期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2003
卷号：100
期号：5
页码：2197-2202
DOI：10.1073/pnas.0437847100
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Given a dictionary D={dk} of vectors dk, we seek to represent a signal S as a linear combination S={sum}k {gamma}(k)dk, with scalar coefficients{gamma} (k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered the special case where D is an overcomplete system consisting of exactly two orthobases and has shown that, under a condition of mutual incoherence of the two bases, and assuming that S has a sufficiently sparse representation, this representation is unique and can be found by solving a convex optimization problem: specifically, minimizing the {ell}1 norm of the coefficients{gamma} . In this article, we obtain parallel results in a more general setting, where the dictionary D can arise from two or several bases, frames, or even less structured systems. We sketch three applications: separating linear features from planar ones in 3D data, noncooperative multiuser encoding, and identification of over-complete independent component models.
