Randomized Subspace Actions and Fusion Frames

A randomized subspace action algorithm is investigated for fusion frame signal recovery problems and for the problem of recovering a signal from projections onto random subspaces. 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 subspace lead to provably fast convergence is addressed. In particular, it is proved 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.

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