Non - Uniform Sampling in Multiplygenerated Shift - Invariant Subspaces
نویسندگان
چکیده
Given the samples ff(x j) : j 2 J g of a function f belonging to a shift invariant subspace of L p (IR d), we give a fast reconstruction algorithm that allows the exact reconstruction of f , as long as the sampling set X = fx j : j 2 J g is suuciently dense.
منابع مشابه
NON-UNIFORM SAMPLING IN MULTIPLY GENERATED SHIFT-INVARIANT SUBSPACES OF Lp(IR)
Given the samples {f(xj) : j ∈ J} of a function f belonging to a shift invariant subspace of Lp(IR), we give a fast reconstruction algorithm that allows the exact reconstruction of f , as long as the sampling set X = {xj : j ∈ J} is sufficiently dense.
متن کاملShift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...
متن کاملSupprrium of Perturbation for Sampling in Shift Invariant Subspaces
In the more general framework ' shift invariant subspace", the paper obtains a different estimate of sampling in function subspace to our former work, by using the Frame Theory. The derived formula is easy to be calculated, and the estimate is relaxed in some shift invariant subspaces.
متن کاملMultivariate vector sampling expansions in shift invariant subspaces
In this paper, we study multivariate vector sampling expansions on general finitely generated shift-invariant subspaces. Necessary and sufficient conditions for a multivariate vector sampling theorem to hold are given.
متن کاملSampling Theorems for Multivariate Shift Invariant Subspaces ∗
Regular and irregular sampling theorems for multivariate shift invariant subspaces are studied. We give a characterization of regular points and an irregular sampling theorem, which covers many known results, e.g., Kadec’s 1/4-theorem. We show that some subspaces may not have a regular point. We also present a reconstruction algorithm which is slightly different from the known one but is more e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007