The wavelet frame systems have been playing an active role in image restoration and many other image processing fields over the past decades, owing to the good capability of sparsely approximating piece-wise smooth functions such as images. In this paper, we propose a novel wavelet frame based sparse recovery model called Support Driven Sparse Regularization (SDSR) for image deblurring, where t...

An interesting method called Oblique Extension Principle (OEP) has been proposed in the literature for constructing compactly supported MRA tight and dual wavelet frames with high vanishing moments and high frame approximation orders. Many compactly supported MRA wavelet frames have been recently constructed from scalar refinable functions via OEP. Despite the great flexibility and popularity o...

In this paper, we propose a new adaptive wavelet thresholding method for using in speech Enhancement. This modified version of the wavelet thresholding method updates an adaptive threshold in each frame. In the proposed method the selection of the wavelet threshold value depends on the estimates of the clean speech signal features. The evaluation results show that by using the specific features...

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of theminimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept ofminimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Se...

In this paper we shall characterize Sobolev spaces of an arbitrary order of smoothness using nonstationary tight wavelet frames for L2(R). In particular, we show that a Sobolev space of an arbitrary fixed order of smoothness can be characterized in terms of the weighted `2-norm of the analysis wavelet coefficient sequences using a fixed compactly supported nonstationary tight wavelet frame in L...

In this paper, we discuss the digitization and applications of smooth affine shear tight frames, a recently developed new class of directional multiscale representation systems. An affine wavelet tight frame is generated by isotropic dilations and translations of directional wavelet generators, while an affine shear tight frame is generated by anisotropic dilations, shears, and translations of ...

For a wavelet frame with polynomial symbols generated by an MRA with a given approximation order, we present the method for parametric description and construction of all dual analysis operators (filter banks) with the maximum number of vanishing moments whose symbols are polynomials. The similar problems related to the maximum frame approximation order and some other wavelet frame properties a...

A filter bank in which cyclic convolutions are used in place of linear convolutions will be referred to as a cyclic convolution filter bank (CCFB). A dyadic tree-structured CCFB can be used to perform a discrete wavelet transform suitable for coding based on symmetric extension methods. This paper derives an implementation technique for the tree-structured CCFB that can be realized by FFT proce...

Rate scalable video compression techniques are very attractive, because they are able to encode the video in embedded way that makes the decoding process more flexible to the bandwidth changes. Embedded wavelet coding technology plays an important role in this area. Traditional wavelet transforms are globally optimized. It is very efficient to code the natural images where sudden transitions ra...

Spline wavelet tight frames of [20] have been used widely in frame based image analysis and restorations (see, e.g. survey articles [15, 22]). However, except for the tight frame property and the approximation order of the truncated series (see [13,20]), there are few other properties of this family of spline wavelet tight frames to be known. This paper is to present a few new properties of thi...