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Author : David Montiel
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (129 download)
Download or read book Phase Retrieval from X-ray Intensity Measurements written by David Montiel and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Carolin Homann
Publisher : Göttingen University Press
ISBN 13 : 3863952103
Total Pages : 126 pages
Book Rating : 4.8/5 (639 download)
Download or read book Phase retrieval problems in x-ray physics written by Carolin Homann and published by Göttingen University Press. This book was released on 2015 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In phase retrieval problems that occur in imaging by coherent x-ray diffraction, one tries to reconstruct information about a sample of interest from possibly noisy intensity measurements of the wave fi eld traversing the sample. The mathematical formulation of these problems bases on some assumptions. Usually one of them is that the x-ray wave fi eld is generated by a point source. In order to address this very idealized assumption, it is common to perform a data preprocessing step, the so-called empty beam correction. Within this work, we study the validity of this approach by presenting a quantitative error estimate. Moreover, in order to solve these phase retrieval problems, we want to incorporate a priori knowledge about the structure of the noise and the solution into the reconstruction process. For this reason, the application of a problem adapted iteratively regularized Newton-type method becomes particularly attractive. This method includes the solution of a convex minimization problem in each iteration step. We present a method for solving general optimization problems of this form. Our method is a generalization of a commonly used algorithm which makes it efficiently applicable to a wide class of problems. We also proof convergence results and show the performance of our method by numerical examples.
Author : Carolin Homann
Publisher :
ISBN 13 :
Total Pages : 126 pages
Book Rating : 4.:/5 (931 download)
Download or read book Phase retrieval problems in x-ray physics: from modeling to efficient algorithms written by Carolin Homann and published by . This book was released on 2015 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In phase retrieval problems that occur in imaging by coherent x-ray diffraction, one tries to reconstruct information about a sample of interest from possibly noisy intensity measurements of the wave fi eld traversing the sample. The mathematical formulation of these problems bases on some assumptions. Usually one of them is that the x-ray wave fi eld is generated by a point source. In order to address this very idealized assumption, it is common to perform a data preprocessing step, the so-called empty beam correction. Within this work, we study the validity of this approach by presenting a quantitative error estimate. Moreover, in order to solve these phase retrieval problems, we want to incorporate a priori knowledge about the structure of the noise and the solution into the reconstruction process. For this reason, the application of a problem adapted iteratively regularized Newton-type method becomes particularly attractive. This method includes the solution of a convex minimization problem in each iteration step. We present a method for solving general optimization problems of this form. Our method is a generalization of a commonly used algorithm which makes it efficiently applicable to a wide class of problems. We also proof convergence results and show the performance of our method by numerical examples.
Author : Anna-Lena Robisch
Publisher : Göttingen University Press
ISBN 13 : 3863952529
Total Pages : 178 pages
Book Rating : 4.8/5 (639 download)
Download or read book Phase retrieval for object and probe in the optical near-field written by Anna-Lena Robisch and published by Göttingen University Press. This book was released on 2016 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lensless, holographic X-ray microscopy is a non-invasive imaging technique that provides resolution on the nanometer scale. Therefore, a divergent, coherent and especially clean wave front impinging on the sample is needed. Yet, focusing X-rays by even the most advanced X-ray mirrors causes so called figure errors of high spatial frequency content. The results are strongly deteriorated intensity profiles that are often even more pronounced than the holographic image of the sample itself. A common strategy to compensate these figure errors is to divide the hologram by the pure intensity profile of the beam (the so called flat field). However, this division is only valid in the limiting case of an illumination focused down to a point source. In reality, as a consequence of a fi nite spot size, one has to accept a loss in resolution when performing the flat field correction. An approach different from the described straightforward procedure is necessary. Here, the simultaneous reconstruction of object and probe is proposed using holograms which were not flat field corrected before phase retrieval. To this end, a method has been developed that allows simultaneously reconstructing object and probe in amplitude and phase from holographic intensity recordings. The experimental way of proceeding was mainly inspired by well-established holographic full-field X-ray imaging techniques that require holograms defocused to different degrees. Consequently, the conclusion seems reasonable that diversity in the optical near-field arises mainly from variation of the propagation distance of light. This so called longitudinal diversity is used to properly phase the transmission function of the sample of interest. The algorithmic strategy of simultaneous phase retrieval for object and probe draws on far-field ptychography where lateral translations of the sample create diverse diffraction patterns. In view of the need for longitudinal diversity realized by shifts of the sample along the optical axis, ptychography has been generalized and adapted for the optical near-field. Hence, translations of the sample in all three dimensions of space need to be exploited to collect enough information about object and probe such that both can be reconstructed simultaneously in amplitude and phase. Concepts have been put into practice by simulations as well as by experiments with coherent visible light and hard X-rays from synchrotron sources. The presented approach offers the opportunity to perform high resolution imaging, to be extended to tomography and to be adapted to super-resolution experiments.
