We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.

An irregular wavelet frame has the form W(ψ,Λ) = {aψ( a − b)}(a,b)∈Λ, where ψ ∈ L (R) and Λ is an arbitrary sequence of points in the affine group A = R ×R. Such irregular wavelet frames are poorly understood, yet they arise naturally, e.g., from sampling theory or the inevitability of perturbations. This paper proves that irregular wavelet frames satisfy a Homogeneous Approximation Property, w...

where A and B are called the lower frame bound and upper frame bound, respectively. In particular, when A= B = 1, we say that {hk}k∈Z is a (normalized) tight frame in H. The 1 Research was partially supported by NSF Grants DMS-9872890, DMS-9706753 and AFOSR Grant F4962098-1-0044. Web: http://www.princeton.edu/~icd. 2 Research was supported by NSERC Canada under Grant G121210654 and by Alberta I...

Other than the conventional fast Fourier transform (FFT) for multicarrier modulation, a new approach for multicarrier modulation (MCM) has been known. Meanwhile, multicarrier modulation involves dividing the broadband channel into many orthogonal but overlapping narrowband carriers. In an OFDM modulation based multicarrier system using the FFT, a cyclic prefix (CP) is inserted after each symbol...

Wavelet frame based models for image restoration have been extensively studied for the past decade [1, 2, 3, 4, 5, 6]. The success of wavelet frames in image restoration is mainly due to their capability of sparsely approximating piecewise smooth functions like images. Most of the wavelet frame based models designed in the past are based on the penalization of the l1 norm of wavelet frame coeff...

In order to improve the quality of multimedia communication and experience, we proposed a crowd service cooperation control protocol based on the opportunistic wavelet model. Firstly, in order to provide real-time and reliable guarantee for mobile multimedia services, we analyze the delay, jitter, and distortion of wireless multimedia streams transmission based on wavelet model. The method of v...

By assuming that images of interest can be sparsely modelled by some transform, the sparsity-based regularization has been one promising approach for solving many ill-posed inverse problems in image recovery. One often-used type of systems for sparsifying images is wavelet tight frames, which can efficiently exploit the sparse nature of local intensity variations of images. However, existing wa...

A multiplicative Schwarz overlapping domain decomposition method is considered for solving elliptic boundary value problems. By equipping the relevant Sobolev spaces on the subdomains with wavelet bases, adaptive wavelet methods are used for approximately solving the subdomain problems. The union of the wavelet bases forms a frame for the Sobolev space on the domain as a whole. The resulting me...

A multiplicative Schwarz overlapping domain decomposition method is considered for solving elliptic boundary value problems. By equipping the relevant Sobolev spaces on the subdomains with wavelet bases, adaptive wavelet methods are used for approximately solving the subdomain problems. The union of the wavelet bases forms a frame for the Sobolev space on the domain as a whole. The resulting me...

Given a real, expansive dilation matrix we prove that any bandlimited function ψ ∈ L(R), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple constr...