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Mean-variance analysis of block-iterative reconstruction algorithms modeling 3D detector response in SPECT

IEEE TRANSACTIONS ON NUCLEAR SCIENCE 1998年第3期45卷 1280-1287页

作者： Lalush, DS Tsui, BMW Univ N Carolina Dept Biomed Engn Chapel Hill NC 27514 USA Univ N Carolina Dept Radiol Chapel Hill NC USA

We study the statistical convergence properties of two Cast iterative reconstruction algorithms, the rescaled block-iterative (RBI) and ordered subset (OS) EM algorithms, in the context of cardiac SPECT with 3D detector response modeling. The Monte Carlo method was used to generate nearly noise-free projection data modeling the effects of attenuation, detector response, and scatter from the MCAT phantom. One thousand noise realizations were generated with an average count level approximating a typical Tl-201 cardiac study. Each noise realization was reconstructed using the RBI and OS algorithms for cases with and without detector response modeling. For each iteration up to twenty, we generated mean and variance images, as well as covariance images for six specific locations. Both OS and RBI converged in the mean to results that were close to the noise-free ML-EM result using the same projection model. When detector response was not modeled in the reconstruction, RBI exhibited considerably lower noise variance than OS for the same resolution. When 3D detector response was modeled, the RBI-EM provided a small improvement in the tradeoff between noise level and resolution recovery, primarily in the axial direction, while OS required about half the number of iterations of RBI to reach the same resolution. We conclude that OS is faster than RBI, but may be sensitive to errors in the projection model. Both OS-EM and RBI-EM are effective alternatives to the ML-EM algorithm, but noise level and speed of convergence depend on the projection model used.

关键词： Algorithm design and analysis Reconstruction algorithms Detectors Noise level Convergence Noise generators Image reconstruction iterative algorithms Context modeling Attenuation

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Hemispherical spatial sampling study and 3D image reconstruction using iterative algorithms for a Compton SPECT camera model

Hemispherical spatial sampling study and 3D image reconstruc...

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IEEE Symposium on Nuclear Science (NSS/MIC)

作者： A.C. Sauve A.O. Hero W.L. Rogers N.H. Clinthorne Department of Electrical Engineering and Computer Science University of Michigan Technical University of Munich Ann Arbor MI USA Department of Nuclear Medicine University of Michigan Technical University of Munich Ann Arbor MI USA

In this paper we will present numerical studies of the performance of a 3D Compton camera being developed at the University of Michigan. We present a physical model of the camera which exploits symmetries by using an adapted spatial sampling pattern in the object domain. This model increases the sparsity of the transition matrix to reduce the very high storage and computation requirements. This model also allows the decomposition of the transition matrix into several small blocks that are easy to store. We also present the transition matrix of our system analytically computed with a real time algorithm. We geometrically optimize our hemispherical sampling and develop a 3D volumetric interpolation. Finally, we present a 3D image reconstruction method which uses the Gauss-Seidel algorithm to minimize a penalized least square objective.

关键词： Image sampling Image reconstruction iterative algorithms Detectors Cameras Object detection Event detection Interpolation Sampling methods Coordinate measuring machines

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Optimally Tuned iterative Reconstruction algorithms for Compressed Sensing

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IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2010年第2期4卷 330-341页

作者： Maleki, Arian Donoho, David L. Stanford Univ Dept Elect Engn Stanford CA 94305 USA Stanford Univ Dept Stat Stanford CA 94305 USA

We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the optimally tuned implementations available at ***;they run "out of the box" with no user tuning: it is not necessary to select thresholds or know the likely degree of sparsity. Our class of algorithms includes iterative hard and soft thresholding with or without relaxation, as well as CoSaMP, subspace pursuit and some natural extensions. As a result, our optimally tuned algorithms dominate such proposals. Our notion of optimality is defined in terms of phase transitions, i.e., we maximize the number of nonzeros at which the algorithm can successfully operate. We show that the phase transition is a well-defined quantity with our suite of random underdetermined linear systems. Our tuning gives the highest transition possible within each class of algorithms. We verify by extensive computation the robustness of our recommendations to the amplitude distribution of the nonzero coefficients as well as the matrix ensemble defining the underdetermined system. Our findings include the following. 1) For all algorithms, the worst amplitude distribution for nonzeros is generally the constant-amplitude random-sign distribution, where all nonzeros are the same amplitude. 2) Various random matrix ensembles give the same phase transitions;random partial isometries may give different transitions and require different tuning. 3) Optimally tuned subspace pursuit dominates optimally tuned CoSaMP, particularly so when the system is almost square.