Author : Rhiannon Lohr
Publisher :
ISBN 13 :
Total Pages : 177 pages
Book Rating : 4.:/5 (112 download)
Download or read book Phase Retrieval Methods for Polychromatic Propagation-based Phase-contrast X-ray Imaging written by Rhiannon Lohr and published by . This book was released on 2019 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: X-ray imaging, based on conventional attenuation methods, is employed in various industrial, medical and scientific imaging application. Phase-contrast X-ray imaging is an emerging modality that has shown promise to image and characterize weakly absorbing objects, such as three-dimensional printed plastics and imaging breast tissue. Propagation-based phase-contrast X-ray imaging is the simplest of the existing phase-contrast methods as it does not require any additional optics and can easily be integrated into current X-ray systems that utilize polychromatic X-ray sources. This novel imaging technique requires post-image processing using an algorithm called phase retrieval to extract phase information from the measured intensity. Although propagation-based phase-contrast X-ray imaging offers the simplest setup, it possesses the most mathematically intensive methods to retrieve the phase. Phase retrieval is a nonlinear inverse technique used to estimate the phase shift, thickness or electron density throughout an image. Many of these phase retrieval methods have been developed assuming a monochromatic source, although can be extended to a polychromatic source. This work compares seven phase retrieval methods under various conditions in the presence of a polychromatic source in simulation of different objects and materials. Six of these phase retrieval methods are single-shot algorithms that require only one phase-contrast image; whereas one method is iterative and requires an absorption and phase-contrast image. Each method is derived under different assumptions, but all should produce the same result of retrieved phase shift, thickness or electron density. Overall, Paganin's method performed the best under all test cases and was further applied to experimental data. Polytetrafluoroethylene, varying in thickness and shape, was imaged using a polychromatic source under numerous conditions and Paganin's method was applied to determine its limitations. In general, Paganin's method resulted in a high relative error in experiment, which is not what was seen in simulation. From these results and analysis, sources of error were determined to arise from the detector, the object and/or the spectrum. Isolating the source of error is difficult to accomplish in experiment because it is hard to eliminate certain variables completely. For this reason, further analysis on the sources of error were accomplished in simulation. The effect of material parameters was investigated using different spectrums, source-to-object distances and object-to-detector distances. This research suggests that Paganin's method is highly material dependent and what is considered sufficiently thin for one material may not apply to another material. Generally, a filtered spectrum using 2 mm of aluminum gives the lowest relative error for all materials. Also, the trend between the retrieved thickness and the measured thickness of the object is observed to be polynomial when the object thickness exceeds 100 micron. Further analysis shows that the polychromatic spectrum needs to be well calibrated to give accurate phase or thickness results and using different X-ray sources can affect the error produced by Paganin's method. Paganin's method uses Fourier filtering that allows it to increase the signal-to-noise ratio in an image and, thus, makes the algorithm resilient to noise. This research suggests that although Paganin's method is one of the best phase retrieval methods derived to date, it has its limitations that include imaging thick materials; therefore it may not be the best-suited for industrial imaging where thick plastic objects are imaged for defects. Another limitation of this method is that it is unable to retrieve the thickness of high-density, high-atomic number materials. Finally, it appears that the spectrum utilized in imaging needs to be well characterized and calibrated for Paganin's method to work.
