In this paper, diffusion wavelet-based multiscale linear minimum mean square-error estimation (LMMSE) scheme for image denoising in conjunction to neural network is proposed, and the determination of the optimal wavelet basis with respect to the proposed scheme is also discussed. Genrally ,the over complete wavelet expansion (OWE) is more effective than the orthogonal wavelet transform (OWT) sp...

this paper deals with continuous frames and continuous riesz bases. we introduce continuous riesz bases and give some equivalent conditions for a continuous frame to be a continuous riesz basis. it is certainly possible for a continuous frame to have only one dual. such a continuous frame is called a riesz-type frame [13]. we show that a continuous frame is riesz-type if and only if it is a con...

The contribution includes the description of nonseparable multidimensional (M-D) multirate systems, the results obtained in their design and application to coding of M-D signals. Nonseparable signals cannot be represented as a factor of 1-D functions. New processing technologies and hardware let implement recent theoretical results and methods. Today there is a lack of the results covering all ...

We investigate Riesz bases of wavelets in Sobolev spaces and their applications to numerical solutions of the biharmonic equation and general elliptic equations of fourth-order. First, we study bicubic splines on the unit square with homogeneous boundary conditions. The approximation properties of these cubic splines are established and applied to convergence analysis of the finite element meth...

In this paper, a new feature which is characterized by the extrema density of 2-D wavelet frames estimated at the output of the corresponding filter bank is proposed for texture segmentation. With and without feature selection, the discrimination ability of features based on pyramidal and treestructured decompositions are comparatively studied using the extrema density, energy, and entropy as f...