Abstract:

Because the weighted frame possesses good redundancy, it supplies useful information for signal reconstruction and image processing. This paper borrows ideas from the research on the Riesz frame perturbation in the Hilbert space, and in particular, discusses the topic that a weighted frame has the similar perturbation result. Furthermore, application of weighted frames in the practical signal denoising is considered, and the idea of the framed threshold de-noising is proposed.

Key words: weighted frames; Riesz frames; perturbation; threshold de-noising; Hilbert space