Local Entropy Analysis Research Articles

A Novel Image Encryption Scheme Using Chaotic Maps and Fuzzy Numbers for Secure Transmission of Information

The complexity of chaotic systems, if used in information encryption, can determine the status of security. The paper proposes a novel image encryption scheme that uses chaotic maps and fuzzy numbers for the secure transmission of information. The encryption method combines logistic and sine maps to form the logistic sine map, as well as the fuzzy concept and the Hénon map to form the fuzzy Hénon map, in which these maps are used to generate secure secret keys, respectively. Additionally, a fuzzy triangular membership function is used to modify the initial conditions of the maps during the diffusion process. The encryption process involves scrambling the image pixels, summing adjacent row values, and XORing the result with randomly generated numbers from the chaotic maps. The proposed method is tested against various attacks, including statistical attack analysis, local entropy analysis, differential attack analysis, signal-to-noise ratio, signal-to-noise distortion ratio, mean error square, brute force attack analysis, and information entropy analysis, while the randomness number has been evaluated using the NIST test. This scheme also has a high key sensitivity, which means that a small change in the secret keys can result in a significant change in the encrypted image The results demonstrate the effectiveness of the proposed scheme in ensuring the secure transmission of information.

Topological pressure of proper map

Based on the Carathéodory–Pesin structure theory [13], we introduce three notions of topological pressure of a proper map and provide some properties of these notions. For the proper map of a locally compact separable metric space, we prove some variational principles and give some applications on the multifractal analysis of local entropies. These are the extensions of results of Pesin, Takens and Verbiski, etc.

Generalised local entropy analysis for crack detection in beam-like structures

Generally, cracks would lead in local discontinuity and sudden change in mode shape, and the local entropy of beam mode will change with the discontinuity of mode shape. Based on this property, cracks can be detected without using a healthy mode shape serving as the baseline. This paper presents a generalised local entropy (GLE) analysis method for crack detection in beam structures, which is a non-baseline mode shape-based damage detection algorithm for beam-type structures. The fundamental and the second-order vibration modes of a cracked cantilever beam are analysed with the presented method. The proposed prediction scheme is validated by simulations and experiments. Based on the results obtained in this paper and the qualities of simplicity and efficiency of GLE method, a mode shape-based crack identification approach is developed as an alternative damage index for structural health monitoring and non-destructive testing.

An entropy-based method to evaluate plane form error for precision assembly

The minimum zone method is currently a traditional means for evaluating form error. However, it cannot reveal the effects of form error on the scale of assembly accuracy. To address this deficiency, however, considering the propagation of geometric error in assembly process, this article proposed an entropy-based evaluation method for plane form error for precision mechanical system, which includes primary evaluation, convex hull search, top plane establishment, local entropy analysis and obtaining comprehensive evaluation index. Experimental results demonstrate that the proposed method can evaluate the plane form distribution error, which suggests the assemblability of parts, with the same form errors accurately and stably.

The entropies and multifractal spectrum of some compact systems

In the present paper, the following two compact systems and their extensions are studied. (i) A compact system ( X , f ) and its inverse limit ( X ¯ , f ¯ ) . (ii) A compact system ( X , f ) and its corresponding symbolic system ( Σ , σ ) , where f is an expansive homeomorphism. For case (i), a relationship of topological entropy of ( X , f ) and ( X ¯ , f ¯ ) is obtained, i.e., h ( f | Z ) = h ( f ¯ | π 0 - 1 Z ) , where Z is any subset of X and π 0 the projection of X ¯ to X such that π 0 ( x 0 , x 1 , … ) = x 0 . For case (ii), we obtain a similar result. Using these results, we show that ( X , f ) and ( X ¯ , f ¯ ) (resp. ( X , f ) and ( Σ , σ ) ) have the same multifractal spectrum relative to the entropy spectrum. Moreover, as some applications of these results, we obtain that (a) The main result in Takens and Verbitski (1999) [Takens F, Verbitski E. Multifractal analysis of local entropies for expansive homeomorphism with specification. Commun Math Phys 1999;203:593–612] holds under weaker conditions. (b) ( X , f ) and ( X ¯ , f ¯ ) (resp. ( X , f ) and ( Σ , σ ) ) have the same multifractal analysis of local entropies. (c) For two positive expansive compact systems ( X , f ) and ( Y , g ) , if they are almost topologically conjugate, then they have the same multifractal spectrum for local entropies. From a physical point of view, the numerical study of dynamical systems and multifractal spectra is also a very useful tool.

Coding Artifact Reduction Based on Local Entropy Analysis

Coding artifacts are very annoying in highly compressed images and video sequences. Most artifact reduction techniques blur the details of the images while removing various coding artifacts. In this paper, we propose a novel and explicit approach for classifying blocks into detailed regions, intermediate regions and smooth regions. The classification is based on the information content of the underlying region. The information content of a region is quantized by local entropy, which is calculated on the PDF of the pixel intensity distribution. Local entropy is used as an indicator of how much smoothing is needed for a certain region. It is well known that blocking artifacts are more visible in flat regions than in detailed regions. We apply mild low-pass filters on detailed regions to preserve the sharpness, and strong low-pass filters on flat regions to remove the severe blocking artifacts. Experimental results show that our proposed algorithm can preserve the details and reduce coding artifacts better than more expensive state of the art techniques .

General multifractal analysis of local entropies

We address the problem of the multifractal analysis of local entropies for arbitrary invariant measures. We obtain an upper estimate on the multifractal spectrum of local entropies, which is similar to the estimate for local dimensions. We show that in the case of Gibbs measures the above estimate becomes an exact equality. In this case the multifractal spectrum of local entropies is a smooth concave function. We discuss possible singularities in the multifractal spectrum and their relation to phase transitions.

Multifractal Analysis of Local Entropies for Expansive Homeomorphisms with Specification

In the present paper we study the multifractal spectrum of local entropies. We obtain results, similar to those of the multifractal analysis of pointwise dimensions, but under much weaker assumptions on the dynamical systems. We assume our dynamical system to be defined by an expansive homeomorphism with the specification property. We establish the variational relation between the multifractal spectrum and other thermodynamical characteristics of the dynamical system, including the spectrum of correlation entropies.

Multifractal Analysis of Local Entropies for Gibbs Measures

Recently in the series of papers L. Barreira, Ya.B. Pesin, J. Schmeling and H. Weiss performed a complete multifractal analysis of local dimensions, entropies and Lyapunov exponents of conformal expanding maps and surface Axion A diffeomorphisms for Gibbs measures. The main goal of these papers was primarily the analysis of the local (pointwise) dimensions. This is an extremely difficult problem and, for example, similar results for hyperbolic systems in dimensions 3 and higher have not been yet obtained.