Author : Julian Moosmann
Publisher :
ISBN 13 : 9783843919739
Total Pages : 210 pages
Book Rating : 4.9/5 (197 download)
Download or read book Nonlinear Approaches to the Inverse Problem of Phase Retrieval from Single-measurement X-ray Intensity Data written by Julian Moosmann and published by . This book was released on 2014 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tim Salditt
Publisher : Springer Nature
ISBN 13 : 3030344134
Total Pages : 634 pages
Book Rating : 4.0/5 (33 download)
Download or read book Nanoscale Photonic Imaging written by Tim Salditt and published by Springer Nature. This book was released on 2020-06-09 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book, edited and authored by a team of world-leading researchers, provides a broad overview of advanced photonic methods for nanoscale visualization, as well as describing a range of fascinating in-depth studies. Introductory chapters cover the most relevant physics and basic methods that young researchers need to master in order to work effectively in the field of nanoscale photonic imaging, from physical first principles, to instrumentation, to mathematical foundations of imaging and data analysis. Subsequent chapters demonstrate how these cutting edge methods are applied to a variety of systems, including complex fluids and biomolecular systems, for visualizing their structure and dynamics, in space and on timescales extending over many orders of magnitude down to the femtosecond range. Progress in nanoscale photonic imaging in Göttingen has been the sum total of more than a decade of work by a wide range of scientists and mathematicians across disciplines, working together in a vibrant collaboration of a kind rarely matched. This volume presents the highlights of their research achievements and serves as a record of the unique and remarkable constellation of contributors, as well as looking ahead at the future prospects in this field. It will serve not only as a useful reference for experienced researchers but also as a valuable point of entry for newcomers.
Author : Manuel Guizar-Sicairos
Publisher :
ISBN 13 :
Total Pages : 564 pages
Book Rating : 4.:/5 (77 download)
Download or read book Methods for Coherent Lensless Imaging and X-ray Wavefront Measurement written by Manuel Guizar-Sicairos and published by . This book was released on 2010 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Advancement and research on phase retrieval techniques are in large part motivated by their application in high resolution lensless laser imaging and x- ray diffractive imaging. In the former a high resolution image can be obtained from measuring the intensity pattern of the propagated field without the use of any imaging optics, thus providing an imaging system that does not increase its thickness along the optical axis as the aperture diameter is increased. For x- ray coherent diffractive imaging, on the other hand, high-resolution conventional imaging is difficult to achieve at these wavelengths because of the difficulty of manufacturing and aligning x-ray focusing elements with sufficient numerical aperture and precision. Thus, in order to achieve resolutions on the order of a nanometer, a coherent x-ray beam is used to illuminate the object of interest and the object is reconstructed from a measurement of its far-field diffraction intensity without any imaging optics. Thus the advancement and application of lensless imaging techniques has become an increasingly important topic of research. X-ray diffractive imaging is set apart from other high-resolution imaging techniques (e.g. scanning electron or atomic force microscopy) for its high penetration depth, which enables tomographic 3D imaging of thick samples and buried structures. Furthermore, using short x-ray pulses, it enables the capability to take ultrafast snapshots, giving a unique opportunity to probe nanoscale dynamics at femtosecond time scales. In this thesis we present improvements to phase retrieval algorithms, assess their performance through numerical simulations, and develop new methods for both imaging and wavefront measurement. Using numerical simulations we identified and explained the origin of the twin-image problem in iterative transform phase retrieval with a centrosymmetric support constraint. We proposed and numerically demonstrated the effectiveness of a modified phase retrieval algorithm that uses Fourier weighted projections to increase the quality and resolution of the reconstructions by mitigating a problem arising from the finite measurement window and finite support constraint. Such an approach is particularly useful when the object presents large phase variations on a length- scale significantly smaller than the resolution, i.e. reconstruction of fully developed speckled images. In order to accurately and efficiently assess phase retrieval algorithm performance, we have developed algorithms for subpixel image registration. Despite being particularly well suited for comparing images from data collected in the Fourier domain (e.g., phase retrieval and holography), these algorithms have al- ready shown a substantial success in other applications as well. Building on the original work by Faulkner and Rodenburg, we developed an improved reconstruction algorithm for phase retrieval with transverse translations of the object relative to the illumination beam. Based on gradient-based non- linear optimization, this algorithm is capable of estimating the object, and at the same time refining the initial knowledge of the incident illumination and the