TY - GEN

T1 - Sampling Strategies for Compressive Imaging Under Statistical Noise

AU - Hoppe, Frederik

AU - Krahmer, Felix

AU - Verdun, Claudio Mayrink

AU - Menzel, Marion I.

AU - Rauhut, Holger

N1 - Publisher Copyright:
© 2023 IEEE.

PY - 2023

Y1 - 2023

N2 - Most of the compressive sensing literature in signal processing assumes that the noise present in the measurement has an adversarial nature, i.e., it is bounded in a certain norm. At the same time, the randomization introduced in the sampling scheme usually assumes an i.i.d. model where rows are sampled with replacement. In this case, if a sample is measured a second time, it does not add additional information. For many applications, where the statistical noise model is a more accurate one, this is not true anymore since a second noisy sample comes with an independent realization of the noise, so there is a fundamental difference between sampling with and without replacement. Therefore, a more careful analysis must be performed. In this short note, we illustrate how one can mathematically transition between these two noise models. This transition gives rise to a weighted LASSO reconstruction method for sampling without replacement, which numerically improves the solution of high-dimensional compressive imaging problems.

AB - Most of the compressive sensing literature in signal processing assumes that the noise present in the measurement has an adversarial nature, i.e., it is bounded in a certain norm. At the same time, the randomization introduced in the sampling scheme usually assumes an i.i.d. model where rows are sampled with replacement. In this case, if a sample is measured a second time, it does not add additional information. For many applications, where the statistical noise model is a more accurate one, this is not true anymore since a second noisy sample comes with an independent realization of the noise, so there is a fundamental difference between sampling with and without replacement. Therefore, a more careful analysis must be performed. In this short note, we illustrate how one can mathematically transition between these two noise models. This transition gives rise to a weighted LASSO reconstruction method for sampling without replacement, which numerically improves the solution of high-dimensional compressive imaging problems.

KW - LASSO

KW - compressed sensing

KW - non-uniform sampling

KW - sparse regression

KW - statistical noise

UR - http://www.scopus.com/inward/record.url?scp=85174269186&partnerID=8YFLogxK

U2 - 10.1109/SampTA59647.2023.10301372

DO - 10.1109/SampTA59647.2023.10301372

M3 - Conference contribution

AN - SCOPUS:85174269186

T3 - 2023 International Conference on Sampling Theory and Applications, SampTA 2023

BT - 2023 International Conference on Sampling Theory and Applications, SampTA 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2023 International Conference on Sampling Theory and Applications, SampTA 2023

Y2 - 10 July 2023 through 14 July 2023

ER -