  Several problems in imaging acquire multiple measurement vectors (MMVs) of
Fourier samples for the same underlying scene. Image recovery techniques from
MMVs aim to exploit the joint sparsity across the measurements in the sparse
domain. This is typically accomplished by extending the use of $\ell_1$
regularization of the sparse domain in the single measurement vector (SMV) case
to using $\ell_{2,1}$ regularization so that the "jointness" can be accounted
for. Although effective, the approach is inherently coupled and therefore
computationally inefficient. The method also does not consider current
approaches in the SMV case that use spatially varying weighted $\ell_1$
regularization term. The recently introduced variance based joint sparsity
(VBJS) recovery method uses the variance across the measurements in the sparse
domain to produce a weighted MMV method that is more accurate and more
efficient than the standard $\ell_{2,1}$ approach. The efficiency is due to the
decoupling of the measurement vectors, with the increased accuracy resulting
from the spatially varying weight. This paper introduces the accelerated VBJS
which reduces computational cost even further by eliminating the requirement to
first approximate the underlying image in order to construct the weights.
Eliminating this preprocessing step moreover reduces the amount of information
lost from the data, so that our method is more accurate. Numerical examples
provided in the paper verify these benefits.
