Fast communication: Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval

Authors:
Laura Rebollo-Neira;Zhiqiang Xu
Affiliations:
Mathematics, Aston University, Birmingham B4 7ET, UK;Mathematics, Aston University, Birmingham B4 7ET, UK and LSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
Venue:
Signal Processing
Year:
2010

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Abstract

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.