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Iterative methods for image reconstruction
 IEEE International Symposium on Biomedical Imaging Tutorial
, 2006
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Image Reconstruction Techniques for PET
"... this report lies on the reconstruction of PET images. Therefore we start, in x2, with a statistical description of the PET measurement process. The algorithms used to reconstruct these images depend on the medical scanner and on the noise in the data. They are subdivided into three major groups. Ana ..."
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this report lies on the reconstruction of PET images. Therefore we start, in x2, with a statistical description of the PET measurement process. The algorithms used to reconstruct these images depend on the medical scanner and on the noise in the data. They are subdivided into three major groups. Analytical algorithms [2] are based on a continuous description of the image and the data. They formulate a continuous solution which is discretized before being implemented as a computer program. These algorithms assume that the measurement space has been uniformly sampled by the scanner and that the noise in the data can be neglected. Sometimes the available data do not satisfy these constraints, or sometimes the measurement space has been sampled too sparsely to obtain an adequate discretisation of the continuous solution. In these cases one needs to use iterative algorithms [3]. Iterative algorithms start from a discretized description of the image as a linear combination of a limited set of basis functions. They try to find the most appropriate weights according to the available data. Iterative algorithms are further subdivided into two groups, depending on whether or not the reconstruction is based on a statistical description of the measurement process. In x3 we are interested in the discretisation of images for the use of iterative reconstruction algorithms. We define constraints on the basis functions in the spatial and in the frequency domain. We find that for PET and CT spatially limited and for MRI frequency limited basis functions result in the most efficient implementations. For PET and CT we also find that the basis functions should decay as fast as possible in the frequency domain, and that for MRI the basis functions should decay as fast as possible in the spati...
Fast Implementations of Algebraic Methods for 3D Reconstruction from ConeBeam Data
 IEEE Transactions on Medical Imaging
, 1998
"... The prime motivation of this work is to devise techniques that make the Algebraic Reconstruction Technique (ART) and related methods more efficient for routine clinical use, while not compromising their accuracy. In particular, we strive to push the overall cost for a ART reconstruction as close ..."
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The prime motivation of this work is to devise techniques that make the Algebraic Reconstruction Technique (ART) and related methods more efficient for routine clinical use, while not compromising their accuracy. In particular, we strive to push the overall cost for a ART reconstruction as close as possible to the theoretical cost for a reconstruction obtained with Filtered Backprojection (FBP). While we focus mostly on fast implementations of ARTtype methods in the context of 3D conebeam reconstruction, different parts of the material presented here is also applicable to speed up reconstruction from fanbeam and parallelbeam data. It was shown in previous research that three iterations are sufficient to obtain a high quality reconstruction for lowcontrast conebeam. Based on the observation that ART typically only requires only half the projections of FBP, we conclude that if the overall cost for ART's projectionbackprojection operations could be cut in half, then one ...
A dataparallel algorithm for iterative tomographic image reconstruction
 In Proceedings of the 7th Symposium on the Frontiers of Massively Parallel Computation
, 1999
"... In the tomographic imaging problem, images are reconstructed from a set of measured projections. Iterative reconstruction methods are computationally intensive alternatives to the more traditional Fourierbased methods. Despite their high cost, the popularity of these methods is increasing because o ..."
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In the tomographic imaging problem, images are reconstructed from a set of measured projections. Iterative reconstruction methods are computationally intensive alternatives to the more traditional Fourierbased methods. Despite their high cost, the popularity of these methods is increasing because of the advantages they pose. Although numerous iterative methods have been proposed over the years, all of these methods can be shown to have a similar computational structure. This paper presents a parallel algorithm that we originally developed for performing the expectation maximization algorithm in emission tomography. This algorithm is capable of exploiting the sparsity and symmetries of the model in a computationally efficient manner. Our parallelization scheme is based upon decomposition of the measurementspace vectors. We demonstrate that such a parallelization scheme is applicable to the vast majority of iterative reconstruction algorithms proposed to date. 1.
Medical Image Reconstruction Using a Multiobjective Genetic Local Search Algorithm
 International J. Computer Math
, 1999
"... Image reconstruction from projections is a key problem in medical image analysis. ..."
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Image reconstruction from projections is a key problem in medical image analysis.
Data inversion for overresolved spectral imaging in astronomy
 Selec. Topics in Signal Proc
, 2008
"... Abstract—We present an original method for reconstructing a 3D object having two spatial dimensions and one spectral dimension from data provided by the infrared slit spectrograph on board the Spitzer Space Telescope. During acquisition, the light flux is deformed by a complex process comprising ..."
