The Karhunen-Loeve transform in computerized tomography

by: Long-Wen Chang, Edward S Angel

Mathematical Biosciences, Vol. 77, No. 1-2. (December 1985), pp. 189-200.

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Abstract

Image coding and image reconstruction from projections have been two major research issues for the engineer and scientist in the past decade. Recently, the need to combine these problems to code the projections of computerized tomography (CT) has arisen. Coding for projected data in CT differs significantly from conventional coding in that we are not necessarily concerned with the accuracy of decoded projections but rather with the accuracy of the reconstructed image. To solve this problem, we investigate a new variant of the Karhunen-Loeve (KL) transform of projected data. The KL transform gives a bound for coding by transform methods. The new variant KL transform is to be equivalent to finding the reconstructed image and then applying the conventional KL transform to this image.

@article{citeulike:2658618, abstract = {Image coding and image reconstruction from projections have been two major research issues for the engineer and scientist in the past decade. Recently, the need to combine these problems to code the projections of computerized tomography (CT) has arisen. Coding for projected data in CT differs significantly from conventional coding in that we are not necessarily concerned with the accuracy of decoded projections but rather with the accuracy of the reconstructed image. To solve this problem, we investigate a new variant of the Karhunen-Loeve (KL) transform of projected data. The KL transform gives a bound for coding by transform methods. The new variant KL transform is to be equivalent to finding the reconstructed image and then applying the conventional KL transform to this image.}, author = {Chang, Long-Wen and Angel, Edward S. }, citeulike-article-id = {2658618}, doi = {http://dx.doi.org/10.1016/0025-5564(85)90097-5}, journal = {Mathematical Biosciences}, keywords = {coding, ct, projections, tomography}, month = {December}, number = {1-2}, pages = {189--200}, posted-at = {2008-04-11 19:46:37}, priority = {5}, title = {The Karhunen-Loeve transform in computerized tomography}, url = {http://dx.doi.org/10.1016/0025-5564(85)90097-5}, volume = {77}, year = {1985} }

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TY - JOUR ID - citeulike:2658618 L3 - citeulike-article-id:2658618 TI - The Karhunen-Loeve transform in computerized tomography JF - Mathematical Biosciences VL - 77 IS - 1-2 SP - 189 EP - 200 N2 - Image coding and image reconstruction from projections have been two major research issues for the engineer and scientist in the past decade. Recently, the need to combine these problems to code the projections of computerized tomography (CT) has arisen. Coding for projected data in CT differs significantly from conventional coding in that we are not necessarily concerned with the accuracy of decoded projections but rather with the accuracy of the reconstructed image. To solve this problem, we investigate a new variant of the Karhunen-Loeve (KL) transform of projected data. The KL transform gives a bound for coding by transform methods. The new variant KL transform is to be equivalent to finding the reconstructed image and then applying the conventional KL transform to this image. KW - coding KW - ct KW - projections KW - tomography AU - Chang, Long-Wen AU - Angel, Edward PY - 1985/12// UR - http://dx.doi.org/10.1016/0025-5564(85)90097-5 ER -

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