Non-uniform B-spline dictionaries on a compact interval are discussed in the context of sparse signal representation. For each given partition, dictionaries of B-spline functions for the corresponding spline space are built up by dividing the partition into subpartitions and joining together the bases for the concomitant subspaces. The resulting slightly redundant dictionaries are composed of B-spline functions of broader support than those corresponding to the B-spline basis for the identical space. Such dictionaries are meant to assist in the construction of adaptive sparse signal representation through a combination of stepwise optimal greedy techniques.
Bibliographical noteNOTICE: this is the author’s version of a work that was accepted for publication in Signal Processing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Rebollo-Neira, Laura and Xu, Zhiqiang. Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval. Signal Processing, 90, 7 (2010). DOI: 10.1016/j.sigpro.2010.02.004.
- non-uniform spline spaces
- sparse representations
- nonlinear approximations
- spline dictionaries