The Properties And Configuration Of4-Band Tight Wavelet Frames

MRA-based wavelet tight frames can be seen as a generalization of the MRA-based orthonormal wavelet. Since compactly supported MRA-based orthonormal wavelet is constructed, wavelet analysis and its applications have been one of most popular research areas in applied mathematics.Algorithms and methods based on wavelet analysis become powerful tools in image and signal processing.One of the successful examples of applications of MRA-based wavelets is image compression by using orthonormal or bi-orthogonal MRA-based wavelet bases.The unitary extension principle derives the explicit construction of MRA-based tight wavelet frames generated by refinement function. The redundancy, sparse approximation and fast decomposition and reconstruction algorithms are the key factors for the wide usage of M-band wavelet frame. The advantage of M-wavlet and wavlet frames Encourage people to study actively.In this paper, a construction method based on MRA4-band tight wavelet frame with symmetry properties is studied by applying the symmetric extension principle. First of all, we establish paraunitary matrix as a starting point, which is relative to multi-nominal one of a meristic stretching of compactly supported wavelet frame with minimum number of generated factors. Secondly, we put forward the symmetry properties for wavelet frame in different filter lengths on by paraunitary matrix. Then, we deal with parameterization of the4-band tight wavelet frame under the condition that the filter length is4N. Eventually, by using the above method, we calculated by appropriately choosing parameters symmetric/antisymmetric wavelet frame filter masks as an example.