Tight wavelet frames

An algorithmic method for the construction of multivariate tight wavelet frames with an arbitrary approximation order for any matrix dilation has been presented. Wavelet frames are of great importance for several applied investigations, primarily for signal processing. To construct a wavelet frame, a refinable mask whose polyphase row satisfies a necessary condition for providing the vanishing moment property and can be extended by trigonometric polynomials is required. It was proved that for any matrix dilation M and any positive integer n, there exists a compactly supported tight wavelet frame with the vanishing moment property (VMn).