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


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
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Document TypeBook chapter
CollectionFaculty of Science and Technology
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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