High-Dimensional Confidence Regions in Sparse MRI
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914889633628160 |
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| author | Hoppe, Frederik Krahmer, Felix Verdun, Claudio Mayrink Menzel, Marion Rauhut, Holger |
| author_facet | Hoppe, Frederik Krahmer, Felix Verdun, Claudio Mayrink Menzel, Marion Rauhut, Holger |
| contents | One of the most promising solutions for uncertainty quantification in high-dimensional statistics is the debiased LASSO that relies on unconstrained $\ell_1$-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 $n \gtrsim \max\{ s_0\log^2 s_0\log p, s_0 \log^2 p \}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-Dimensional Confidence Regions in Sparse MRI Hoppe, Frederik Krahmer, Felix Verdun, Claudio Mayrink Menzel, Marion Rauhut, Holger Signal Processing Information Theory Machine Learning Image and Video Processing Statistics Theory Applications One of the most promising solutions for uncertainty quantification in high-dimensional statistics is the debiased LASSO that relies on unconstrained $\ell_1$-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 $n \gtrsim \max\{ s_0\log^2 s_0\log p, s_0 \log^2 p \}$. |
| title | High-Dimensional Confidence Regions in Sparse MRI |
| topic | Signal Processing Information Theory Machine Learning Image and Video Processing Statistics Theory Applications |
| url | https://arxiv.org/abs/2407.18964 |