153 research outputs found
Solving ptychography with a convex relaxation
Ptychography is a powerful computational imaging technique that transforms a
collection of low-resolution images into a high-resolution sample
reconstruction. Unfortunately, algorithms that are currently used to solve this
reconstruction problem lack stability, robustness, and theoretical guarantees.
Recently, convex optimization algorithms have improved the accuracy and
reliability of several related reconstruction efforts. This paper proposes a
convex formulation of the ptychography problem. This formulation has no local
minima, it can be solved using a wide range of algorithms, it can incorporate
appropriate noise models, and it can include multiple a priori constraints. The
paper considers a specific algorithm, based on low-rank factorization, whose
runtime and memory usage are near-linear in the size of the output image.
Experiments demonstrate that this approach offers a 25% lower background
variance on average than alternating projections, the current standard
algorithm for ptychographic reconstruction.Comment: 8 pages, 8 figure
Phase Retrieval via Matrix Completion
This paper develops a novel framework for phase retrieval, a problem which
arises in X-ray crystallography, diffraction imaging, astronomical imaging and
many other applications. Our approach combines multiple structured
illuminations together with ideas from convex programming to recover the phase
from intensity measurements, typically from the modulus of the diffracted wave.
We demonstrate empirically that any complex-valued object can be recovered from
the knowledge of the magnitude of just a few diffracted patterns by solving a
simple convex optimization problem inspired by the recent literature on matrix
completion. More importantly, we also demonstrate that our noise-aware
algorithms are stable in the sense that the reconstruction degrades gracefully
as the signal-to-noise ratio decreases. Finally, we introduce some theory
showing that one can design very simple structured illumination patterns such
that three diffracted figures uniquely determine the phase of the object we
wish to recover
On recovery guarantees for angular synchronization
The angular synchronization problem of estimating a set of unknown angles
from their known noisy pairwise differences arises in various applications. It
can be reformulated as a optimization problem on graphs involving the graph
Laplacian matrix. We consider a general, weighted version of this problem,
where the impact of the noise differs between different pairs of entries and
some of the differences are erased completely; this version arises for example
in ptychography. We study two common approaches for solving this problem,
namely eigenvector relaxation and semidefinite convex relaxation. Although some
recovery guarantees are available for both methods, their performance is either
unsatisfying or restricted to the unweighted graphs. We close this gap,
deriving recovery guarantees for the weighted problem that are completely
analogous to the unweighted version.Comment: 20 pages, 5 figure
Adorym: A multi-platform generic x-ray image reconstruction framework based on automatic differentiation
We describe and demonstrate an optimization-based x-ray image reconstruction
framework called Adorym. Our framework provides a generic forward model,
allowing one code framework to be used for a wide range of imaging methods
ranging from near-field holography to and fly-scan ptychographic tomography. By
using automatic differentiation for optimization, Adorym has the flexibility to
refine experimental parameters including probe positions, multiple hologram
alignment, and object tilts. It is written with strong support for parallel
processing, allowing large datasets to be processed on high-performance
computing systems. We demonstrate its use on several experimental datasets to
show improved image quality through parameter refinement
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