Sparsity Equivalence of Anisotropic Decompositions

Details Sparsity Equivalence of Anisotropic Decompositions Sparsity Equivalence of Anisotropic Decompositions

2011-01-19

arxiv.org/abs/1101.3638v1

Mathematics

Functional Analysis

20 pages, 4 figures

Scientific paper

Anisotropic decompositions using representation systems such as curvelets, contourlet, or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse approximations of functions exhibiting singularities on lower dimensional embedded manifolds. The literature now contains various direct proofs of this fact and of related sparse approximation results. However, it seems quite cumbersome to prove such a canon of results for each system separately, while many of the systems exhibit certain similarities. In this paper, with the introduction of the concept of sparsity equivalence, we aim to provide a framework which allows categorization of the ability for sparse approximations of representation systems. This framework, in particular, enables transferring results on sparse approximations from one system to another. We demonstrate this concept for the example of curvelets and shearlets, and discuss how this viewpoint immediately leads to novel results for both systems.

Affiliated with

Also associated with

No associations

Rating

Sparsity Equivalence of Anisotropic Decompositions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sparsity Equivalence of Anisotropic Decompositions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sparsity Equivalence of Anisotropic Decompositions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-156122