High-Dimensional Confidence Regions in Sparse MRI

IEEE International Conference on Acoustics Speech and Signal Processing, pp. 1–5

Abstract

One of the most promising solutions for uncertainty quantification in high-dimensional statistics is the debiased LASSO that relies on unconstrained ℓ1-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 $n \gtrsim \max \left\{ {{s_0}{{\log }^2}{s_0}\log p,{s_0}{{\log }^2}p} \right\}$.

Authors 5

1. Frederik Hoppe Aachen Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Department of Mathematics,Aachen,Germany

   Department of Mathematics, RWTH Aachen University, Aachen, Germany

2. Felix Krahmer

   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

3. Claudio Mayrink Verdun

   Technical University of Munich

   Affiliation as printed

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

   Chair of Theoretical Information Technology, Technical University of Munich, Munich, Germany

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

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Department of Mathematics,Aachen,Germany

   Department of Mathematics, RWTH Aachen University, Aachen, Germany