High-Dimensional Confidence Regions in Sparse MRI

Frederik Hoppe; Felix Krahmer; Claudio Mayrink Verdun; Marion I. Menzel; Holger Rauhut

doi:10.1109/ICASSP49357.2023.10096320

High-Dimensional Confidence Regions in Sparse MRI

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

Associate Professorship of Optimization and Data Analysis

RWTH Aachen University
Technical University of Munich
Ingolstadt
GE Healthcare, Germany

Research output: Contribution to journal › Conference article › peer-review

2 Scopus citations

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 ≳ max {s0 log 2 s0 log p, s0 log 2 p}.

Original language	English
Journal	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
DOIs	https://doi.org/10.1109/ICASSP49357.2023.10096320
State	Published - 2023
Event	48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023 - Rhodes Island, Greece Duration: 4 Jun 2023 → 10 Jun 2023

Keywords

MRI
compressed sensing
confidence regions
debiased LASSO

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10.1109/ICASSP49357.2023.10096320

Cite this

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title = "High-Dimensional Confidence Regions in Sparse MRI",

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 ≳ max \{s0 log 2 s0 log p, s0 log 2 p\}.",

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author = "Frederik Hoppe and Felix Krahmer and \{Mayrink Verdun\}, Claudio and Menzel, \{Marion I.\} and Holger Rauhut",

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T1 - High-Dimensional Confidence Regions in Sparse MRI

AU - Hoppe, Frederik

AU - Krahmer, Felix

AU - Mayrink Verdun, Claudio

AU - Menzel, Marion I.

AU - Rauhut, Holger

PY - 2023

Y1 - 2023

N2 - 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 ≳ max {s0 log 2 s0 log p, s0 log 2 p}.

AB - 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 ≳ max {s0 log 2 s0 log p, s0 log 2 p}.

KW - MRI

KW - compressed sensing

KW - confidence regions

KW - debiased LASSO

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DO - 10.1109/ICASSP49357.2023.10096320

M3 - Conference article

AN - SCOPUS:85172437640

SN - 1520-6149

JO - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

JF - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

T2 - 48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023

Y2 - 4 June 2023 through 10 June 2023

ER -

High-Dimensional Confidence Regions in Sparse MRI

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Keywords

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