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Study of noise propagation and the effects of insufficient numbers of projection angles and detector samplings for iterative reconstruction using planar‐integral data
Author(s) -
Zhang B.,
Zeng G. L.
Publication year - 2006
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2266270
Subject(s) - line integral , collimator , iterative reconstruction , planar , noise (video) , detector , integral imaging , projection (relational algebra) , optics , iterative method , physics , mathematics , geometry , integral equation , mathematical analysis , algorithm , computer vision , computer science , image (mathematics) , computer graphics (images)
A rotating slat collimator can be used to acquire planar‐integral data. It achieves higher geometric efficiency than a parallel‐hole collimator by accepting more photons, but the planar‐integral data contain less tomographic information that may result in larger noise amplification in the reconstruction. Lodge evaluated the rotating slat system and the parallel‐hole system based on noise behavior for an FBP reconstruction. Here, we evaluate the noise propagation properties of the two collimation systems for iterative reconstruction. We extend Huesman's noise propagation analysis of the line‐integral system to the planar‐integral case, and show that approximately 2.0 ( D ∕ d p ) SPECT angles, 2.5 ( D ∕ d p ) self‐spinning angles at each detector position, and a 0.5 d p detector sampling interval are required in order for the planar‐integral data to be efficiently utilized. Here, D is the diameter of the object and d p is the linear dimension of the voxels that subdivide the object. The noise propagation behaviors of the two systems are then compared based on a least‐square reconstruction using the ratio of the SNR in the image reconstructed using a planar‐integral system to that reconstructed using a line‐integral system. The ratio is found to be proportional toF ∕ D, where F is a geometric efficiency factor. This result has been verified by computer simulations. It confirms that for an iterative reconstruction, the noise tradeoff of the two systems is not only dependent on the increase of the geometric efficiency afforded by the planar projection method, but also dependent on the size of the object. The planar‐integral system works better for small objects, while the line‐integral system performs better for large ones. This result is consistent with Lodge's results based on the FBP method.