Geodesic
Bounding the restricted isometry constants for a~tight frame
Sbornik. Mathematics, Tome 208 (2017) no. 11, pp. 1646-1660

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The standard restricted isometry condition for a tight frame (frequently used as a compressed sensing matrix) is considered, and deterministic lower bounds are obtained for the constants involved. These bounds depend only on the matrix sizes and sparsity level. The sharpness of the new estimates is discussed as well as their interplay with the existing compressed sensing theory. Bibliography: 18 titles.
Keywords: compressed sensing, $k$-equivolume tight frame, restricted isometry property, Jacobi polynomials, extreme roots. 
@article{SM_2017_208_11_a4,
     author = {I. E. Kaporin},
     title = {Bounding the restricted isometry constants for a~tight frame},
     journal = {Sbornik. Mathematics},
     pages = {1646--1660},
     publisher = {mathdoc},
     volume = {208},
     number = {11},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_11_a4/}
}
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I. E. Kaporin. Bounding the restricted isometry constants for a~tight frame. Sbornik. Mathematics, Tome 208 (2017) no. 11, pp. 1646-1660. http://geodesic.mathdoc.fr/item/SM_2017_208_11_a4/