Fast PET image reconstruction based on SVD decomposition of the system matrix

Selivanov, V.

doi:10.1109/23.940160

Cited by 29 publications

(10 citation statements)

References 15 publications

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“…Reconstruction of temperature distribution via the travel time of numerous ultrasound paths is an inversion problem, a notable feature of which is the presence of ill-posed problem. Though is always an ill-conditioned matrix in this inversion problem, effective regularization estimate can be achieved by using the method of singular values decomposition (SVD) [27,28]. Known from analysis based on matrix theory, any real matrix ∈ × can be decomposed as follows:…”

Section: Reconstruction Algorithm Based On Markov Radial Basis Functimentioning

confidence: 99%

Temperature Distribution Monitoring Using Ultrasonic Thermometry Based on Markov Radial Basis Function Approximation and Singular Values Decomposition

Shen

Xiong

Shi

et al. 2014

Mathematical Problems in Engineering

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Information about temperature distribution is complex but of critical importance for the control of various microwave applications. In this paper, an innovative way of temperature distribution monitoring using ultrasonic thermometry in microwave field is investigated. The principle of ultrasonic thermometry in the situation of ideal gas is elaborated, and reconstruction algorithm based on Markov radial basis function approximation and singular values decomposition is presented and described in detail. In order to validate the performance of temperature distribution reconstruction of our presented algorithm, four two-dimensional temperature distribution models with different complexities are utilized in simulation experiments. Especially, simulation experiments taking error of measurement into account are studied to verify the robustness. Figure profiles show remarkable correspondence between the reconstructed ones and their models, while quantitative analysis, including the overall temperature error analysis and the hotspot positioning analysis, shows that different kinds of errors calculated are all within the limit ranges. In addition, the time analysis of simulation experiments also demonstrates its well real-time capability.

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Section: Reconstruction Algorithm Based On Markov Radial Basis Functimentioning

confidence: 99%

Temperature Distribution Monitoring Using Ultrasonic Thermometry Based on Markov Radial Basis Function Approximation and Singular Values Decomposition

Shen

Xiong

Shi

et al. 2014

Mathematical Problems in Engineering

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“…There is much research activity at present on the topic of iterative algorithms, involving a wide variety of methods, as summarized in [123]. Non-iterative algorithms have also been investigated for SPECT [124] and PET [125], although their use is limited to 2-D applications at present because of their computational demands. Iterative algorithms also have large computational demands, especially when used with the data sets produced by the current generation of high resolution PET scanners, and work is underway to implement these algorithms on clusters of commodity PC processors [84], [126].…”

Section: Notes and Referencesmentioning

confidence: 99%

Overview of methods for image reconstruction from projections in emission computed tomography

2003

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Emission computed tomography (ECT) is a technology for medical imaging whose importance is increasing rapidly. There is a growing appreciation for the value of the functional (as opposed to anatomical) information that is provided by ECT and there are significant advancements taking place, both in the instrumentation for data collection, and in the computer methods for generating images from the measured data. These computer methods are designed to solve the inverse problem known as "image reconstruction from projections." This paper uses the various models of the data collection process as the framework for presenting an overview of the wide variety of methods that have been developed for image reconstruction in the major subfields of ECT, which are positron emission tomography (PET) and single-photon emission computed tomography (SPECT). The overall sequence of the major sections in the paper, and the presentation within each major section, both proceed from the more realistic and general models to those that are idealized and application specific. For most of the topics, the description proceeds from the three-dimensional case to the two-dimensional case. The paper presents a broad overview of algorithms for PET and SPECT, giving references to the literature where these algorithms and their applications are described in more detail.

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“…Reconstructions carried out with ART exhibit the same artifact suggesting that the problem is linked to the model itself. We focus here on an alternative reconstruction technique, the Singular Value Decomposition (SVD) [10,11] which has been previously used in related problems of image reconstruction from projections [12][13][14]. In particular, we study the inversion of the TV transform using SVD, and we compare its reconstruction performance with our previous results.…”

Section: Introductionmentioning

confidence: 99%

SVD inversion for the bi-dimensional Conical Radon Transform

Cebeiro

Morvidone

2013

J. Phys.: Conf. Ser.

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Abstract.In nuclear medicine, the Conical Radon Transforms family includes 2D and 3D models for scatter radiation imaging. The underlying idea is taking advantage of Comptom effect in order to provide image reconstruction without rotating the detector system. Several techniques currently applied for the classical Radon transform may also be useful in this new context. Nevertheless, since the physical model is rather different, it is necessary to assess the performance of each method. In previous works, we have studied inversion by filtered-backprojection and adaptive algebraic reconstruction techniques. In this paper we study the performance of a method based in the factorization of the projection matrix in order to invert the projections. Particularly, we test our algorithms on the bi-dimensional Conical Radon Transform, a simple member of the Conical Radon family. We obtain useful results on the performance of the three methods which should be valuable in the more realistic 3D context.

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Fast PET image reconstruction based on SVD decomposition of the system matrix

Cited by 29 publications

References 15 publications

Temperature Distribution Monitoring Using Ultrasonic Thermometry Based on Markov Radial Basis Function Approximation and Singular Values Decomposition

Temperature Distribution Monitoring Using Ultrasonic Thermometry Based on Markov Radial Basis Function Approximation and Singular Values Decomposition

Overview of methods for image reconstruction from projections in emission computed tomography

SVD inversion for the bi-dimensional Conical Radon Transform

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