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Sparse Reconstruction of Signals in hardy Spaces
Shuang Li; Tao Qian
2013-05-06
Source PublicationQuaternion and Clifford Fourier Transforms and Wavelets
PublisherBirkhäuser, Basel
Abstract

 

Mathematically, signals can be seen as functions in certain spaces. And processing is more efficient in a sparse representation where few coefficients reveal the information. Such representations are constructed by decomposing signals into elementary waveforms. A set of all elementary waveforms is called a dictionary. In this chapter, we introduce a new kind of sparse representation of signals in Hardy space  H2(D)via the compressed sensing (CS) technique with the dictionary D={ea:ea(z)=1−|a|2√1−a¯z,a∈D}.D={ea:ea(z)=1−|a|21−a¯z,a∈D}.

where ⅅ denotes the unit disk. In addition, we give examples exhibiting the algorithm.

KeywordHardy Space Compressed Sensing Analytic Signals Reproducing Kernels Sparse Representation Redundant Dictionary L1minimization
DOIhttps://doi.org/10.1007/978-3-0348-0603-9_16
Language英语
ISBN978-3-0348-0602-2
Fulltext Access
Citation statistics
Document TypeBook chapter
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
AffiliationDepartment of Mathematics,University of Macau,Macau,People’s Republic of China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Shuang Li,Tao Qian. Sparse Reconstruction of Signals in hardy Spaces:Birkhäuser, Basel,2013.
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