Sparsity Equivalence of Anisotropic Decompositions

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.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Gitta Kutyniok
• Keywords: CORR 2011, Dimensional Embedded Manifolds, Education, Sparse Approximation, Various Direct Proofs