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The Restricted Isometry Property and Its Implications for Compressed Sensing
Restricted Isometry Property Compressed Sensing
2015/6/17
It is now well-known that one can reconstruct sparse or compressible signals accurately from a very limited number of measurements, possibly contaminated with noise. This technique known as “compresse...
Quantum isometry groups of symmetric groups
quantum group quantum isometry spectral triple Hopf algebra
2011/8/30
Abstract: We identify the quantum isometry groups of spectral triples built on the symmetric groups with length functions arising from the nearest-neighbor transpositions as generators. It turns out t...
Almost-isometry between Teichmüller metric and length-spectra metric on moduli space
Teichm¨uller metric length-spectra metric almost isometry
2011/1/19
We prove an analogue of Farb-Masur’s theorem that the lengthspectra metric on moduli space is “almost isometric” to a simple model V(S) which is induced by the cone metric over the complex of curves. ...
Orthogonal symmetric Toeplitz matrices for compressed sensing: Statistical isometry property
Orthogonal symmetric Toeplitz matrices compressed sensing Statistical isometry property
2011/3/1
Recently, the statistical restricted isometry property (RIP) has been formulated to analyze the performance of deterministic sampling matrices for compressed sensing.
The Galilean Conformal Algebra (GCA) arises in taking the non-relativistic limit of the symmetries of a relativistic Conformal Field Theory in any dimensions. It is known to be infinite-dimensional i...
New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property
New improved Johnson-Lindenstrauss embeddings Restricted Isometry Property
2010/11/29
Consider an m×N matrix with the Restricted Isometry Property of order k and level δ, that is, the norm of any k-sparse vector in RN is preserved to within a multiplicative factor of 1±δ under applic...
Restricted p-isometry property and its application for nonconvex compressive sensing
Compressed sensing lp minimization instance optimality stability
2018/4/19
Compressed sensing is a new scheme which shows the ability to recover sparse signal from fewer measurements, using l1 minimization. Recently, Chartrand and Staneva shown in [7] that the lp minimizatio...