object translations. The advantages of this algorithm over the original iterative transform approach are shown through numerical simulations. Phase retrieval has already shown substantial success in wavefront sensing at optical wavelengths. Although in principle the algorithms can be used at any wavelength, in practice the focus-diversity mechanism that makes optical phase retrieval robust is not practical to implement for x-rays. In this thesis we also describe the novel application of phase retrieval with transverse translations to the problem of x-ray wavefront sensing. This approach allows the characterization of the complex-valued x-ray field in-situ and at-wavelength and has several practical and algorithmic advantages over conventional focused beam measurement techniques. A few of these advantages include improved robustness through diverse measurements, reconstruction from far-field intensity measurements only, and significant relaxation of experimental requirements over other beam characterization approaches. Furthermore, we show that a one-dimensional version of this technique can be used to characterize an x-ray line focus produced by a cylindrical focusing element. We provide experimental demonstrations of the latter at hard x-ray wavelengths, where we have characterized the beams focused by a kinoform lens and an elliptical mirror. In both experiments the reconstructions exhibited good agreement with independent measurements, and in the latter a small mirror misalignment was inferred from the phase retrieval reconstruction. These experiments pave the way for the application of robust phase retrieval algorithms for in-situ alignment and performance characterization of x-ray optics for nanofocusing. We also present a study on how transverse translations help with the well-known uniqueness problem of one-dimensional phase retrieval. We also present a novel method for x-ray holography that is capable of reconstructing an image using an off-axis extended reference in a non-iterative computation, greatly generalizing an earlier approach by Podorov et.al. The approach, based on the numerical application of derivatives on the field autocorrelation, was developed from first mathematical principles. We conducted a thorough theoret- ical study to develop technical and intuitive understanding of this technique and derived sufficient separation conditions required for an artifact-free reconstruction. We studied the effects of missing information in the Fourier domain, and of an im- perfect reference, and we provide a signal-to-noise ratio comparison with the more traditional approach of Fourier transform holography. We demonstrated this new holographic approach through proof-of-principle optical experiments and later ex- perimentally at soft x-ray wavelengths, where we compared its performance to Fourier transform holography, iterative phase retrieval and state-of-the-art zone-plate x-ray imaging techniques (scanning and full-field). Finally, we present a demonstration of the technique using a single 20 fs pulse from a high-harmonic table-top source. Holography with an extended reference is shown to provide fast, good quality images that are robust to noise and artifacts that arise from missing information due to a beam stop."--Leaves viii-xi.
Download or read book PHASE RETRIEVAL FROM TWO DEFOCUSED IMAGES BY THE TRANSPORT OF INTENSITY EQUATION FORMALISM WITH FAST FOURIER TRANSFORM. written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of phase retrieval from intensity measurements plays an important role in many fields of physical research, e.g. optics, electron and x-ray microscopy, crystallography, diffraction tomography and others. In practice the recorded images contain information only on the intensity distribution I(x, y)=[Psi]*[Psi]=[vert-bar]A[vert-bar][sup 2] of the imaging wave function[Psi]= A*exp( -i[var-phi]) and the phase information[var-phi](x, y) is usually lost. In general, the phase problem can be solved either by special holographic/interferometric methods, or by non-interferometric approaches based on intensity measurements in far Fraunhofer zone or in the Fresnel zone at two adjacent planes orthogonal to the optical axis. The latter approach uses the transport-of-intensity equation (TIE) formalism, introduced originally by Teague[1] and developed later in[2]. Applications of TIE to nonmagnetic materials and magnetic inductance mapping were successfully made in[3,4]. However, this approach still needs further improvement both in mathematics and in practical solutions, since the result is very sensitive to many experimental parameters.
Author : Andreas Maier
Publisher : Springer
ISBN 13 : 3319965204
Total Pages : 263 pages
Book Rating : 4.3/5 (199 download)
Download or read book Medical Imaging Systems written by Andreas Maier and published by Springer. This book was released on 2018-08-02 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book gives a complete and comprehensive introduction to the fields of medical imaging systems, as designed for a broad range of applications. The authors of the book first explain the foundations of system theory and image processing, before highlighting several modalities in a dedicated chapter. The initial focus is on modalities that are closely related to traditional camera systems such as endoscopy and microscopy. This is followed by more complex image formation processes: magnetic resonance imaging, X-ray projection imaging, computed tomography, X-ray phase-contrast imaging, nuclear imaging, ultrasound, and optical coherence tomography.
