Phase retrieval problems in x-ray physics

Homann, C.

doi:10.17875/gup2015-816

Cited by 2 publications

(3 citation statements)

References 70 publications

(122 reference statements)

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“…The performance of algorithm 6 depends on the computational effort caused by the resolvents. We have seen in (89) that…”

Section: ¯( )mentioning

confidence: 95%

“…As an alternative to the more commonly used projection methods, phase retrieval problems can also be solved by regularized Newton methods [85,88,89,98,109]. Although more difficult to implement than algorithms 9-11, these methods offer more flexibility in treating different experimental setups and different types of a priori information.…”

Section: Projection Methods For Phase Retrieval Problemsmentioning

confidence: 99%

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Inverse problems with Poisson data: statistical regularization theory, applications and algorithms

2016

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Inverse problems with Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. The design of regularization methods and estimators for such problems has been studied intensively over the last two decades. In this review we give an overview of statistical regularization theory for such problems, the most important applications, and the most widely used algorithms. The focus is on variational regularization methods in the form of penalized maximum likelihood estimators, which can be analyzed in a general setup. Complementing a number of recent convergence rate results we will establish consistency results. Moreover, we discuss estimators based on a wavelet-vaguelette decomposition of the (necessarily linear) forward operator. As most prominent applications we briefly introduce Positron emission tomography, inverse problems in fluorescence microscopy, and phase retrieval problems. The computation of a penalized maximum likelihood estimator involves the solution of a (typically convex) minimization problem. We also review several efficient algorithms which have been proposed for such problems over the last five years.

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“…The performance of algorithm 6 depends on the computational effort caused by the resolvents. We have seen in (89) that…”

Section: ¯( )mentioning

confidence: 95%

Section: Projection Methods For Phase Retrieval Problemsmentioning

confidence: 99%

Inverse problems with Poisson data: statistical regularization theory, applications and algorithms

2016

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“…As a preparation for the subsequent analysis, we summarize some basic properties of the Fresnel propagator, see also [10,16,22]:…”

Section: Properties Of the Fresnel Propagatormentioning

confidence: 99%

Locality estimates for Fresnel-wave-propagation and stability of x-ray phase contrast imaging with finite detectors

Maretzke

2018

Inverse Problems

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Coherent wave-propagation in the near-field Fresnel-regime is the underlying contrast-mechanism to (propagation-based) X-ray phase contrast imaging (XPCI), an emerging lensless technique that enables 2D-and 3D-imaging of biological soft tissues and other light-element samples down to nanometer-resolutions. Mathematically, propagation is described by the Fresnel-propagator, a convolution with an arbitrarily non-local kernel. As real-world detectors may only capture a finite field-of-view, this non-locality implies that the recorded diffraction-patterns are necessarily incomplete. This raises the question of stability of image-reconstruction from the truncated data -even if the complex-valued wave-field, and not just its modulus, could be measured. Contrary to the latter restriction of the acquisition, known as the phase-problem, the finite-detector-problem has not received much attention in literature. The present work therefore analyzes locality of Fresnelpropagation in order to establish stability of XPCI with finite detectors. Image-reconstruction is shown to be severely ill-posed in this setting -even without a phase-problem. However, quantitative estimates of the leaked wave-field reveal that Lipschitz-stability holds down to a sharp resolution limit that depends on the detector-size and varies within the field-of-view. The smallest resolvable lengthscale is found to be ≈ 1/f times the detector's aspect length, wheref is the Fresnel number associated with the latter scale. The stability results are extended to phaseless imaging in the linear contrast-transfer-function regime.(1) Although we will refer to "real-valued" signals throughout the work, note that all the results obtained for such trivially extend to signals given by real-functions multiplied by a global complex phase.

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Phase retrieval problems in x-ray physics

Cited by 2 publications

References 70 publications

Inverse problems with Poisson data: statistical regularization theory, applications and algorithms

Inverse problems with Poisson data: statistical regularization theory, applications and algorithms

Locality estimates for Fresnel-wave-propagation and stability of x-ray phase contrast imaging with finite detectors

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