Fusion frames and randomized subspace actions
Provides theoretical guarantees for optimal probability distributions in randomized subspace action algorithms, benefiting researchers working on fusion frame signal recovery.
The paper studies randomized subspace action algorithms for fusion frame signal recovery, proving which probability distributions on random fusion frames minimize Kaczmarz bounds and thus provide optimal control on error moment upper bounds. Uniqueness of optimal distributions is also established.
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.