Complex approximately analytic wavelets provide a local multiscale description of images with good directional selectivity and invariance to shifts and in-plane rotations. Similar to Gabor wavelets, they are insensitive to illumination variations and facial expression changes. The complex wavelet transform is, however, less redundant and computationally efficient. In this paper, we first constr...

In this paper an attempt has been made to derive the lifting scheme for a set of new bi-orthogonal wavelets and apply on image compression. Four new bi-orthogonal wavelets are designed by taking different basis functions which are selected so as to capture the sharp edges which are common in images. For these classical wavelets, lifting versions are calculated and presented in this paper. The l...

For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including eecient numerical estimates if the number L of decomposition levels is small, as well as growth estima...

This chapter takes up the design of discrete wavelet transforms based on oversampled filter banks. In this case the wavelets form an overcomplete basis, or frame. In particular, we consider the design of systems that are analogous to Daubechies’ orthonormal wavelets — that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case....

Drought forecasting is essential for risk management and preparedness of drought mitigation measures. The present study aims to evaluate the effectiveness proposed hybrid technique regional forecasting. Multiple Linear Regression (MLR), Artificial Neural Network (ANN), two wavelet techniques, namely, Discrete Wavelet Transform (DWT) Packet (WPT), were evaluated in up a lead time six months. Sta...

‎In this paper‎, ‎Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems‎. ‎Firstly‎, ‎using necessary conditions for optimality‎, ‎the problem is changed into a two-boundary value problem (TBVP)‎. ‎Next‎, ‎Haar wavelets are applied for converting the TBVP‎, ‎as a system of differential equations‎, ‎in to a system of matrix algebraic equations‎...

This paper first shows that the Cohen-Daubechies-Feauveau (C-D-F) biorthogonal wavelet can be derived from the interpolating wavelet through a lifting process. Its high-pass filter measures the interpolation error of the averaged data. Next, we propose a new wavelet method, called the difference wavelet method, for efficient representation for functions on R. Its analysis part is simply averagi...

It is well known that the Haar and Shannon wavelets in L2(R) are at opposite extremes, in the sense that the Haar wavelet is localized in time but not in frequency, whereas the Shannon wavelet is localized in freqency but not in time. We present a rich setting where the Haar and Shannon wavelets coincide and are localized both in time and in frequency. More generally, if R is replaced by a grou...

<p style='text-indent:20px;'>Caputo derivative operational matrices of the arbitrary scaled Legendre and Chebyshev wavelets are introduced by deriving directly from these wavelets. The Caputo used in quadratic optimization systems having fractional or integer orders differential equations. Using matrices, a new programming wavelet-based method without doing any integration operation for f...

In this paper, the use of nonseparable wavelets for tomographic reconstruction is investigated. Local tomography is also presented. The algorithm computes both the quincunx approximation and detail coefficients of a function from its projections. Simulation results showed that nonseparable wavelets provide a reconstruction improvement versus separable wavelets.