The image de-noising naturally corrupted by noise is a classical problem in the field of signal or image processing. Additive random noise can easily be removed using simple threshold methods. De-noising of natural images corrupted by Gaussian noise using wavelet techniques are very effective because of its ability to capture the energy of a signal in few energy transform values. The wavelet de...

The potential of wavelets as a discretization tool for the numerical treatment of operator equations hinges on the validity of norm equivalences for Besov or Sobolev spaces in terms of weighted sequence norms of wavelet expansion coeecients and on certain cancellation properties. These features are crucial for the construction of optimal preconditioners, for matrix compression based on sparse r...

This paper deals with the construction of biorthogonal p -wavelet packets on R+ related to the Walsh polynomials and their properties are investigated by means of Walsh-Fourier transform. Three biorthogonal formulas regarding these p -wavelet packets are derived. Moreover, it is shown how to obtain several new Riesz bases of the space L2(R+) by constructing a series of subspaces of these p -wav...

In this paper we investigate spline wavelets on general triangulations. In particular, we are interested in C1 wavelets generated from piecewise quadratic polynomials. By using the Powell-Sabin elements, we set up a nested family of spaces of C1 quadratic splines, which are suitable for multiresolution analysis of Besov spaces. Consequently, we construct C1 wavelet bases on general triangulatio...

In this paper we investigate spline wavelets on general triangulations. In particular, we are interested in C1 wavelets generated from piecewise quadratic polynomials. By using the Powell-Sabin elements, we set up a nested family of spaces of C1 quadratic splines, which are suitable for multiresolution analysis of Besov spaces. Consequently, we construct C1 wavelet bases on general triangulatio...

The orthonormal basis generated by a wavelet of L(R) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of L(R) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized...

In this paper Legendre wavelet bases have been used for finding approximate solutions to singular boundary value problems arising in physiology. When the number of basis functions are increased the algebraic system of equations would be ill-conditioned (because of the singularity), to overcome this for large $M$, we use some kind of Tikhonov regularization. Examples from applied sciences are pr...

19 and = 1 + 1 m ; m a positive integer. If we let w(x) 1 p 2 R 1 ?1 e ixx ()dd, then w is a \mother function" that generates a wavelet basis (giving us a Multi Resolution Analysis) m ; m a positive integer. x6. Concluding remarks. We repeat that the local bases we developed in x2. were introduced by Coifman and Meyer, and their use in obtaining the smooth wavelet bases were pointed out to us b...

Discrete wavelet coefficients of input and output of a Linear Time Invariant system, respectively, are shown to be related by a transformation matrix whose elements depend upon characteristics of the system and choice of wavelet bases. A filter bank implementation of the matrix using digital filters, Upand Down-samplers is also given.

In this paper, we present denoising algorithm using wavelet packet transform based on VAD(Voice Activity Detection). For the purpose, the weighting parameter estimation method based on speech dominant indicator and the modified Berouti’s method are suggested. Subjective evaluation shows that the performance of the proposed algorithm with wavelet bases is better than that with Fourier basis.