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A comparison of rotation-based methods for iterative reconstruction algorithms

IEEE TRANSACTIONS ON NUCLEAR SCIENCE 1996年第6期43卷 3370-3376页

作者： DiBella, EVR Barclay, AB Eisner, RL Schafer, RW EMORY UNIV CRAWFORD LONG HOSPCARLYLE FRASER HEART CTRATLANTAGA 30365

Rotation-based projectors and backprojectors offer unique trade-offs between accuracy, computational complexity, and smoothing, We analyzed six different rotation methods for generating projections and iterative reconstructions of tomographic data, Nearest neighbor, upsampled nearest neighbor, bilinear interpolation, and bicubic interpolation were all used to determine the values at rotated grid points, A decomposition of the rotation transformation matrix into three components was also investigated, Linear and cubic interpolation were used in the three-pass method. For all of the methods, mean normalized square errors were computed, Our results demonstrate the tradeoffs associated with the different methods and suggest that the three-pass method with cubic interpolation offers a computationally efficient approach with accuracy between that of bilinear and bicubic interpolation.

关键词： Iterative methods reconstruction algorithms Interpolation Image reconstruction Nearest neighbor searches Computational complexity Smoothing methods Tomography Shearing Matrix decomposition

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On the local minima in phase reconstruction algorithms

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RADIO SCIENCE 1996年第6期31卷 1887-1899页

作者： Isernia, T Soldovieri, F Leone, G Pierri, R SECONDA UNIV NAPOLI DIPARTIMENTO INGN INFORMAZ I-81031 AVERSA ITALY

Signal reconstruction from phaseless data occurs in electromagnetics both in the diagnostics of large reflector antennas and in the near-field testing of microwave and millimeter wave antennas. The main difficulty in solving such problems arises from its inherent nonlinearity. Because of the latter, in fact, the solution procedure can converge to a function which has nothing to deal with the actual solution. In this paper we review and summarize the properties of a recently proposed approach to phase retrieval problems which allows to understand and possibly avoid the false solution problem. To this end, ill-posedness of the problem is briefly recalled, and a convenient generalized solution is introduced as the global minimum of a proper functional whose local minima are indeed the false solutions of the problem. Then the geometrical meaning of such a functional is considered, and properties of the solution are discussed according to the formulation of the problem as a quadratic inverse one. In particular, the relevance of using nonredundant representations for the unknown of the problem and as many independent data as possible are discussed in full detail from both a theoretical and a numerical point of view. Finally, it is shown how the proposed solution procedure, descending from the adopted formulation based on a weaker nonlinearity with respect to the other ones, has indeed a better behavior as far as local minima problem is concerned.

关键词： Frequency measurement Phase measurement reconstruction algorithms Correlation Microwave imaging Image reconstruction Electron optics

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Attenuation and scatter correction of list-mode data driven iterative and analytic image reconstruction algorithms for rotating 3D PET systems

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 1999年第6期46卷 2218-2226页

作者： Reader, AJ Erlandsson, K Ott, RJ Flower, MA Royal Marsden NHS Trust Canc Res Inst Joint Dept Phys Sutton SM2 5PT Surrey England

Image reconstruction directly from list-mode data requires different data correction techniques to standard projection-data based reconstruction, particularly in the case of iterative reconstruction. Attenuation and scatter correction techniques have been developed for two list-mode data driven reconstruction algorithms (FAIR-B (iterative) and Atrax (analytic/iterative)) recently proposed by the authors, and the results compared with two fast projection-data based algorithms (FORE+OSEM (iterative) and FORE+FBP (analytic)). List-mode data driven algorithms require event-by-event correction schemes, or alternatively image space procedures, as no direct operations to the completely sampled projection data set can be practically carried out. The methods developed in this work allow correction of list-mode data driven EM-ML type algorithms, such as FAIR, as well as analytic list-mode algorithms. The correction schemes have been applied to simulated data from various activity and attenuating medium distributions for a rotating 3D PET system. Both list-mode algorithms show some improvements in noise-contrast behaviour compared to the projection-data based methods.