Author : Kannara Mom
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (143 download)
Download or read book Deep Learning Based Phase Retrieval for X-ray Phase Contrast Imaging written by Kannara Mom and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of highly coherent X-ray sources, such as third-generation synchrotron radiation facilities, has significantly contributed to the advancement of phase contrast imaging. The high degree of coherence of these sources enables efficient implementation of phase contrast techniques, and can increase sensitivity by several orders of magnitude. This novel imaging technique has found applications in a wide range of fields, including material science, paleontology, bone research, medicine, and biology. It enables the imaging of samples with low absorption constituents, where traditional absorption-based methods may fail to provide sufficient contrast. Several phase-sensitive imaging techniques have been developed, among them, propagation-based imaging requires no equipment other than the source, object and detector. Although the intensity can be measured at one or several propagation distances, the phase information is lost and must be estimated from those diffraction patterns, a process called phase retrieval. Phase retrieval in this context is a nonlinear ill-posed inverse problem. Various classical methods have been proposed to retrieve the phase, either by linearizing the problem to obtain an analytical solution, or by iterative algorithms. The main purpose of this thesis was to study what new deep learning approaches could bring to this phase retrieval problem. Various deep learning algorithms have been proposed and evaluated to address this problem. In the first part of this work, we show how neural networks can be used to reconstruct directly from measurements data, without model information. The architecture of the Mixed Scale Dense Network (MS-D Net) is introduced, combining dilated convolution and dense connection. In the second part of this thesis, we propose a nonlinear primal-dual algorithm for the retrieval of phase shift and absorption from a single X-ray in-line phase contrast. We showed that choosing different regularizers for absorption and phase can improve the reconstructions. In the third part, we propose to integrate neural networks into an existing optimization scheme using so-called unrolling approaches, in order to give the convolutional neural networks a specific role in the reconstruction. The performance of theses algorithms are evaluated using simulated noisy data as well as images acquired at NanoMAX (MAX IV, Lund, Sweden).
Author : David Paganin
Publisher : Oxford University Press on Demand
ISBN 13 : 0198567286
Total Pages : 424 pages
Book Rating : 4.1/5 (985 download)
Download or read book Coherent X-Ray Optics written by David Paganin and published by Oxford University Press on Demand. This book was released on 2006-01-12 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: X-ray optics is undergoing a renaissance, which may be paralleled to that experienced by visible-light optics following the invention of the laser. The associated surge of activity in "coherent" x-ray optics has been documented in this monograph, the first of its type in the field.
Author : Alexander H. Barnett
Publisher : Cambridge University Press
ISBN 13 : 1316518876
Total Pages : 321 pages
Book Rating : 4.3/5 (165 download)
Download or read book Geometry of the Phase Retrieval Problem written by Alexander H. Barnett and published by Cambridge University Press. This book was released on 2022-05-05 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a theoretical foundation and conceptual framework for the problem of recovering the phase of the Fourier transform.
Author : N.E. Hurt
Publisher : Springer Science & Business Media
ISBN 13 : 9781402003370
Total Pages : 328 pages
Book Rating : 4.0/5 (33 download)
Download or read book Phase Retrieval and Zero Crossings written by N.E. Hurt and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi, ... , si j'avait su comment en :revenir, One scrvice mathematics has rendered the je n'y scrais point alle.' human race. lt has put common sense back Jules Veme where it bdongs, on the topmost shelf next to the dusty canister labclled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Erle T. Bc1l 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'.All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Author : Pramod Rastogi
Publisher : CRC Press
ISBN 13 : 146659831X
Total Pages : 370 pages
Book Rating : 4.4/5 (665 download)
Download or read book Phase Estimation in Optical Interferometry written by Pramod Rastogi and published by CRC Press. This book was released on 2014-11-21 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase Estimation in Optical Interferometry covers the essentials of phase-stepping algorithms used in interferometry and pseudointerferometric techniques. It presents the basic concepts and mathematics needed for understanding the phase estimation methods in use today. The first four chapters focus on phase retrieval from image transforms using a single frame. The next several chapters examine the local environment of a fringe pattern, give a broad picture of the phase estimation approach based on local polynomial phase modeling, cover temporal high-resolution phase evaluation methods, and present methods of phase unwrapping. The final chapter discusses experimental imperfections that are liable to adversely influence the accuracy of phase measurements. Responding to the push for the deployment of novel technologies and fast-evolving techniques, this book provides a framework for understanding various modern phase estimation methods. It also helps readers get a comparative view of the performance and limitations of the approaches.
