56,986 research outputs found
Phase retrieval from power spectra of masked signals
In diffraction imaging, one is tasked with reconstructing a signal from its
power spectrum. To resolve the ambiguity in this inverse problem, one might
invoke prior knowledge about the signal, but phase retrieval algorithms in this
vein have found limited success. One alternative is to create redundancy in the
measurement process by illuminating the signal multiple times, distorting the
signal each time with a different mask. Despite several recent advances in
phase retrieval, the community has yet to construct an ensemble of masks which
uniquely determines all signals and admits an efficient reconstruction
algorithm. In this paper, we leverage the recently proposed polarization method
to construct such an ensemble. We also present numerical simulations to
illustrate the stability of the polarization method in this setting. In
comparison to a state-of-the-art phase retrieval algorithm known as PhaseLift,
we find that polarization is much faster with comparable stability.Comment: 18 pages, 3 figure
PhasePack: A Phase Retrieval Library
Phase retrieval deals with the estimation of complex-valued signals solely
from the magnitudes of linear measurements. While there has been a recent
explosion in the development of phase retrieval algorithms, the lack of a
common interface has made it difficult to compare new methods against the
state-of-the-art. The purpose of PhasePack is to create a common software
interface for a wide range of phase retrieval algorithms and to provide a
common testbed using both synthetic data and empirical imaging datasets.
PhasePack is able to benchmark a large number of recent phase retrieval methods
against one another to generate comparisons using a range of different
performance metrics. The software package handles single method testing as well
as multiple method comparisons.
The algorithm implementations in PhasePack differ slightly from their
original descriptions in the literature in order to achieve faster speed and
improved robustness. In particular, PhasePack uses adaptive stepsizes,
line-search methods, and fast eigensolvers to speed up and automate
convergence
Spectral pre-modulation of training examples enhances the spatial resolution of the Phase Extraction Neural Network (PhENN)
The Phase Extraction Neural Network (PhENN) is a computational architecture,
based on deep machine learning, for lens-less quantitative phase retrieval from
raw intensity data. PhENN is a deep convolutional neural network trained
through examples consisting of pairs of true phase objects and their
corresponding intensity diffraction patterns; thereafter, given a test raw
intensity pattern PhENN is capable of reconstructing the original phase object
robustly, in many cases even for objects outside the database where the
training examples were drawn from. Here, we show that the spatial frequency
content of the training examples is an important factor limiting PhENN's
spatial frequency response. For example, if the training database is relatively
sparse in high spatial frequencies, as most natural scenes are, PhENN's ability
to resolve fine spatial features in test patterns will be correspondingly
limited. To combat this issue, we propose "flattening" the power spectral
density of the training examples before presenting them to PhENN. For phase
objects following the statistics of natural scenes, we demonstrate
experimentally that the spectral pre-modulation method enhances the spatial
resolution of PhENN by a factor of 2.Comment: 12 pages, 10 figure
Illumination strategies for intensity-only imaging
We propose a new strategy for narrow band, active array imaging of localized
scat- terers when only the intensities are recorded and measured at the array.
We consider a homogeneous medium so that wave propagation is fully coherent. We
show that imaging with intensity-only measurements can be carried out using the
time reversal operator of the imaging system, which can be obtained from
intensity measurements using an appropriate illumination strategy and the
polarization identity. Once the time reversal operator has been obtained, we
show that the images can be formed using its singular value decomposition
(SVD). We use two SVD-based methods to image the scatterers. The proposed
approach is simple and efficient. It does not need prior information about the
sought image, and guarantees exact recovery in the noise-free case.
Furthermore, it is robust with respect to additive noise. Detailed numerical
simulations illustrate the performance of the proposed imaging strategy when
only the intensities are captured
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