关键词： Compressed sensing iterative algorithms phase transition random matrices thresholding

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A comparison between quadratic and sign adaptive iterative algorithms for spikey deconvolution

A comparison between quadratic and sign adaptive iterative a...

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Mediterranean Electrotechnical Conference (MELECON)

作者： A. Artes-Rodriguez A.R. Figueiras Vidal D. Docampo-Amoedo J.R. Casar-Corredera DTC ETSI de Telecomunicacion Pontevedra Spain DSSR ETSI-Telecomunicacion UPM Ciudad Universitaria Madrid Spain

The authors introduce two algorithms in quadratic and sign gradient-type versions for spikey deconvolution based on a double (detection-estimation) formulation of the problem. Both algorithms are based on the application of a selection operator to detect the nonzero values of a solution provided by a standard approach. In the first algorithm, a gradient-type iterative reduction of the error is used. The second algorithm minimizes the signal to be obtained. Their performances using l/sub 1/ and l/sub 2/ norms in the minimization are compared in terms of resolution, robustness, speed of convergence, and computational load.< >

关键词： iterative algorithms Deconvolution Integrated circuit modeling Computer simulation Paints Signal processing Minimization methods Independent component analysis Computational modeling Poles and zeros

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Performance tuning of iterative algorithms in signal processing

Performance tuning of iterative algorithms in signal process...

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International Conference on Field Programmable Logic and Applications

作者： Z. Pohl J. Kadlec P. Sucha Z. Hanzdlek Institute of Information Theory and Automation Academy of Sciences슠of the슠Czech Republic Czech Republic Academy of Sciences of the Czech Republic Institute of Information Theory and Automation CAK Czech Technical University in Prague Czech Republic CAK Czech Technical University in Prague

Presented high-level synthesis describes scheduling for wide class of DSP algorithms. Several FPGA vendors or even ASIC designs are targeted via Handel-C compiled by Celoxica DK3.1 compiler. Using the authors' approach, the designer can easily change type of used pipelined arithmetic modules and then check new performance. The optimal time schedule is found by cyclic scheduling using integer linear programming while minimizing the schedule period in the terms of clock cycles. Experimental results in HW implementation, performed on logarithmic arithmetic and floating-point arithmetic, confirm significant influence of the period on the resulting performance of DSP algorithms.

关键词： iterative algorithms Signal processing algorithms Digital signal processing Floating-point arithmetic High level synthesis Scheduling algorithm Field programmable gate arrays Application specific integrated circuits Integer linear programming Clocks

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Regularization methods in iterative algorithms for variance reduction on compressed sinogram random coincidences

Regularization methods in iterative algorithms for variance ...

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IEEE Symposium on Nuclear Science (NSS/MIC)

作者： V. Y. Panin Molecular Imaging Knoxville TN USA

The Poisson model based image reconstruction algorithms in PET require the estimation of the mean value of random coincidences. The random data are often acquired with a delayed coincidence technique, and expected randoms are estimated through variance reduction (VR) of measured delayed coincidences. In the past we have developed iterative VR algorithms that estimate singles rates from random compressed sinograms. The final estimation of singles rates can be noisy in short scans. In the present work, we apply commonly used and specific regularization methods. A sequential coordinate ascent algorithm is used to maximize the penalized Poisson Likelihood objective function. Measured data from a Siemens TruePoint clinical scanner are used to validate the algorithm performance.

