Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematical foundation of sparsity-based multi-illumination
  super-resolution   It is well-known that the resolution of a traditional optical imaging system
is limited by the so-called Rayleigh limit, which is of several hundreds of
nanometers. By employing fluorescence techniques, modern microscopic methods
can resolve point scatterers separated much lower than the Rayleigh limit.
Localization-based fluorescence subwavelength imaging techniques such as PALM
and STORM can achieve a spatial resolution of several tens of nanometers.
However, these techniques have limited temporal resolution as they require tens
of thousands of exposures. Employing sparsity-based models and recovery
algorithms is a natural way to reduce the number of exposures and hence obtain
high temporal resolution. Recently, a new multi-illumination imaging technique
called Brownian Excitation Amplitude Modulation microscopy (BEAM) is
introduced. BEAM achieves a threefold resolution improvement by applying a
compressive sensing recovery algorithm over only few frames. Motivated by BEAM,
our aim in this paper is to pioneer the mathematical foundation for
sparsity-based multi-illumination super-resolution. We consider several
diffraction-limited images from samples exposed to different illumination
patterns and recover the source by considering the sparsest solution. We
estimate the minimum separation distance between point scatterers so that they
could be stably recovered. By this estimation, we reveal the dependence of the
resolution on the cut-off frequency of the imaging system, the SNR, the
sparsity of point scatterers, and the incoherence of illumination patterns. Our
theory particularly highlights the importance of the high incoherence of
illumination patterns in enhancing the resolution. It also demonstrates that
super-resolution can be achieved using sparsity-based multi-illumination
imaging with very few frames, whereby the spatio-temporal super-resolution
becomes possible.

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph