# High-Dimensional Confidence Regions in Sparse MRI

arXiv: https://arxiv.org/abs/2407.18964 · HTML: https://mlsanity.com/paper/2407.18964/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 4 of 4)

- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [De-biasing the Lasso: Optimal Sample Size for Gaussian Designs](https://mlsanity.com/paper/1508.02757/) (2015)
- [De-Biasing The Lasso With Degrees-of-Freedom Adjustment](https://mlsanity.com/paper/1902.08885/) (2019)
- [The Restricted Isometry Property of Subsampled Fourier Matrices](https://mlsanity.com/paper/1507.01768/) (2015)

## Abstract (arXiv)

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 s0log2 s0log p, s0 log2 p .