scholarly journals On Low Rank Matrix Approximations with Applications to Synthesis Problem in Compressed Sensing

2011 ◽  
Vol 32 (3) ◽  
pp. 1019-1029 ◽  
Author(s):  
Anatoli Juditsky ◽  
Fatma Kilinç karzan ◽  
Arkadi Nemirovski
Keyword(s):  
Compressed Sensing ◽  
Synthesis Problem ◽  
Low Rank ◽  
Rank Matrix ◽  
Low Rank Matrix ◽  
Matrix Approximations

scholarly journals Quantization for low-rank matrix recovery

2018 ◽  
Vol 8 (1) ◽  
pp. 161-180
Author(s):  
Eric Lybrand ◽  
Rayan Saab
Keyword(s):  
Compressed Sensing ◽  
Reconstruction Error ◽  
Linear Operators ◽  
Low Rank ◽  
Quantization Scheme ◽  
Reconstruction Algorithms ◽  
Finite Frame ◽  
Rank Matrix ◽  
Band Limited ◽  
Low Rank Matrix

Abstract We study Sigma–Delta $(\varSigma\!\varDelta) $ quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the oversampling factor, and we leverage our results to obtain root-exponential accuracy by optimizing over the choice of quantization scheme. Additionally, we show that a random encoding scheme, applied to the quantized measurements, yields a near-optimal exponential bit rate. As an added benefit, our schemes are robust both to noise and to deviations from the low-rank assumption. In short, we provide a full generalization of analogous results, obtained in the classical setup of band-limited function acquisition, and more recently, in the finite frame and compressed sensing setups to the case of low-rank matrices sampled with sub-Gaussian linear operators. Finally, we believe our techniques for generalizing results from the compressed sensing setup to the analogous low-rank matrix setup is applicable to other quantization schemes.

scholarly journals Subspace-Orbit Randomized Decomposition for Low-Rank Matrix Approximations

2018 ◽  
Vol 66 (16) ◽  
pp. 4409-4424 ◽  
Author(s):  
Maboud Farzaneh Kaloorazi ◽  
Rodrigo C. de Lamare
Keyword(s):  
Low Rank ◽  
Rank Matrix ◽  
Low Rank Matrix ◽  
Matrix Approximations

Low-rank matrix approximations for Coherent point drift

2015 ◽  
Vol 52 ◽  
pp. 53-58 ◽  
Author(s):  
Ján Dupej ◽  
Václav Krajíček ◽  
Josef Pelikán
Keyword(s):  
Low Rank ◽  
Rank Matrix ◽  
Coherent Point Drift ◽  
Low Rank Matrix ◽  
Matrix Approximations

From Compressed Sensing to Low-rank Matrix Recovery: Theory and Applications

2013 ◽  
Vol 39 (7) ◽  
pp. 981-994 ◽  
Author(s):  
Yi-Gang PENG ◽  
Jin-Li SUO ◽  
Qiong-Hai DAI ◽  
Wen-Li XU
Keyword(s):  
Compressed Sensing ◽  
Low Rank ◽  
Matrix Recovery ◽  
Rank Matrix ◽  
Low Rank Matrix Recovery ◽  
Low Rank Matrix
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