  A randomized subspace action algorithm is investigated for fusion frame
signal recovery problems. It is noted that Kaczmarz bounds provide upper bounds
on the algorithm's error moments. The main question of which probability
distributions on a random fusion frame lead to provably fast convergence is
addressed. In particular, it is proven which distributions give minimal
Kaczmarz bounds, and hence give best control on error moment upper bounds
arising from Kaczmarz bounds. Uniqueness of the optimal distributions is also
addressed.
