74 research outputs found
Dictionary learning from phaseless measurements
International audienceWe propose a new algorithm to learn a dictionary along with sparse representations from signal measurements without phase. Specifically, we consider the task of reconstructing a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider sparse phase retrieval when the sparsifying dictionary is not known in advance, and we learn a dictionary such that each patch of the reconstructed image can be sparsely represented. Our numerical experiments demonstrate that our proposed scheme can obtain significantly better reconstructions for noisy phase retrieval problems than methods that cannot exploit such " hidden " sparsity
DOLPHIn - Dictionary Learning for Phase Retrieval
We propose a new algorithm to learn a dictionary for reconstructing and
sparsely encoding signals from measurements without phase. Specifically, we
consider the task of estimating a two-dimensional image from squared-magnitude
measurements of a complex-valued linear transformation of the original image.
Several recent phase retrieval algorithms exploit underlying sparsity of the
unknown signal in order to improve recovery performance. In this work, we
consider such a sparse signal prior in the context of phase retrieval, when the
sparsifying dictionary is not known in advance. Our algorithm jointly
reconstructs the unknown signal - possibly corrupted by noise - and learns a
dictionary such that each patch of the estimated image can be sparsely
represented. Numerical experiments demonstrate that our approach can obtain
significantly better reconstructions for phase retrieval problems with noise
than methods that cannot exploit such "hidden" sparsity. Moreover, on the
theoretical side, we provide a convergence result for our method
Advanced Denoising for X-ray Ptychography
The success of ptychographic imaging experiments strongly depends on
achieving high signal-to-noise ratio. This is particularly important in
nanoscale imaging experiments when diffraction signals are very weak and the
experiments are accompanied by significant parasitic scattering (background),
outliers or correlated noise sources. It is also critical when rare events such
as cosmic rays, or bad frames caused by electronic glitches or shutter timing
malfunction take place.
In this paper, we propose a novel iterative algorithm with rigorous analysis
that exploits the direct forward model for parasitic noise and sample
smoothness to achieve a thorough characterization and removal of structured and
random noise. We present a formal description of the proposed algorithm and
prove its convergence under mild conditions. Numerical experiments from
simulations and real data (both soft and hard X-ray beamlines) demonstrate that
the proposed algorithms produce better results when compared to
state-of-the-art methods.Comment: 24 pages, 9 figure
Signal Recovery from Pooling Representations
In this work we compute lower Lipschitz bounds of pooling operators
for as well as pooling operators preceded by
half-rectification layers. These give sufficient conditions for the design of
invertible neural network layers. Numerical experiments on MNIST and image
patches confirm that pooling layers can be inverted with phase recovery
algorithms. Moreover, the regularity of the inverse pooling, controlled by the
lower Lipschitz constant, is empirically verified with a nearest neighbor
regression.Comment: 17 pages, 3 figure
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