  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 $n \gtrsim
\max\{ s_0\log^2 s_0\log p, s_0 \log^2 p \}$.
