Wavelet Theory: Applications of the Wavelet

In this Chapter, continuous Haar wavelet functions base and spline base have been discussed. Haar wavelet approximations are used for solving of differential equations (DEs). The numerical solutions of ordinary differential equations (ODEs) and fractional differential equations (FrDEs) using Haar wavelet base and spline base have been discussed. Also, Haar wavelet base and collocation techniques are used to approximate the solution of Lane-Emden equation of fractional-order showing that the applicability and efficacy of Haar wavelet method. The numerical results have clearly shown the advantage and the efficiency of the techniques in terms of accuracy and computational time. Wavelet transform studied as a mathematical approach and the applications of wavelet transform in signal processing field have been discussed. The frequency content extracted by wavelet transform (WT) has been effectively used in revealing important features of 1D and 2D signals. This property proved very useful in speech and image recognition. Wavelet transform has been used for signal and image compression

Randomness analysis on blowfish block cipher using ECB and CBC modes

Randomness of the output is one of the significant factors in measuring the security of any cryptographic algorithm.Non-random block cipher is vulnerable to any type of attack.This paper presents the National Institute of Standard and Technology (NIST) statistical tests of the Blowfish algorithm to investigate its randomness.Blowfish algorithm with Electronic Codebook (ECB) and Cipher Block Chaining (CBC) modes were conducted for these tests.In addition, comparisons between them were introduced.The analysis showed that Blowfish algorithm with ECB mode was inappropriate with data such as text and image files which have large strings of identical bytes.This inconsistency is due to the majority of the 188 statistical tests of NIST statistical tests failing in all rounds

On the reliability and stability of direct explicit Runge-Kutta integrators

Recently, efficient direct numerical integrators of Runge-Kuta type (called RKD and RKT methods) for solving third order ordinary differential equations (ODEs) of the form y\u27\u27\u27 = f(x,x) have been proposed. In this paper, we investigate the reliability of the RKD and RKT approaches, with focus on their stability and accuracy. We compare the stability regions of RKD and RKT methods. It is found that RKD stability region is adaptable, in the sense that its area can be controlled using a free parameter to get a more stable solution. To test the accuracy of RKD, we present some examples of this approach towards solving third-order ordinary differential equations. Simulation results show that the RKD approach, n addition to outperforming the existing RKT methods in terms of accuracy and time consumption, gives better control over stability region

Schoenberg logarithmic image similarity in Prewitt-Gabor-Zernike domain

This paper represents a new approach for face recognition that incorporates Prewitt edge detection, Gabor filter and Zernike moments to transform the image into a unified domain. On this joint domain, five distance metrics are constructed using Schoenberg transform for the purpose of defining efficient similarity measures for holistic face recognition. The proposed Schoenberg similarity applies Schoenberg transform to the logarithm of five existing distance metrics: Minkowski, City-Block, Euclidean, Soergel and Lorentzian metrics. The constructed Schoenberg logarithmic metrics are called SL-Minkowski, SL-City-Block, SL-Euclidean, SL-Soergel and SL-Lorentzian. These distance metrics are utilized as similarity measures after being normalized over the range [0,1] for fair comparison with existing measures. The proposed Schoenberg system can resist three problems: Change in illumination, pose and facial expression. Simulation results show that the proposed distance measures have superior performance as compared to the classical metrics: Structural Similarity Index Measure (SSIM) and Feature-based Similarity Measure (FSIM). Performance criteria are the recognition rate and the recognition confidence, defined as the similarity difference between the best match and the second-best match in the face database