8,737 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
Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems
Like many other advanced imaging methods, x-ray phase contrast imaging and
tomography require mathematical inversion of the observed data to obtain
real-space information. While an accurate forward model describing the
generally nonlinear image formation from a given object to the observations is
often available, explicit inversion formulas are typically not known. Moreover,
the measured data might be insufficient for stable image reconstruction, in
which case it has to be complemented by suitable a priori information. In this
work, regularized Newton methods are presented as a general framework for the
solution of such ill-posed nonlinear imaging problems. For a proof of
principle, the approach is applied to x-ray phase contrast imaging in the
near-field propagation regime. Simultaneous recovery of the phase- and
amplitude from a single near-field diffraction pattern without homogeneity
constraints is demonstrated for the first time. The presented methods further
permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval
and tomographic inversion. We demonstrate the potential of this approach by
three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may
be made for personal use only. Systematic reproduction and distribution,
duplication of any material in this paper for a fee or for commercial
purposes, or modifications of the content of this paper are prohibite
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