  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. However,
the reconstructed image generally presents artifacts when perturbations occur
in both the measured data and the estimated coil sensitivity maps. In this
paper, we aim at achieving good reconstructed image quality when using low
magnetic field and high reduction factor. Under these severe experimental
conditions, neither the SENSE method nor the Tikhonov regularization in the
image domain give convincing results. To this aim, we present a novel method
for SENSE-based reconstruction which proceeds with regularization in the
complex wavelet domain. To further enhance the reconstructed image quality,
local convex constraints are added in the regularization process. In vivo
experiments carried out on Gradient-Echo (GRE) anatomical and Echo-Planar
Imaging (EPI) functional MRI data at 1.5 Tesla indicate that the proposed
algorithm provides reconstructed images with reduced artifacts for high
reduction factor.
