Wavelet Frames: Multiresolution Analysis and Extension Principles

After reviewing the basic ideas of frame theory from a functional analysis point of view, we discuss two approaches for the construction of (affine) wavelet frames. The theory of Frame Multiresolution Analysis as introduced in [1] is presented in a streamlined form, and the main result of the theory is completed. The interplay between redundancy and robustness in frame expansions is illustrated by a simple example. We then restate Ron and Shen’s Unitary Extension Principle and give a simple direct proof different from the original derivation in [2].

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