  We consider the recovery of a low rank and jointly sparse matrix from under
sampled measurements of its columns. This problem is highly relevant in the
recovery of dynamic MRI data with high spatio-temporal resolution, where each
column of the matrix corresponds to a frame in the image time series; the
matrix is highly low-rank since the frames are highly correlated. Similarly the
non-zero locations of the matrix in appropriate transform/frame domains (e.g.
wavelet, gradient) are roughly the same in different frame. The superset of the
support can be safely assumed to be jointly sparse. Unlike the classical
multiple measurement vector (MMV) setup that measures all the snapshots using
the same matrix, we consider each snapshot to be measured using a different
measurement matrix. We show that this approach reduces the total number of
measurements, especially when the rank of the matrix is much smaller than than
its sparsity. Our experiments in the context of dynamic imaging shows that this
approach is very useful in realizing free breathing cardiac MRI.