关键词： Attenuation Scattering Image analysis Image reconstruction Iterative methods Iterative algorithms Positron emission tomography Algorithm design and analysis reconstruction algorithms Bayesian methods

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Computational performance comparison of wavefront reconstruction algorithms for the European Extremely Large Telescope on multi-CPU architecture

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APPLIED OPTICS 2012年第16期51卷 3564-3583页

作者： Feng, Lu Fedrigo, Enrico Bechet, Clementine Brunner, Elisabeth Pirani, Werther Natl Observ China Beijing 100012 Peoples R China European So Observ D-85748 Garching Germany Univ Lyon F-69000 Lyon France Univ Lyon 1 F-69622 Villeurbanne France Observ Lyon Ctr Rech Astrophys Lyon F-69561 St Genis Laval France Ecole Normale Super Lyon F-69364 Lyon France CNRS UMR 5574 Lyon France

The European Southern Observatory (ESO) is studying the next generation giant telescope, called the European Extremely Large Telescope (E-ELT). With a 42 m diameter primary mirror, it is a significant step from currently existing telescopes. Therefore, the E-ELT with its instruments poses new challenges in terms of cost and computational complexity for the control system, including its adaptive optics (AO). Since the conventional matrix-vector multiplication (MVM) method successfully used so far for AO wavefront reconstruction cannot be efficiently scaled to the size of the AO systems on the E-ELT, faster algorithms are needed. Among those recently developed wavefront reconstruction algorithms, three are studied in this paper from the point of view of design, implementation, and absolute speed on three multicore multi-CPU platforms. We focus on a single-conjugate AO system for the E-ELT. The algorithms are the MVM, the Fourier transform reconstructor (FTR), and the fractal iterative method (FRiM). This study enhances the scaling of these algorithms with an increasing number of CPUs involved in the computation. We discuss implementation strategies, depending on various CPU architecture constraints, and we present the first quantitative execution times so far at the E-ELT scale. MVM suffers from a large computational burden, making the current computing platform undersized to reach timings short enough for AO wavefront reconstruction. In our study, the FTR provides currently the fastest reconstruction. FRiM is a recently developed algorithm, and several strategies are investigated and presented here in order to implement it for real-time AO wavefront reconstruction, and to optimize its execution time. The difficulty to parallelize the algorithm in such architecture is enhanced. We also show that FRiM can provide interesting scalability using a sparse matrix approach. (C) 2012 Optical Society of America

关键词： Adaptive optics Deformable mirrors Fourier transforms Large telescopes reconstruction algorithms Spatial resolution

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Comparison of Tomographic SAR Reflectivity reconstruction algorithms for Forest Applications at L-band

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2020年第1期58卷 147-164页

作者： Cazcarra-Bes, Victor Pardini, Matteo Tello, Marivi Papathanassiou, Konstantinos P. Deutsch Zentrum Luftund Raumfahrt DLR Standort Ob Microwaves & Radar Inst D-82234 Wessling Germany Swiss Fed Inst Technol CH-8092 Zurich Switzerland

Forest structure is a key parameter for forest applications, but it is difficult to be estimated at the required spatial and temporal scales. In this context, synthetic aperture radar Tomography (TomoSAR) that allows, at lower frequencies, the 3-D imaging of natural volume scatterers with high spatial and temporal resolution may be a game changer. The aim of this article is to evaluate three TomoSAR algorithms, Fourier beamforming (FB), Capon beamforming (CB), and compressive sensing (CS) with respect to their performance in the reconstruction of the 3-D forest reflectivity. The implications of volumetric forest scattering, as well as the temporal decorrelation of scatterers, are analyzed. The algorithms are compared on a set of simulated scenarios and then evaluated on an experimental L-band data set composed by four acquisition dates, each one consisting of five tomographic tracks. The data were acquired in 2014, within a time span of two months, over the Traunstein forest (Germany) using the F-SAR system. Additionally, discrete airborne Lidar has been used for a qualitative evaluation. The results indicate that the CS reconstruction is, for many practical cases, superior when compared to FB or CB reconstructions as they achieve higher vertical resolution, especially in cases with a lower number of acquisitions and complex forest scenarios. By combining acquisitions performed at different days, the effect of temporal decorrelation on each algorithm for two different tomographic implementations (repeat-pass vs. single-pass) has been assessed. The results indicate that simultaneously acquired image pairs allow a better reconstruction of the 3-D forest reflectivity.

