Fan-beam Reconstruction Methods
In a previous paper a technique was developed for finding reconstruction algorithms for arbitrary ray-sampling schemes. The resulting algorithms use a general linear operator, the kernel of which depends on the details of the scanning geometry. Here this method is applied to the problem of re...
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| Language: | en_US |
| Published: |
2004
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| Online Access: | http://hdl.handle.net/1721.1/5749 |
| _version_ | 1811090475906498560 |
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| author | Horn, Berthold K.P. |
| author_facet | Horn, Berthold K.P. |
| author_sort | Horn, Berthold K.P. |
| collection | MIT |
| description | In a previous paper a technique was developed for finding reconstruction algorithms for arbitrary ray-sampling schemes. The resulting algorithms use a general linear operator, the kernel of which depends on the details of the scanning geometry. Here this method is applied to the problem of reconstructing density distributions from arbitrary fan-beam data. The general fan-beam method is then specialized to a number of scanning geometries of practical importance. Included are two cases where the kernel of the general linear operator can be factored and rewritten as a function of the difference of coordinates only and the superposition integral consequently simplifies into a convolution integral. Algorithms for these special cases of the fan-beam problem have been developed previously by others. In the general case, however, Fourier transforms and convolutions do not apply, and linear space-variant operators must be used. As a demonstration, details of a fan-beam method for data obtained with uniform ray-sampling density are developed. |
| first_indexed | 2024-09-23T14:46:46Z |
| id | mit-1721.1/5749 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:46:46Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/57492019-04-11T03:10:25Z Fan-beam Reconstruction Methods Horn, Berthold K.P. In a previous paper a technique was developed for finding reconstruction algorithms for arbitrary ray-sampling schemes. The resulting algorithms use a general linear operator, the kernel of which depends on the details of the scanning geometry. Here this method is applied to the problem of reconstructing density distributions from arbitrary fan-beam data. The general fan-beam method is then specialized to a number of scanning geometries of practical importance. Included are two cases where the kernel of the general linear operator can be factored and rewritten as a function of the difference of coordinates only and the superposition integral consequently simplifies into a convolution integral. Algorithms for these special cases of the fan-beam problem have been developed previously by others. In the general case, however, Fourier transforms and convolutions do not apply, and linear space-variant operators must be used. As a demonstration, details of a fan-beam method for data obtained with uniform ray-sampling density are developed. 2004-10-01T20:33:53Z 2004-10-01T20:33:53Z 1977-11-01 AIM-448 http://hdl.handle.net/1721.1/5749 en_US AIM-448 42 p. 6372636 bytes 4597398 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | Horn, Berthold K.P. Fan-beam Reconstruction Methods |
| title | Fan-beam Reconstruction Methods |
| title_full | Fan-beam Reconstruction Methods |
| title_fullStr | Fan-beam Reconstruction Methods |
| title_full_unstemmed | Fan-beam Reconstruction Methods |
| title_short | Fan-beam Reconstruction Methods |
| title_sort | fan beam reconstruction methods |
| url | http://hdl.handle.net/1721.1/5749 |
| work_keys_str_mv | AT hornbertholdkp fanbeamreconstructionmethods |