We study Schauder basis properties for the Haar system in Besov spaces \(B^s_{p,q}(\mathbb {R}^d)\). give a complete description of limiting cases, obtaining various positive results \(q\leq \min \{1,p\}\), and providing new counterexamples other situations. The is based on suitable estimates dyadic averaging operators \(\mathbb {E}_N\); particular we find asymptotically optimal growth rates no...

A method for the design of Fast Haar wavelet for signal processing & image processing has been proposed. In the proposed work, the analysis bank and synthesis bank of Haar wavelet is modified by using polyphase structure. Finally, the Fast Haar wavelet was designed and it satisfies alias free and perfect reconstruction condition. Computational time and computational complexity is reduced in Fas...

Large exposure of skin area of an image is considered obscene. This only fact may lead to many false images having skin-like objects and may not detect those images which have partially exposed skin area but have exposed erotogenic human body parts. This paper presents a novel method for detecting nipples from pornographic image contents. Nipple is considered as an erotogenic organ to identify ...

Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.

In this work, a composite numerical scheme based on finite difference and Haar wavelets is proposed to solve time dependent coupled Burgers’ equation with appropriate initial and boundary conditions. Time derivative is discretized by forward difference and then quasilinearization technique is used to linearize the coupled Burgers’ equation. Space derivatives discretization with Haar wavelets le...

There is an abundant literature on face detection due to its important role in many vision applications. Since Viola and Jones proposed the first real-time AdaBoost based face detector, Haar-like features have been adopted as the method of choice for frontal face detection. In this work, we show that simple features other than Haar-like features can also be applied for training an effective fac...

In this paper, a minimization of Haar wavelet series for simplification of circuits and Haar based decision diagrams representing discrete multiple-valued functions is proposed. The minimization is performed by permutation of indices of generalized Haar functions. Experimental results show that this method provides reasonable reduction in the number of non-zero coefficients. The Haar series red...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...