Magnetic resonance imaging (MRI) is a versatile imaging technique that allows
different contrasts depending on the acquisition parameters. Many clinical
imaging studies acquire MRI data for more than one of these contrasts---such as
for instance T1 and T2 weighted images---which makes the overall scanning
procedure very time consuming. As all of these images show the same underlying
anatomy one can try to omit unnecessary measurements by taking the similarity
into account during reconstruction. We will discuss two modifications of total
variation---based on i) location and ii) direction---that take structural a
priori knowledge into account and reduce to total variation in the degenerate
case when no structural knowledge is available. We solve the resulting convex
minimization problem with the alternating direction method of multipliers that
separates the forward operator from the prior. For both priors the
corresponding proximal operator can be implemented as an extension of the fast
gradient projection method on the dual problem for total variation. We tested
the priors on six data sets that are based on phantoms and real MRI images. In
all test cases exploiting the structural information from the other contrast
yields better results than separate reconstruction with total variation in
terms of standard metrics like peak signal-to-noise ratio and structural
similarity index. Furthermore, we found that exploiting the two dimensional
directional information results in images with well defined edges, superior to
those reconstructed solely using a priori information about the edge location.Engineering and Physical Sciences Research Council (Grant ID: EP/H046410/1)This is the final version of the article. It first appeared from Society for Industrial and Applied Mathematics via http://dx.doi.org/10.1137/15M1047325