TY - GEN
T1 - Recovery guarantees for Compressed Sensing with unknown errors
AU - Brugiapaglia, Simone
AU - Adcock, Ben
AU - Archibald, Richard K.
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - From a numerical analysis perspective, assessing the robustness of ℓ1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori estimates of the noise, which can be very hard to obtain in practice, especially when the noise term also includes unknown discrepancies between the finite model and data. In this work, we study the performance of ℓ1-minimization when these estimates are not available, providing robust recovery guarantees for quadratically constrained basis pursuit and random sampling in bounded orthonormal systems. Several applications of this work are approximation of high-dimensional functions, infinite-dimensional sparse regularization for inverse problems, and fast algorithms for non-Cartesian Magnetic Resonance Imaging.
AB - From a numerical analysis perspective, assessing the robustness of ℓ1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori estimates of the noise, which can be very hard to obtain in practice, especially when the noise term also includes unknown discrepancies between the finite model and data. In this work, we study the performance of ℓ1-minimization when these estimates are not available, providing robust recovery guarantees for quadratically constrained basis pursuit and random sampling in bounded orthonormal systems. Several applications of this work are approximation of high-dimensional functions, infinite-dimensional sparse regularization for inverse problems, and fast algorithms for non-Cartesian Magnetic Resonance Imaging.
UR - http://www.scopus.com/inward/record.url?scp=85031698548&partnerID=8YFLogxK
U2 - 10.1109/SAMPTA.2017.8024421
DO - 10.1109/SAMPTA.2017.8024421
M3 - Conference contribution
AN - SCOPUS:85031698548
T3 - 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017
SP - 533
EP - 537
BT - 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017
A2 - Anbarjafari, Gholamreza
A2 - Kivinukk, Andi
A2 - Tamberg, Gert
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 12th International Conference on Sampling Theory and Applications, SampTA 2017
Y2 - 3 July 2017 through 7 July 2017
ER -