The object of this paper is to construct extension operators in the Sobolev spacesHk(]−∞,0]) andHk([0,+∞[) (k≥ 0). Thenwe use these extensions to get biorthogonal wavelet bases inHk(R). We also give a construction in L2([−1,1]) to see how to obtain boundaries functions. 2000 Mathematics Subject Classification. 41A58, 42C15.

In this paper we construct a compactly supported biorthogonal wavelet basis adapted to some simple diierential operators. Moreover, we estimate the condition numbers of the corresponding stiiness matrices.

This paper is concerned with developing conditions on a given nite collection of compactly supported algebraically linearly independent reenable functions that insure the existence of biorthog-onal systems of reenable functions with similar properties. In particular we address the close connection of this issue with stationary subdivision schemes. 1 Introduction During the past few years the co...

-Based on the statistical characters of remote sensing image, this paper proposed firstly partition remote sensing image into sub-block images of suitable sizes, and then decomposing these sub-block images with biorthogonal 7/5 wavelet. A novel construction method of wavelet set of coefficients is adopted to embed binary watermarking image into sub-bands except low frequency sub-bands, and real...

Moving object detection is a fundamental task for a variety of traffic applications. In this paper the Daubechies and biorthogonal wavelet families are exploited for extracting the relevant movement information in moving image sequences in a 3D wavelet-based segmentation algorithm. The proposed algorithm is applied for traffic monitoring systems. The objective and subjective experimental result...

For a square integrable vector-valued process f on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for f are presented. The process f is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for f involving the biorthogo...

The selection of most suitable mother wavelet function is still an open research problem in various signal and image processing applications. This paper presents a comparative study of different wavelet families (Daubechies, Symlets, Coiflets, and Biorthogonal) for analysis of wrist motions from electromyography (EMG) signals. EMG signals are decomposed into three levels using discrete wavelet ...

In this paper, we propose a new M-channel wavelet bases called the cosine-modulated wavelets. We first generalize the theory of two-channel biorthogonal compactly supported wavelet bases to the M-channel case. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel compactly supported wavelet bases is given. By using this condition, a family of orthog...

—Pointwise-supported generalised wavelets are introduced, based on Dirac, doublet and further derivatives of (t). A generalised biorthogonal analysis leads to standard Taylor series and new Dual-Taylor series that may be interpreted as Laurent Schwartz distributions. A Parseval-like identity is also derived for Taylor series, showing that Taylor series support an energy theorem. New representa...

Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...