12 research outputs found
Synthetic aperture imaging with intensity-only data
We consider imaging the reflectivity of scatterers from intensity-only data
recorded by a single moving transducer that both emits and receives signals,
forming a synthetic aperture. By exploiting frequency illumination diversity,
we obtain multiple intensity measurements at each location, from which we
determine field cross-correlations using an appropriate phase controlled
illumination strategy and the inner product polarization identity. The field
cross-correlations obtained this way do not, however, provide all the missing
phase information because they are determined up to a phase that depends on the
receiver's location. The main result of this paper is an algorithm with which
we recover the field cross-correlations up to a single phase that is common to
all the data measured over the synthetic aperture, so all the data are
synchronized. Thus, we can image coherently with data over all frequencies and
measurement locations as if full phase information was recorded
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Synthetic Aperture Imaging With Intensity-Only Data.
We consider imaging the reflectivity of scatterers from intensity-only data
recorded by a single moving transducer that both emits and receives signals,
forming a synthetic aperture. By exploiting frequency illumination diversity,
we obtain multiple intensity measurements at each location, from which we
determine field cross-correlations using an appropriate phase controlled
illumination strategy and the inner product polarization identity. The field
cross-correlations obtained this way do not, however, provide all the missing
phase information because they are determined up to a phase that depends on the
receiver's location. The main result of this paper is an algorithm with which
we recover the field cross-correlations up to a single phase that is common to
all the data measured over the synthetic aperture, so all the data are
synchronized. Thus, we can image coherently with data over all frequencies and
measurement locations as if full phase information was recorded
Hadamard Wirtinger Flow for Sparse Phase Retrieval
We consider the problem of reconstructing an -dimensional -sparse
signal from a set of noiseless magnitude-only measurements. Formulating the
problem as an unregularized empirical risk minimization task, we study the
sample complexity performance of gradient descent with Hadamard
parametrization, which we call Hadamard Wirtinger flow (HWF). Provided
knowledge of the signal sparsity , we prove that a single step of HWF is
able to recover the support from (modulo logarithmic term)
samples, where is the largest component of the signal in magnitude.
This support recovery procedure can be used to initialize existing
reconstruction methods and yields algorithms with total runtime proportional to
the cost of reading the data and improved sample complexity, which is linear in
when the signal contains at least one large component. We numerically
investigate the performance of HWF at convergence and show that, while not
requiring any explicit form of regularization nor knowledge of , HWF adapts
to the signal sparsity and reconstructs sparse signals with fewer measurements
than existing gradient based methods
A Stochastic ADMM Algorithm for Large-Scale Ptychography with Weighted Difference of Anisotropic and Isotropic Total Variation
Ptychography, a prevalent imaging technique in fields such as biology and
optics, poses substantial challenges in its reconstruction process,
characterized by nonconvexity and large-scale requirements. This paper presents
a novel approach by introducing a class of variational models that incorporate
the weighted difference of anisotropic--isotropic total variation. This
formulation enables the handling of measurements corrupted by Gaussian or
Poisson noise, effectively addressing the nonconvex challenge. To tackle the
large-scale nature of the problem, we propose an efficient stochastic
alternating direction method of multipliers, which guarantees convergence under
mild conditions. Numerical experiments validate the superiority of our approach
by demonstrating its capability to successfully reconstruct complex-valued
images, especially in recovering the phase components even in the presence of
highly corrupted measurements.Comment: submitte