Construction of biorthogonal wavelets starting from any two multiresolutions
نویسندگان
چکیده
Starting from any two given multiresolution analyses of L2, fV 1 j gj 2Z, and fV 2 j gj 2Z, we construct biorthogonal wavelet bases that are associated with this chosen pair of multiresolutions. Thus, our construction method takes a point of view opposite to the one of Cohen–Daubechies–Feauveau (CDF), which starts from a well-chosen pair of biorthogonal discrete filters. In our construction, the necessary and sufficient condition is the nonperpendicularity of the multiresolutions.
منابع مشابه
Diagrammatic Tools for Generating Biorthogonal Multiresolutions
In a previous work [1] we introduced a construction designed to produce biorthogonal multiresolutions from given subdivisions. This construction was formulated in matrix terms, which is appropriate for curves and tensor-product surfaces. For mesh surfaces of non-tensor connectivity, however, matrix notation is inconvenient. This work introduces diagrams and diagram interactions to replace matri...
متن کاملReversing Subdivision Using Local Linear Conditions: Generating Multiresolutions on Regular Triangular Meshes
In a previous work [1] we investigated how to reverse subdivision rules using local linear conditions based upon least squares approximation. We outlined a general approach for reversing subdivisions and showed how to use the approach to construct multiresolutions with finite decomposition and reconstruction filters. These multiresolutions correspond to biorthogonal wavelet systems that use inn...
متن کاملA Note on Construction of Biorthogonal Multi - Scaling Functions
In many applications biorthogonal wavelets prove to be more ee-cient than orthogonal ones. In this note we present a procedure for constructing biorthogonal multi-scaling functions with any given approximation order, starting from a low pass multi-lter H 0. We show that dual low pass multi-lter F 0 can be found if det(H 0 (z)) and det(H 0 (?z)) do not have common roots. We also suggest \two-sca...
متن کاملOBLIQUE PROJECTIONS IN DISCRETE SIGNAL SUBSPACES OF l2 AND THE WAVELET TRANSFORM
We study the general problem of oblique projections in discrete shift-invariant spaces of 12 and we give error bounds on the approximation. We define the concept of discrete multiresolutions and wavelet spaces and show that the oblique projections on certain subclasses of discrete multiresolutions and their associated wavelet spaces can be obtained using perfect reconstruction filter banks. The...
متن کاملConstruction of compactly supported biorthogonal wavelets
This paper presents a construction of compactly supported biorthogonal spline wavelets in L2(IR ). In particular, a concrete method for the construction of bivariate compactly supported biorthogonal wavelets from box splines of increasing smoothness is provided. Several examples are given to illustrate the method. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IEEE Trans. Signal Processing
دوره 46 شماره
صفحات -
تاریخ انتشار 1998