Compressive Identification of Linear Operators

Details Compressive Identification of Linear Operators Compressive Identification of Linear Operators

2011-05-26

arxiv.org/abs/1105.5215v1

Computer Science

Information Theory

To be presented at IEEE Int. Symp. Inf. Theory 2011, St Petersburg, Russia

Scientific paper

We consider the problem of identifying a linear deterministic operator from an input-output measurement. For the large class of continuous (and hence bounded) operators, under additional mild restrictions, we show that stable identifiability is possible if the total support area of the operator's spreading function satisfies D <= 1/2. This result holds for arbitrary (possibly fragmented) support regions of the spreading function, does not impose limitations on the total extent of the support region, and, most importantly, does not require the support region of the spreading function to be known prior to identification. Furthermore, we prove that asking for identifiability of only almost all operators, stable identifiability is possible if D <= 1. This result is surprising as it says that there is no penalty for not knowing the support region of the spreading function prior to identification.

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