Super-Resolution of Positive Sources
SIAM Journal on Imaging Sciences(2016)
摘要
In single-molecule microscopy it is necessary to
locate with high precision point sources from noisy observations
of the spectrum of the signal at frequencies capped by ${f_c}$,
which is just about the frequency of natural light. This paper
rigorously establishes that this super-resolution problem can be
solved via linear programming in a stable manner. We prove that
the quality of the reconstruction crucially depends on the
Rayleigh regularity of the support of the signal; that is, on the
maximum number of sources that can occur within a square of side
length about $1/{f_c}$. The theoretical performance guarantee is
complemented with a converse result showing that our simple convex
program is nearly optimal. Finally, numerical experiments
illustrate our methods.
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关键词
super-resolution,single-molecule imaging,diffraction limit,Rayleigh regularity,sparsity,stable reconstruction via convex optimization,42A05,42A15,94A08,94A20,90C05,90C25
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