Abstract
Let L2(R,H) denote the space of all square integrable quaternionic-valued functions. In this article, let Φ∈L2(R,H). We consider the perturbation problems of wavelet frame {Φm,n,a0,b0,m,n∈Z} about translation parameter b0 and dilation parameter a0. In particular, we also research the stability of irregular wavelet frame {SmΦ(Smx−nb),m,n∈Z} for perturbation problems of sampling.
Highlights
Frame theory plays a significant role in both harmonic analysis and wavelet theory [1]
We study sampling perturbation of irregular wavelet frames of quaternionic-valued functions
Our results show that a small perturbation does not change the stability of a wavelet frame when Φ satisfies some conditions, and we can reconstruct uniquely and stably any element through a wavelet transform
Summary
Frame theory plays a significant role in both harmonic analysis and wavelet theory [1]. Perturbation of Wavelet Frames of QuaternionicValued Functions. He et al [17] studied the stability of wavelet frames for perturbation problems of mother wavelet and sampling. Motivated by [17], our paper aims at studying the perturbation problems of wavelet frames about translation and dilation parameters b0 and a0.
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