computational harmonic analysis
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2019 ◽  
Vol 10 (3) ◽  
pp. 221-239
Author(s):  
Enrico Au-Yeung

Abstract The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much lower-dimensional vector space. This is the setting of compressed sensing, where the projection is given by a matrix with many more columns than rows. We introduce a class of random matrices that can be used to reconstruct sparse vectors in this paradigm. These matrices satisfy the restricted isometry property with overwhelming probability. We also discuss an application in dimensionality reduction where we initially discovered this class of matrices.







2009 ◽  
Vol 11 (1) ◽  
pp. 8-18 ◽  
Author(s):  
David L. Donoho ◽  
Arian Maleki ◽  
Inam Ur Rahman ◽  
Morteza Shahram ◽  
Victoria Stodden




2006 ◽  
Vol 20 (2) ◽  
pp. 159-160
Author(s):  
Akram Aldroubi ◽  
Charles Chui




2005 ◽  
Vol 19 (3) ◽  
pp. 283-284
Author(s):  
Akram Aldroubi ◽  
Charles Chui


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