Non-Separable Meyer-like Wavelet Frames

Abstract

In the theory of wavelet frames, the known Daubechies wavelet bases have been generalized to compactly supported (Daubechies-like) wavelet frames, while the known bandlimited Meyer wavelet bases have not been generalized to date. In this study, we will generalize known Meyer wavelet basis into non-separable Meyer-like wavelet frames. By using a characteristic function to mask the Fourier transform of the one-dimensional Meyer scaling function with a width parameter, we can produce a family of Meyer-like frame scaling functions and associated Meyer-like wavelet frames. After that, by inserting a real-valued function into the width parameter of a one-dimensional Meyer-like frame scaling function, we propose a novel approach to construct non-separable Meyer-like frame scaling functions with unique circular symmetry. Finally, we construct the corresponding non-separable Meyer-like wavelet frames.