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Characterization for minimum-energy bivariate framelets. (Chinese. English summary) Zbl 1389.42061

Summary: Aiming at the effective application for the bivariate wavelet frames in image procession, we investigate the properties of minimum-energy bivariate wavelet frames. The sufficient and necessary conditions on the existence for the minimum-energy bivariate wavelet frames are established. The characterization for minimum energy bivariate wavelet frames is performed. Decomposition and reconstruction algorithms for minimum-energy bivariate wavelet frames are formulated by implementing the polyphase decomposition on the mask functions that correspond to the refinable functions and the wavelet functions. Two numerical examples are provided.

MSC:

42C15 General harmonic expansions, frames
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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