  The ability of having a sparse representation for a certain class of signals
has many applications in data analysis, image processing, and other research
fields. Among sparse representations, the cosparse analysis model has recently
gained increasing interest. Many signals exhibit a multidimensional structure,
e.g. images or three-dimensional MRI scans. Most data analysis and learning
algorithms use vectorized signals and thereby do not account for this
underlying structure. The drawback of not taking the inherent structure into
account is a dramatic increase in computational cost. We propose an algorithm
for learning a cosparse Analysis Operator that adheres to the preexisting
structure of the data, and thus allows for a very efficient implementation.
This is achieved by enforcing a separable structure on the learned operator.
Our learning algorithm is able to deal with multidimensional data of arbitrary
order. We evaluate our method on volumetric data at the example of
three-dimensional MRI scans.
