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Fast image reconstruction for Compton camera using stochastic origin ensemble approach
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10.1118/1.3528170
/content/aapm/journal/medphys/38/1/10.1118/1.3528170
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/38/1/10.1118/1.3528170

Figures

Image of FIG. 1.
FIG. 1.

The principle of image formation in a Compton camera.

Image of FIG. 2.
FIG. 2.

The central slice through the initial density matrix for the point source. Acceptance rules will work in the following way: (a) A new position will be accepted with 100% probability as in this case the event density increases; (b) the new position will be accepted with low probability due to the sharp decrease in event density.

Image of FIG. 3.
FIG. 3.

The difference between (a) SOE for Compton camera and (b) SOE for PET. The small dots indicate the current photon origin candidates; the small stars indicate the true source locations. Events are “moved” by the algorithm on (a) half-cone surfaces for Compton camera or on (b) lines for PET.

Image of FIG. 4.
FIG. 4.

(a) A location on the conical surface in SOE algorithm is parametrized by distance z and angle . (b) Forward and backprojection realized by multiple ray tracing through the surface of the cone was used for list-mode ML-EM.

Image of FIG. 5.
FIG. 5.

3D phantoms (left column) and corresponding initial event density images (right column) for (a) single point source, (b) 12 spheres, (c) ellipsoidal phantom with hot and cold regions, and (d) same phantom as in (c) with Poisson noise added. In each case the central slice of the phantom is shown. Note that the right column images have much lower intensity than in the left column.

Image of FIG. 6.
FIG. 6.

Point source reconstructions: (a) SOE 1000 iterations and (b) SOE 50 000 iterations. The central slice of the image with 2 mm voxel size is presented (please note the difference in intensity scale).

Image of FIG. 7.
FIG. 7.

Number of correctly assigned events versus iteration number. Ideally, in this case, the total number of events in the central voxel should be equal to 100 000, but this number is never reached.

Image of FIG. 8.
FIG. 8.

Central slice through the reconstructed images of the 3D phantom (experiment B) obtained with (a) realistic resolution SOE 100 iterations, (b) realistic resolution SOE 2000 iterations, and (c) realistic resolution ML-EM 50 iterations. Images were scaled to the same maximum.

Image of FIG. 9.
FIG. 9.

Central slice through the reconstructed images of the 3D phantom (experiment B) obtained with (a) perfect resolution SOE 100 iterations, (b) perfect resolution SOE 2000 iterations, and (c) perfect resolution ML-EM 50 iterations. Images were scaled to the same maximum.

Image of FIG. 10.
FIG. 10.

Central slice through the reconstructed images of the 3D phantom (experiment C) obtained with (a) SOE 100 iterations, (b) SOE 2000 iterations, (c) SOE 2000 iterations, postfiltered with Gaussian of 2.5 mm FWHM, (d) ML-EM 50 iterations (not filtered), and (e) profiles drawn through the centers of the large hot and small cold spheres in images (c) and (d). All images are scaled to the same maximum.

Image of FIG. 11.
FIG. 11.

Central slice through a reconstructed image of 3D phantom with noise, of counts [Fig. 5(d)]: (a) 100 SOE iterations, (b) 2000 SOE iterations, (c) 2000 SOE iterations, postfiltered with Gaussian of 3 mm FWHM, and (d) 50 ML-EM iterations (not filtered). All images are scaled to the same maximum.

Image of FIG. 12.
FIG. 12.

(a) Bias versus variance plot comparing the first 50 iterations (in one iteration increments) of ML-EM and the first 5000 iterations (in 100 iterations increments) of SOE. Also shown are (b) the result of 50 iterations of ML-EM, (c) 5000 SOE iteration, and (d) same 5000 SOE iterations postsmoothed with Gaussian filter of 1.5 voxels (3 mm) FWHM. The images are with 2 mm voxels.

Tables

Generic image for table
TABLE I.

Average values (avg) and standard deviation (std) of the reconstructed intensity for the selected ROIs in the ellipsoidal phantom (experiment C).

Generic image for table
TABLE II.

Average values (avg) and standard deviation (std) of the reconstructed intensity for the selected ROIs in the ellipsoidal phantom with noise (experiment D).

Generic image for table
TABLE III.

NMSE values measured in % for the reconstructed phantoms.

Generic image for table
TABLE IV.

The reconstructions times of the algorithms investigated in this paper.

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/content/aapm/journal/medphys/38/1/10.1118/1.3528170
2010-12-28
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Fast image reconstruction for Compton camera using stochastic origin ensemble approach
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/38/1/10.1118/1.3528170
10.1118/1.3528170
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