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The spatial resolution and noise properties of a computed tomography (CT) image may be altered by two-dimensional linear filtering of the initial image. In this paper, we derive filters that minimize the noise variance subject to a constraint on the spatial resolution. The resulting filter functions can reduce the noise variance by 17% in comparison with conventional filters. The method for obtaining these filters requires knowledge of the noise and imaging properties of the system. We derive theoretical expressions for these properties and introduce experimental techniques for their measurement. The statistical characteristics are shown to be anisotropic, spatially variant, and object dependent. We discuss the implications of this result both for optimal filtering and for the general problem of CT image noise property measurement.
Alvarez et al. (Thu,) studied this question.