A generalized uncertainty principle and sparse representation in pairs of basesIEEE Transactions on Information Theory - Tập 48 Số 9 - Trang 2558-2567 - 2002
M. Elad, A.M. Bruckstein
An elementary proof of a basic uncertainty principle concerning pairs of representations of R/sup N/ vectors in different orthonormal bases is provided. The result, slightly stronger than stated before, has a direct impact on the uniqueness property of the sparse representation of such vectors using pairs of orthonormal bases as overcomplete dictionaries. The main contribution in this paper is the...... hiện toàn bộ
#Dynamic programming #Minimization methods #Signal representations
Data-dependent k/sub n/-NN and kernel estimators consistent for arbitrary processesIEEE Transactions on Information Theory - Tập 48 Số 10 - Trang 2785-2788 - 2002
S.R. Kulkarni, S.E. Posner, S. Sandilya
Let X/sub 1/, X/sub 2/,... be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with X/sub i/ we observe Y/sub i/ drawn from an unknown conditional distribution F(y|X/sub i/=x) with continuous regression function m(x)=E[Y|X=x]. The problem of interest is to estimate Y/sub n/ based on X/sub n/ and the data {(X/sub i/, Y/sub i/)}/sub i=1//s...... hiện toàn bộ
#Stochastic processes #Parameter estimation #Set theory
On sampling in shift invariant spacesIEEE Transactions on Information Theory - Tập 48 Số 10 - Trang 2802-2810 - 2002
Wen Chen, S. Itoh, J. Shiki
A necessary and sufficient condition for sampling in the general framework of shift invariant spaces is derived. Then this result is applied, respectively, to the regular sampling and the perturbation of regular sampling in shift invariant spaces. A simple necessary and sufficient condition for regular sampling in shift invariant spaces is attained. Furthermore, an improved estimate for the pertur...... hiện toàn bộ
#Signal sampling #Signal reconstruction #Spline functions #Wavelet transforms