55 research outputs found
GESPAR: Efficient Phase Retrieval of Sparse Signals
We consider the problem of phase retrieval, namely, recovery of a signal from
the magnitude of its Fourier transform, or of any other linear transform. Due
to the loss of the Fourier phase information, this problem is ill-posed.
Therefore, prior information on the signal is needed in order to enable its
recovery. In this work we consider the case in which the signal is known to be
sparse, i.e., it consists of a small number of nonzero elements in an
appropriate basis. We propose a fast local search method for recovering a
sparse signal from measurements of its Fourier transform (or other linear
transform) magnitude which we refer to as GESPAR: GrEedy Sparse PhAse
Retrieval. Our algorithm does not require matrix lifting, unlike previous
approaches, and therefore is potentially suitable for large scale problems such
as images. Simulation results indicate that GESPAR is fast and more accurate
than existing techniques in a variety of settings.Comment: Generalized to non-Fourier measurements, added 2D simulations, and a
theorem for convergence to stationary poin
Phase Retrieval with Application to Optical Imaging
This review article provides a contemporary overview of phase retrieval in
optical imaging, linking the relevant optical physics to the information
processing methods and algorithms. Its purpose is to describe the current state
of the art in this area, identify challenges, and suggest vision and areas
where signal processing methods can have a large impact on optical imaging and
on the world of imaging at large, with applications in a variety of fields
ranging from biology and chemistry to physics and engineering
Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing
We demonstrate that sub-wavelength optical images borne on
partially-spatially-incoherent light can be recovered, from their far-field or
from the blurred image, given the prior knowledge that the image is sparse, and
only that. The reconstruction method relies on the recently demonstrated
sparsity-based sub-wavelength imaging. However, for
partially-spatially-incoherent light, the relation between the measurements and
the image is quadratic, yielding non-convex measurement equations that do not
conform to previously used techniques. Consequently, we demonstrate new
algorithmic methodology, referred to as quadratic compressed sensing, which can
be applied to a range of other problems involving information recovery from
partial correlation measurements, including when the correlation function has
local dependencies. Specifically for microscopy, this method can be readily
extended to white light microscopes with the additional knowledge of the light
source spectrum.Comment: 16 page
Deep-STORM: super-resolution single-molecule microscopy by deep learning
We present an ultra-fast, precise, parameter-free method, which we term
Deep-STORM, for obtaining super-resolution images from stochastically-blinking
emitters, such as fluorescent molecules used for localization microscopy.
Deep-STORM uses a deep convolutional neural network that can be trained on
simulated data or experimental measurements, both of which are demonstrated.
The method achieves state-of-the-art resolution under challenging
signal-to-noise conditions and high emitter densities, and is significantly
faster than existing approaches. Additionally, no prior information on the
shape of the underlying structure is required, making the method applicable to
any blinking data-set. We validate our approach by super-resolution image
reconstruction of simulated and experimentally obtained data.Comment: 7 pages, added code download reference and DOI for the journal
versio
DeepSTORM3D: dense three dimensional localization microscopy and point spread function design by deep learning
Localization microscopy is an imaging technique in which the positions of
individual nanoscale point emitters (e.g. fluorescent molecules) are determined
at high precision from their images. This is the key ingredient in
single/multiple-particle-tracking and several super-resolution microscopy
approaches. Localization in three-dimensions (3D) can be performed by modifying
the image that a point-source creates on the camera, namely, the point-spread
function (PSF). The PSF is engineered using additional optical elements to vary
distinctively with the depth of the point-source. However, localizing multiple
adjacent emitters in 3D poses a significant algorithmic challenge, due to the
lateral overlap of their PSFs. Here, we train a neural network to receive an
image containing densely overlapping PSFs of multiple emitters over a large
axial range and output a list of their 3D positions. Furthermore, we then use
the network to design the optimal PSF for the multi-emitter case. We
demonstrate our approach numerically as well as experimentally by 3D STORM
imaging of mitochondria, and volumetric imaging of dozens of
fluorescently-labeled telomeres occupying a mammalian nucleus in a single
snapshot.Comment: main text: 9 pages, 5 figures, supplementary information: 29 pages,
20 figure
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