Aldroubi, Akram; Huang, L; Krishtal, I; Lederman, Roy R Dynamical sampling with random noise Inproceedings 2017 International Conference on Sampling Theory and Applications (SampTA), pp. 409–412, 2017. Abstract | Links | BibTeX | Tags: Dynamical Sampling, evolution operator, signal reconstruction, signal recovery, signal sampling @inproceedings{aldroubi_dynamical_2017, title = {Dynamical sampling with random noise}, author = {Akram Aldroubi and L Huang and I Krishtal and Roy R Lederman}, doi = {10.1109/SAMPTA.2017.8024372}, year = {2017}, date = {2017-01-01}, booktitle = {2017 International Conference on Sampling Theory and Applications (SampTA)}, pages = {409--412}, abstract = {In this paper we consider a system of dynamical sampling, i.e. sampling a signal f that evolves in time under the action of an evolution operator A. We discuss the error in the recovery of the original signal when the samples are corrupted by additive, independent and identically distributed (i.i.d) noise. We focus on the study of the mean squared error E(∥ϵn∥22) between the original signal and the reconstructed signal obtained by solving a least squares problem. In the theoretical part, we give a formula for E(∥ϵn∥22) and prove that E(∥ϵn∥22) decreases as the number of the samples increases. In addition, we discuss several numerical experiments that verify the theoretical results.}, keywords = {Dynamical Sampling, evolution operator, signal reconstruction, signal recovery, signal sampling}, pubstate = {published}, tppubtype = {inproceedings} } In this paper we consider a system of dynamical sampling, i.e. sampling a signal f that evolves in time under the action of an evolution operator A. We discuss the error in the recovery of the original signal when the samples are corrupted by additive, independent and identically distributed (i.i.d) noise. We focus on the study of the mean squared error E(∥ϵn∥22) between the original signal and the reconstructed signal obtained by solving a least squares problem. In the theoretical part, we give a formula for E(∥ϵn∥22) and prove that E(∥ϵn∥22) decreases as the number of the samples increases. In addition, we discuss several numerical experiments that verify the theoretical results. |