Stable Super-Resolution of Positive Sources

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Veniamin Morgenshtern
Stanford University
Thu, 02/05/2015 - 11:00am - 12:00pm
Jack Xin

In single-molecule microscopy it is necessary to reconstruct a signal that consists of positive point sources from noisy observations of the spectrum of the signal in the low-frequency band [−fc,fc]. It is shown that the problem can be solved using convex optimization in a stable fashion. The stability of reconstruction depends on Rayleigh-regularity of the support of the signal, i.e., on how many point sources can occur within an interval of length 1.87/fc. The stability estimate is complimented by a converse result: the performance of convex algorithm is nearly optimal. The results are generalized to multi-dimension signals. Applications in microscopy are briefly discussed.