关键词： Forestry Synthetic aperture radar Image reconstruction Decorrelation Estimation reconstruction algorithms Capon beamforming (CB) compressive sensing (CS) forest applications forest structure Fourier beamforming (FB) L-band synthetic aperture radar (SAR) tomography

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Comparison of reconstruction algorithms for optical diffraction tomography

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2005年第11期22卷 2338-2347页

作者： Guo, PY Devaney, AJ Northeastern Univ Dept Elect & Comp Engn Boston MA 02115 USA

A recently developed inverse scattering algorithm [A. J. Devaney and M. Dennison, Inverse Probl., 19, 855 (2003) and M. Dennison and A. J. Devaney, Inverse Probl., 20, 1307 (2004)] is described and applied in a computer simulation study of optical diffraction tomography (ODT). The new algorithm is superior to standard ODT reconstruction algorithms, such as the filtered backpropagation algorithm, in applications employing a limited number of scattering experiments (the so-called limited-view case) and also in cases where multiple scattering occurs between the object being interrogated and the (known) background in which the object is embedded. The new algorithm is compared and contrasted with the filtered backpropagation algorithm in a computer simulation of ODT of weakly inhomogeneous cylindrical objects being interrogated in a limited number of scattering experiments employing incident plane waves. Our study has potential applications in biomedical imaging and tomographic microscopy. (c) 2005 Optical Society of America.

关键词： Inverse scattering Medical imaging Multiple scattering Phase retrieval reconstruction algorithms Tomography

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The Benefits of Acting Locally: reconstruction algorithms for Sparse in Levels Signals With Stable and Robust Recovery Guarantees

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 3160-3175页

作者： Adcock, Ben Brugiapaglia, Simone King-Roskamp, Matthew Simon Fraser Univ Dept Math Burnaby BC V5A 1S6 Canada Concordia Univ Dept Math & Stat Montreal PQ H3G 1M8 Canada

The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel acquisition, radar, and the sparse corruptions problem. reconstruction strategies for sparse in levels signals usually rely on a suitable convex optimization program. Notably, although iterative and greedy algorithms can outperform convex optimization in terms of computational efficiency and have been studied extensively in the case of standard sparsity, little is known about their generalizations to the sparse in levels setting. In this paper, we bridge this gap by showing new stable and robust uniform recovery guarantees for sparse in level variants of the iterative hard thresholding and the CoSaMP algorithms. Our theoretical analysis generalizes recovery guarantees currently available in the case of standard sparsity and favorably compare to sparse in levels guarantees for weighted l(1) minimization. In addition, we also propose and numerically test an extension of the orthogonal matching pursuit algorithm for sparse in levels signals.

关键词： Compressed sensing reconstruction algorithms iterative algorithms greedy algorithms

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3-DIMENSIONAL ITERATIVE reconstruction algorithms WITH ATTENUATION AND GEOMETRIC POINT RESPONSE CORRECTION

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 1991年第2期38卷 693-702页

作者： ZENG, GL GULLBERG, GT TSUI, BMW TERRY, JA UNIV N CAROLINA CURRICULUM BIOMED ENGNCHAPEL HILLNC 27514 UNIV N CAROLINA DEPT RADIOLCHAPEL HILLNC 27514

