We study the action of A on f ∈ L 2 (R) and on its wavelet coefficients, where A = (a lmjk) lmjk is a double infinite matrix. We find the frame condition for A-transform of f ∈ L 2 (R) whose wavelet series expansion is known. 1. Introduction. The notation of frame goes back to Duffin and Schaeffer [7] in the early 1950s to deal with the problems in nonharmonic Fourier series. There has been ren...

In recent years, the research of wavelet frames on graph has become a hot topic in harmonic analysis. this paper, we mainly introduce relevant knowledge graph, including concepts, construction methods, and related theory. Meanwhile, because tight framelets is closely to classical ℝ , give new id="M2"> . Based pseudosplin...

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

Embedded coders provide a better rate-distortion tradeoff while the coded bit stream can be truncated at any point without a significant perceptible distortion. In this work, we investigate rate control for an embedded wavelet video coder by converting the rate control problem to a bit allocation problem for each frame. Then, a computationally efficient rate control algorithm is derived by expl...

In this paper we introduce a block-classified bidirectional motion compensation scheme for our previously developed wavelet-based video codec [24,25], where multiresolution motion estimation is performed in the wavelet domain. The frame classification structure described in this paper is similar to that used in the MPEG standard. Specifically, the I-frames are intraframe coded, the P-frames are...

A wavelet-based speech enhancement algorithm for removing additive background noise from a single channel of noisy speech is proposed. In the algorithm, the enhancement is performed on a frame-by-frame basis, and each frame is classified into either voiced or unvoiced frame to deterimine the appropriate threshold in removing noise. The performance of the proposed algorithm is evaluated on Auror...

Abstract. Dual Gramian analysis is one of the fundamental tools developed in a series of papers [37, 40, 38, 39, 42] for studying frames. Using dual Gramian analysis, the frame operator can be represented as a family of matrices composed of the Fourier transforms of the generators of (generalized) shiftinvariant systems, which allows us to characterize most properties of frames and tight frames...