Sampling Strategies for Compressive Imaging Under Statistical Noise

MCML Authors

Felix Krahmer

Prof. Dr.

Principal Investigator

Optimization & Data Analysis

Claudio Mayrink Verdun

Dr.

* Former Member

→ Group Felix Krahmer
 Optimization & Data Analysis

Holger Rauhut

Prof. Dr.

Principal Investigator

Mathematical Data Science and Artificial Intelligence

Abstract

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.

inproceedings

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SampTA 2023

14th International Conference on Sampling Theory and Applications. Yale, CT, USA, Jul 10-14, 2023.

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Authors

F. Hoppe • F. Krahmer • C. M. Verdun • M. I. Menzel • H. Rauhut

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Links

DOI

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Research Area

 A2 | Mathematical Foundations