Author : Valentina Ion
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (881 download)
Download or read book Nonlinear Approaches for Phase Retrieval in the Fresnel Region for Hard X-ray Imaging written by Valentina Ion and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of highly coherent X-ray sources offers new possibilities to image biological structures at different scales exploiting the refraction of X-rays. The coherence properties of the third-generation synchrotron radiation sources enables efficient implementations of phase contrast techniques. One of the first measurements of the intensity variations due to phase contrast has been reported in 1995 at the European Synchrotron Radiation Facility (ESRF). Phase imaging coupled to tomography acquisition allows threedimensional imaging with an increased sensitivity compared to absorption CT. This technique is particularly attractive to image samples with low absorption constituents. Phase contrast has many applications, ranging from material science, paleontology, bone research to medicine and biology. Several methods to achieve X-ray phase contrast have been proposed during the last years. In propagation based phase contrast, the measurements are made at different sample-to-detector distances. While the intensity data can be acquired and recorded, the phase information of the signal has to be "retrieved" from the modulus data only. Phase retrieval is thus an illposed nonlinear problem and regularization techniques including a priori knowledge are necessary to obtain stable solutions. Several phase recovery methods have been developed in recent years. These approaches generally formulate the phase retrieval problem as a linear one. Nonlinear treatments have not been much investigated. The main purpose of this work was to propose and evaluate new algorithms, in particularly taking into account the nonlinearity of the direct problem. In the first part of this work, we present a Landweber type nonlinear iterative scheme to solve the propagation based phase retrieval problem. This approach uses the analytic expression of the Fréchet derivative of the phase-intensity relationship and of its adjoint, which are presented in detail. We also study the effect of projection operators on the convergence properties of the method. In the second part of this thesis, we investigate the resolution of the linear inverse problem with an iterative thresholding algorithm in wavelet coordinates. In the following, the two former algorithms are combined and compared with another nonlinear approach based on sparsity regularization and a fixed point algorithm. The performance of theses algorithms are evaluated on simulated data for different noise levels. Finally the algorithms were adapted to process real data sets obtained in phase CT at the ESRF at Grenoble.
Author : Lei Tian (Ph. D.)
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.:/5 (86 download)
Download or read book Compressive Phase Retrieval written by Lei Tian (Ph. D.) and published by . This book was released on 2013 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recovering a full description of a wave from limited intensity measurements remains a central problem in optics. Optical waves oscillate too fast for detectors to measure anything but time{averaged intensities. This is unfortunate since the phase can reveal important information about the object. When the light is partially coherent, a complete description of the phase requires knowledge about the statistical correlations for each pair of points in space. Recovery of the correlation function is a much more challenging problem since the number of pairs grows much more rapidly than the number of points. In this thesis, quantitative phase imaging techniques that works for partially coherent illuminations are investigated. In order to recover the phase information with few measurements, the sparsity in each underly problem and ecient inversion methods are explored under the framework of compressed sensing. In each phase retrieval technique under study, diffraction during spatial propagation is exploited as an effective and convenient mechanism to uniformly distribute the information about the unknown signal into the measurement space. Holography is useful to record the scattered field from a sparse distribution of particles; the ability of localizing each particles using compressive reconstruction method is studied. When a thin sample is illuminated with partially coherent waves, the transport of intensity phase retrieval method is shown to be eective to recover the optical path length of the sample and remove the eect of the illumination. This technique is particularly suitable for X-ray phase imaging since it does not require a coherent source or any optical components. Compressive tomographic reconstruction, which makes full use of the priors that the sample consists of piecewise constant refractive indices, are demonstrated to make up missing data. The third technique, known as the phase space tomography (PST), addresses the correlation function recovery problem. Implementing the PST involves measuring many intensity images under spatial propagation. Experimental demonstration of a compressive reconstruction method, which finds the sparse solution by decomposing the correlation function into a few mutually uncorrelated coherent modes, is presented to produce accurate reconstruction even when the measurement suers from the 'missing cone' problem in the Fourier domain.
