  Modern reconstruction methods for magnetic resonance imaging (MRI) exploit
the spatially varying sensitivity profiles of receive-coil arrays as additional
source of information. This allows to reduce the number of time-consuming
Fourier-encoding steps by undersampling. The receive sensitivities are a priori
unknown and influenced by geometry and electric properties of the (moving)
subject. For optimal results, they need to be estimated jointly with the image
from the same undersampled measurement data. Formulated as an inverse problem,
this leads to a bilinear reconstruction problem related to multi-channel blind
deconvolution. In this work, we will discuss some recently developed approaches
for the solution of this problem.
