High-Dimensional Confidence Regions in Sparse MRI
Frederik Hoppe, Felix Krahmer, Claudio Mayrink Verdun, Marion I. Menzel, Holger Rauhut
Abstract
One of the most promising solutions for uncertainty quantification in high-dimensional statistics is the debiased LASSO that relies on unconstrained ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -minimization. The initial works focused on real Gaussian designs as a toy model for this problem. However, in medical imaging applications, such as compressive sensing for MRI, the measurement system is represented by a (subsampled) complex Fourier matrix. The purpose of this work is to extend the method to the MRI case in order to construct confidence intervals for each pixel of an MR image. We show that a sufficient amount of data is $n \gtrsim \max \left\{ {{s_0}{{\log }^2}{s_0}\log p,{s_0}{{\log }^2}p} \right\}$.
BibTeX
@inproceedings{icassp2023_highdimensionalc,
title = {High-Dimensional Confidence Regions in Sparse MRI},
author = {Frederik Hoppe and Felix Krahmer and Claudio Mayrink Verdun and Marion I. Menzel and Holger Rauhut},
booktitle = {ICASSP 2023},
year = {2023}
}