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231223s2009 xx |||||o 00| ||eng c |
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|a 10.1109/TIP.2009.2023724
|2 doi
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|a eng
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|a Cao, Guangzhi
|e verfasserin
|4 aut
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|a Noniterative MAP reconstruction using sparse matrix representations
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|c 2009
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|a Text
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|2 rdacontent
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|a ƒaComputermedien
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|a ƒa Online-Ressource
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|a Date Completed 06.10.2009
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|a Date Revised 13.08.2009
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|a published: Print-Electronic
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|a Citation Status MEDLINE
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|a We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms. We demonstrate the potential of the noniterative MAP reconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods
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|a Journal Article
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|a Research Support, U.S. Gov't, Non-P.H.S.
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|a Bouman, Charles A
|e verfasserin
|4 aut
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|a Webb, Kevin J
|e verfasserin
|4 aut
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| 773 |
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|i Enthalten in
|t IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
|d 1992
|g 18(2009), 9 vom: 05. Sept., Seite 2085-99
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|x 1941-0042
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|g volume:18
|g year:2009
|g number:9
|g day:05
|g month:09
|g pages:2085-99
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|u http://dx.doi.org/10.1109/TIP.2009.2023724
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