Best Basis Selection for Approximation in L p

Best Basis Selection for Approximation in Lp

We study the approximation of a function class F in Lp by choosing first a basis B and then using n-term approximation with the elements of B. Into the competition for best bases we enter all greedy (i.e. democratic and unconditional [20]) bases for Lp. We show that if the function class F is well oriented with respect to a particular basis B then, in a certain sense, this basis is the best cho...

Some Results on p-Best Approximation in Vector Spaces

Best Approximation in TVS

In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.

Measures and algorithms for best basis selection

A general framework based on majorization, Schur-concavity, and concavity is given that facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed diversity measures useful for best basis selection. Admissible sparsity measures are given by the Schur-concave functions, which are the class of functions consistent with the partial ordering on vecto...

Forward Sequential Algorithms for Best Basis Selection∗

Recently, the problem of signal representation in terms of basis vectors from a large, ”overcomplete”, spanning dictionary has been the focus of much research. Achieving a succinct, or ”sparse”, representation is known as the problem of best basis representation. We consider methods which seek to solve this problem by sequentially building up a basis set for the signal. Three distinct algorithm...