For many problems in medical imaging we assume a parameterized form for the object function, an activity distribution in
SPECT imaging for example, and use the data from the imaging system to estimate values for the parameters. In the
simplest and most widely used case the parameters of interest are voxel values for a scalar valued function, but other
parameterizations can be used that take into account our prior knowledge of the function, such as a non-negativity or
geometric constraints. In registration problems the function is vector valued and may contain parameters corresponding to
translations, rotations and other more complicated motions. For segmentation problems the parameters describe surfaces
and correspond to different aspects of shape. Ideally we want to use as few parameters as possible without losing essential
aspects of the object, and we want the data to give us good estimates of these parameters. The second requirement is
related to the problem of estimability, which we will discuss with an example from FMRI imaging. We believe that the first
problem must be addressed by specifying the task or tasks for which the images are being made, the observer who will use
these images, and the statistical properties of the data, including measurement noise and object variability. We will
illustrate this approach with a tumor detection task in SPECT imaging.
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