal switching. The results suggest that spike noise enlarges an invariant set and generates a new bifurcation structure of the chaotic attractor.     

On the generation of high-quality white noise series

A new approach to the simulation of white-noise time-series is presented. The approach is based on the frequency-domain property of white-noise as having a flat power spectrum density (PSD). From such a PSD, a linear complex spectrum of random-phase multisinusoidal series (MS) may be generated. Next, the fast Fourier transform is applied to this linear spectrum to generate a random-phase multisinusoidal N-sample series, simulating the white-noise series. The properties of some MS series are discussed including a gaussian white noise multisinusoidal series. The idea is illustrated by a number of examples. They demonstrate that the spectral and correlation properties of such series are enhanced in comparison to the properties of the random phases used to generate them. They also demonstrate that the spectral and correlation properties of such series are better, especially for short series, in comparison with standard white noise generators.     

Some recent results in finitely additive white noise theory

We present a short survey of some very recent results on the finitely additive white noise theory. We discuss the Markov property of the solution of a stochastic differential equation driven directly by a white noise, study the Radon-Nikodym derivative of the measure induced by nonlinear transformation on a Hilbert space with respect to the canonical Gauss measure thereon and obtain a representation for nonlinear filter maps.