Sampling Strategies for Compressive Imaging Under Statistical Noise

International Conference on Sampling Theory and Applications, pp. 1–5

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.

Authors 5

1. Frederik Hoppe Aachen Chair of Mathematics of Information Processing

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Chair of Mathematics of Information Processing,Aachen,Germany

   Chair of Mathematics of Information Processing, RWTH Aachen University, Aachen, Germany

2. Felix Krahmer

   Munich Center for Machine Learning · Technical University of Munich

   Affiliation as printed

   Technical University of Munich,Department of Mathematics,Munich,Germany

   Department of Mathematics, Technical University of Munich, Munich, Germany

   Munich Center for Machine Learning, Munich, Germany

   Munich Data Science Institute, Technical University of Munich

3. Claudio Mayrink Verdun

   Munich Center for Machine Learning · Technical University of Munich

   Affiliation as printed

   Technical University of Munich,Department of Mathematics,Munich,Germany

   Department of Mathematics, Technical University of Munich, Munich, Germany

   Munich Center for Machine Learning, Munich, Germany

4. Marion Irene Menzel

   Technische Hochschule Ingolstadt · Technical University of Munich

   Affiliation as printed

   Technische Hochschule Ingolstadt,AImotion Bavaria,Ingolstadt,Germany

   AImotion Bavaria, Technische Hochschule Ingolstadt, Ingolstadt, Germany

   Department of Physics, Technical University of Munich, Garching, Germany

   GE Healthcare, Munich, Germany

5. Holger Rauhut Aachen Chair of Mathematics of Information Processing

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Chair of Mathematics of Information Processing,Aachen,Germany

   Chair of Mathematics of Information Processing, RWTH Aachen University, Aachen, Germany