关键词： iterative algorithms Frequency estimation Image reconstruction Delay estimation Virtual reality Maximum likelihood estimation Convergence Positron emission tomography Equations Data compression

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The use of some iterative deconvolution algorithms to improve the spatial resolution of a flat magnetic sensor

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SENSORS AND ACTUATORS A-PHYSICAL 1997年第1期63卷 7-13页

作者： Fenniri, H Moineau, A Delaunay, G Laboratoire d'Applications de la Microelectronique Universite de Reims BP 1039 51687 Reims Cedex 2 France

In this paper we present an application of some iterative algorithms to solve a deconvolution problem. The aim is to solve an integral equation between an impulse response of a sensor and a desired and not accessible input signal. Experimentally, we want to remove the distortion effects of the measuring system on an input signal. The applications concern the measurement of the distance between a flat eddy-current proximity sensor and a metallic surface in front of it. Numerical results are presented as an illustration. Experiments have been carried out to ascertain the performance of the conjugate gradient algorithm outlined in this paper. We also compare its performance to that of the iterative sequential algorithm of Placko et al. (C) 1997 Elsevier Science S.A.

关键词： deconvolution iterative algorithms restoration of sensor images

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New iterative algorithms and architectures of modular multiplication for cryptography

New iterative algorithms and architectures of modular multip...

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IEEE International Conference on Electronics, Circuits and Systems (ICECS)

作者： O. Nibouche A. Bouridane M. Nibouche School of Computer Science Queen''s University Belfast UK

algorithms and architectures for performing modular multiplication operations, which is central to crypto-system and authentication schemes, are important in today's needs of secure communications. This paper presents two new iterative algorithms for modular multiplication. The implementation of these algorithms yields to scalable architectures that can be used for any modulus without altering the design. In addition, the Radix-2 algorithm shows almost similar features when compared with similar architectures available in the literature. Furthermore, the radix-4 algorithm can be used to develop higher radix algorithms since it only requires the use of powers of two of the modulus.

关键词： iterative algorithms Cryptography Computer architecture Authentication Algorithm design and analysis Information security Computer science Wireless communication Smart cards Communication system security

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Factor graphs and iterative algorithms

Factor graphs and iterative algorithms

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Information Theory and Networking Workshop

作者： R. Koetter Coordinated Science Laboratory University of Illinois Urbana IL USA

We review the notion of factor graphs and give an overview of recent developments in the field. Factor graphs provide a framework in which iterative algorithms and iteratively decodable codes are easily described. They are obtained as a slight modification of the graphs, which were introduced by Wiberg, Loeliger and Koetter (1995). The notion of factor graphs is related to other graphical models, such as Bayesian networks and Markov random fields, and allows an easy integration of the decoding task and related problems in a communication system, such as channel estimation and equalization. Recently a number of research topics involving factor graphs have developed. These include the construction and representation of codes on graphs and an analysis of iterative decoding algorithm stemming from the theory of dynamical systems.

关键词： iterative algorithms iterative decoding Algorithm design and analysis Codes Explosions Bayesian methods Markov random fields Communication systems Channel estimation Visualization

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Fast iterative algorithms for the fine detail analysis of planar scatterers

Fast iterative algorithms for the fine detail analysis of pl...

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IEEE Convention of the Electrical and ELectronic Engineers in Israel

作者： B. Finkelstein R. Kastner Department of Physical Electronics Faculty of Engineering Tel-Aviv University Tel-Aviv Israel

A class of very efficient iterative algorithms is presented for the analysis of planar scatterers at the very fine detail regime. The mechanisms causing slow convergence in these cases have been identified and their effect corrected in a newly introduced algorithm. Further convergence enhancement is achieved by one or two additional minimization steps. The resultant new algorithms converge very fast for problems with fine details sampled faster than 0.001/spl lambda/, where other methods fail.

关键词： iterative algorithms Algorithm design and analysis Scattering Convergence Character generation Gradient methods Sampling methods Minimization methods Transmission line matrix methods Roundoff errors

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