Analysis of noise reduction in redundant expansions under distributed processing requirements

We considered signal reconstruction with redundant expansions under distributed processing in noisy environments. Redundant expansions have the ability to reduce noise corrupting the coefficients, but distributed processing schemes will not be able to take full advantage of the redundancy present. We apply frame theory and a generalization called "frames of subspaces" to find conditions when distributed reconstruction suffers no loss in noise reduction ability, and we bound performance loss in more general cases.