Sampling strategies for compressive imaging under statistical noise

Frederik Hoppe, Felix Krahmer, Claudio Mayrink Verdun, Marion Menzel, Holger Rauhut

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.

Submission Type: Full Paper