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Several problems in imaging acquire multiple measurement vectors (MMVs) ofFourier samples for the same underlying scene. Image recovery techniques fromMMVs aim to exploit the joint sparsity across the measurements in the sparsedomain. This is typically accomplished by extending the use of $\ell_1$regularization of the sparse domain in the single measurement vector (SMV) caseto using $\ell_{2,1}$ regularization so that the "jointness" can be accountedfor. Although effective, the approach is inherently coupled and thereforecomputationally inefficient. The method also does not consider currentapproaches 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 sparsedomain to produce a weighted MMV method that is more accurate and moreefficient than the standard $\ell_{2,1}$ approach. The efficiency is due to thedecoupling of the measurement vectors, with the increased accuracy resultingfrom the spatially varying weight. This paper introduces the accelerated VBJSwhich reduces computational cost even further by eliminating the requirement tofirst approximate the underlying image in order to construct the weights.Eliminating this preprocessing step moreover reduces the amount of informationlost from the data, so that our method is more accurate. Numerical examplesprovided in the paper verify these benefits.

Accelerated Variance Based Joint Sparsity Recovery of Images from Fourier Data