Probabilistic Bounds on Error Amplification of Randomly Generated Frames

Hilbert space frames have recently attracted attention in the signal processing community. In this paper, we consider the problem of describing the statistical distribution of the error amplification and lower bound of a frame obtained by randomly picking vectors from a larger frame (the
frame

pool
). The key result of this paper is an analytic bound to the probability of having an error amplification larger than a given value. We also consider the possibility of content reconstruction using an approximate, but efficient, algorithm. The theoretical results are completed by means of numerical experiments.