Dual-tree wavelet decompositions have recently gained much popularity, mainly
due to their ability to provide an accurate directional analysis of images
combined with a reduced redundancy. When the decomposition of a random process
is performed -- which occurs in particular when an additive noise is corrupting
the signal to be analyzed -- it is useful to characterize the statistical
properties of the dual-tree wavelet coefficients of this process.

Parallel MRI is a fast imaging technique that enables the acquisition of
highly resolved images in space. It relies on $k$-space undersampling and
multiple receiver coils with complementary sensitivity profiles in order to
reconstruct a full Field-Of-View (FOV) image. The performance of parallel
imaging mainly depends on the reconstruction algorithm, which can proceed
either in the original $k$-space (GRAPPA, SMASH) or in the image domain
(SENSE-like methods).

To reduce scanning time and/or improve spatial/temporal resolution in some
MRI applications, parallel MRI (pMRI) acquisition techniques with multiple
coils acquisition have emerged since the early 1990s as powerful 3D imaging
methods that allow faster acquisition of reduced Field of View (FOV) images. In
these techniques, the full FOV image has to be reconstructed from the resulting
acquired undersampled k-space data. To this end, several reconstruction
techniques have been proposed such as the widely-used SENSE method.