The point response resolution of a gamma camera deteriorates with increased distance from the face of the collimator. This results in reconstruction artifacts that are seen as shape distortion and density non-uniformity. For parallel, fan, and cone beam geometries, iterative reconstruction algorithms have been developed which eliminate these artifacts by incorporating the three-dimensional spatially varying geometric point response into models for the projection and backprojection operations which also model photon attenuation. The algorithms have been tested on an IBM 3090-600S supercomputer. The iterative EM reconstruction algorithm is 50 times longer with geometric response and photon attenuation models than without modeling these physical effects. We have demonstrated an improvement in image quality in the reconstruction of projection data collected from a single photon emission computed tomography (SPECT) imaging system. Using phantom experiments, we observe that the modeling of the spatial system response imposes a smoothing without loss of resolution.

关键词： reconstruction algorithms Solid modeling Attenuation Image quality Spatial resolution Geometry Iterative algorithms Testing Supercomputers Single photon emission computed tomography

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Full- and minimal-scan reconstruction algorithms for fan-beam diffraction tomography

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APPLIED OPTICS 2001年第20期40卷 3334-3345页

作者： Anastasio, MA Pan, XC Univ Chicago Dept Radiol Grad Program Med Phys Chicago IL 60637 USA

Diffraction tomography (DT) is a tomographic inversion technique that reconstructs the spatially variant refractive-index distribution of a scattering object. In fan-beam DT, the interrogating radiation is not a plane wave but rather a cylindrical wave front emanating from a line source located a finite distance from the scattering object. We reveal and examine the redundant information that is inherent in the fan-beam DT data function. Such redundant information can be exploited to reduce the reconstructed image variance or, alternatively, to reduce the angular scanning requirements of the fan-beam DT experiment. We develop novel filtered backpropagation and estimate-combination reconstruction algorithms for full-scan and minimal-scan fan-beam DT. The full-scan algorithms utilize measurements taken over the angular range 0 less than or equal to phi phi less than or equal to 2 pi, whereas the minimal-scan reconstruction algorithms utilize only measurements taken over the angular range 0 less than or equal to phi less than or equal to phi (min) where pi less than or equal to phi (min) less than or equal to 3 pi /2 is a specified function that describes the fan-beam geometry. We demonstrate that the full- and minimal-scan fan-beam algorithms are mathematically equivalent. An implementation of the algorithms and numerical results obtained with noiseless and noisy simulated data are presented. (C) 2001 Optical Society of America.

关键词： Computed tomography Fast Fourier transforms Numerical analysis reconstruction algorithms Tomographic image reconstruction Wavefronts

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Highly accurate wavefront reconstruction algorithms over broad spatial-frequency bandwidth

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OPTICS EXPRESS 2011年第20期19卷 18997-19014页

作者： Bahk, Seung-Whan Univ Rochester Laser Energet Lab Rochester NY 14623 USA

New algorithms for reconstructing wavefront from slopes data are developed, which exhibit high accuracy over broad spatial-frequency bandwidth. Analyzing wavefront reconstructors in the frequency domain lends new insight into ways to improve frequency response and to understand noise propagation. The mathematical tools required to analyze the frequency domain are first developed for discrete band-limited signals. These tools are shown to improve frequency response in either spatialor frequency-domain reconstruction algorithms. A new spatial-domain iterative reconstruction algorithm based on the Simpson rule is presented. The local phase estimate is averaged over 8 neighboring points whereas the traditional reconstructors use 4 points. Analytic results and numerical simulations show that the Simpson-rule-based reconstructor provides high accuracy up to 85% of the bandwidth. The previously developed rectangular-geometry band-limited algorithm in frequency domain is adapted to hexagonal geometry, which adds flexibility when applying frequency-domain algorithms. Finally, a generalized analytic expression for error propagation coefficient is found for different reconstructors and compared with numerical simulations. (C) 2011 Optical Society of America

关键词： High power lasers Image reconstruction Laser beams Numerical simulation reconstruction algorithms Spatial frequency

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