Smoothing the rough edges of tomographic regions of interest: An approach to variance reduction
- Lawrence Berkeley National Lab., CA (United States)
We present an approach to reducing the variance of regional estimates of tracer concentration from emission tomographic data. The standard procedure for estimating regional tracer concentrations form emission tomographic data may be summarized as follows. A region of interest (ROI) is defined within the organ of interest. The concentration estimate is obtained by integrating the reconstructed image over the ROI and dividing by the volume of the ROI. This estimate may be written as {integral} m(x){line_integral}(x)dx, where m is the normalized mask function of the ROI and {line_integral} is the reconstructed image. We propose replacing the mask function with a smooth aperture function {phi} that is 0 outside the ROI and normalized so that {integral} {phi}(x)dx = 1. The corresponding concentration estimate is then given by {integral}{phi}(x){line_integral}(x)dx. We have found that, with an appropriate choice of {phi}, estimates obtained using this procedure have a smaller variance than those obtained using the standard procedure. It is to be noted that if the tracer concentration is not constant over the ROI, the two approaches may give somewhat different results. Roughly speaking, the concentration estimates obtained using the new procedure will be weighted more toward the center of the organ. The significance of this point will depend on the particular application. The reduction in variance obtained using this technique depends essentially on the correlation properties of the statistical errors in reconstructed tomographic images. In the analogous non-tomographic planar-imaging problem, it may be shown that the mask function for an ROI minimizes the variance of concentration estimates with respect to all functions that are 0 outside the ROI. We present simple examples showing that this technique can substantially reduce the variance of tracer concentration estimates. The improvement is particularly significant for a 3D ROI.
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 447772
- Report Number(s):
- CONF-960659-; ISSN 0161-5505; CNN: Grant HL25840; TRN: 97:000961-0052
- Journal Information:
- Journal of Nuclear Medicine, Vol. 37, Issue Suppl.5; Conference: 43. annual meeting of the Society of Nuclear Medicine, Denver, CO (United States), 3-6 Jun 1996; Other Information: PBD: May 1996
- Country of Publication:
- United States
- Language:
- English
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