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Abstract—We present an original method for reconstructing a 3D object having two spatial dimensions and one spectral dimension from data provided by the infrared slit spectrograph on board the Spitzer Space Telescope. During acquisition, the light flux is deformed by a complex process comprising four main elements (the telescope aperture, the slit, the diffraction grating, and optical distortion) before it reaches the 2D sensor. The originality of this work lies in the physical modeling, in integral form, of this process of data formation in continuous variables. The inversion is also approached with continuous variables in a semiparametric format decomposing the object into a family of Gaussian functions. The estimate is built in a deterministic regularization framework as the minimizer of a quadratic criterion. These specificities give our method the power to overresolve. Its performance is illustrated using real and simulated data. We also present a study of the resolution showing a 1.5fold improvement relative to conventional methods. Index Terms—Bayesian estimation, interpolation, inverse problems, irregular sampling, IRS Spitzer, overresolved imaging, spectral imaging. I.
3D Reconstruction of 2D Crystals in Real Space
"... Abstract—A new algorithm for threedimensional reconstruction of twodimensional crystals from projections is presented, and its applicability to biological macromolecules imaged using transmission electron microscopy (TEM) is investigated. Its main departures from the traditional approach is that i ..."
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Abstract—A new algorithm for threedimensional reconstruction of twodimensional crystals from projections is presented, and its applicability to biological macromolecules imaged using transmission electron microscopy (TEM) is investigated. Its main departures from the traditional approach is that it works in real space, rather than in Fourier space, and it is iterative. This has the advantage of making it convenient to introduce additional constraints (such as the support of the function to be reconstructed, which may be known from alternative measurements) and has the potential of more accurately modeling the TEM image formation process. Phantom experiments indicate the superiority of the new approach even without the introduction of constraints in addition to the projection data. Index Terms—3D reconstruction, crystals, electron microscopy, image reconstruction, projections. I.
Accurate LowContrast 3D ConeBeam Reconstruction With Algebraic Methods
"... This paper examines the use of the Algebraic Reconstruction Method (ART) and related techniques to reconstruct 3D objects from a relatively sparse set of conebeam projection data. Although ART has been widely used for conebeam reconstruction of highcontrast objects, e.g. in computed angiograph ..."
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This paper examines the use of the Algebraic Reconstruction Method (ART) and related techniques to reconstruct 3D objects from a relatively sparse set of conebeam projection data. Although ART has been widely used for conebeam reconstruction of highcontrast objects, e.g. in computed angiography, we are interested in the more challenging lowcontrast case which represents a little investigated scenario for ART. Preliminary experiments indicate that for cone angles greater than 20, traditional ART produces reconstructions with strong aliasing artifacts, obliterating much object detail. By analyzing the reconstruction process using signal processing principles it is revealed that the source of these artifacts is the nonuniform reconstruction grid sampling of the conebeam rays. To eliminate these errors, we devise a new way of computing the weights of the reconstruction matrix. This new method is more adequate for conebeam and replaces the usual constantsize interpolation...
Fast Implementations of Algebraic Methods for ThreeDimensional Reconstruction from ConeBeam Data
 IEEE Trans. Med. Imag.,vol
, 1999
"... The prime motivation of this work is to devise techniques that make the algebraic reconstruction technique (ART) and related methods more efficient for routine clinical use, while not compromising their accuracy. Since most of the computational effort of ART is spent for projection/backprojection op ..."
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The prime motivation of this work is to devise techniques that make the algebraic reconstruction technique (ART) and related methods more efficient for routine clinical use, while not compromising their accuracy. Since most of the computational effort of ART is spent for projection/backprojection operations, we first seek to optimize the projection algorithm. Existing projection algorithms are surveyed and it is found that these algorithms either lack accuracy or speed, or are not suitable for conebeam reconstruction. We hence devise a new and more accurate extension to the splatting algorithm, a wellknown voxeldriven projection method. We also describe a new threedimensional (3D) raydriven projector that is considerably faster than the voxeldriven projector and, at the same time, more accurate and perfectly suited for the demands of cone beam. We then devise caching schemes for both ART and simultaneous ART (SART), which minimize the number of redundant computations for projecti...
Nonuniform Sampling: Exact Reconstruction From Nonuniformly Distributed . . .
, 2002
"... this article, we discuss the problem of reconstructing a function f in a latticeinvariant subspace of L (IR ) from a family of nonuniformly distributed, weightedaverages fhf; x j i : j 2 Jg using an approximationprojection iterative algorithm ..."
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this article, we discuss the problem of reconstructing a function f in a latticeinvariant subspace of L (IR ) from a family of nonuniformly distributed, weightedaverages fhf; x j i : j 2 Jg using an approximationprojection iterative algorithm