China
Africa
Explore chapters and articles related to this topic
Review of Image Tampering Detection Techniques
Published in S. Ramakrishnan, Cryptographic and Information Security, 2018
In [45], a 2-D noncausal Markov model is proposed with model parameters considered as the discriminative features to differentiate the spliced images from pristine. The model is applied in the BDCT domain and the discrete Meyer wavelet transform domain. The cross-domain features are treated as the final discriminative features used for classification using a support vector machine.
A framework for short-term traffic flow forecasting using the combination of wavelet transformation and artificial neural networks
Published in Journal of Intelligent Transportation Systems, 2019
Seyed Omid Mousavizadeh Kashi, Meisam Akbarzadeh
Dmey is the discrete approximation of Meyer wavelet. The Meyer wavelet is an orthogonal wavelet that is defined in frequency domain (Mallat, 2008). Equations (8)–(10) present the formulation. where:
The bi-Helmholtz equation with Cauchy conditions: ill-posedness and regularization methods
Published in Inverse Problems in Science and Engineering, 2021
Hussien Lotfinia, Nabi Chegini, Reza Mokhtari
In this paper, a Cauchy problem of the bi-Helmholtz equation has been studied. It has been shown that this problem may be ill-posed. This situation means that the solution does not depend continuously on the given data. We have figured out that the usage of the regularization technique is mandatory. Among the various regularization methods, wavelet and Fourier regularization methods have been selected. The bi-Helmholtz equation has been transformed to the Fourier domain and explicit expressions of the Fourier transformations of the Meyer wavelet and scaling functions are defined in this domain. Moreover, these functions are analytic in the Fourier domain. Based on these reasons, the wavelet which fits well to our analysis is the Meyer wavelet. By deriving some essential error estimates, we have shown that applying the Meyer wavelet leads to the stability of solutions. Numerical results indicate that Shannon wavelet regularization method is able to regularize the perturbed problem. The Meyer and Shannon wavelets have compact support in the frequency space as well as the Meyer wavelet. So this property of wavelets acts as a low-pass filter for high frequencies which are the source of ill-posedness. There are some restriction when we use wavelets as frequency filters. For instance at finer level of multiresolution and larger regularization parameter , the support of wavelets in frequency space increase exponentially, therefore in practice they can not filter any frequencies. On the other hand, if we choose a small level of multiresolution, wavelets are not able to approximate measured data as much as possible. We suggest a formula for instead of to reduce the restrictions. Also, error estimates of the Fourier regularization method show that this method is applicable as well as wavelet regularization methods. In this method, we transform measured data to frequency space and remove high frequencies. The parameter of regularization in Fourier method is the number of components that we choose as high frequencies. From the illustrated examples, wavelet and Fourier regularization methods are two valuable tools to reduce the effect of the ill-posedness as much as possible for solving the bi-Helmholtz equation with Cauchy conditions. We predict that wavelet and Fourier regularization methods can exploit to overcome the ill-posedness of the backward heat conduction problem with time-fractional derivative and a class of non-linear time-dependent partial differential equations. Due to the complexity of the Meyer wavelet method and the nature of the bi-Helmholtz equation, we have obtained the regularization parameter using an a-priori choice rule and we leave an a-posteriori choice rule to the future works.