"Handbook of Medical Imaging, Volume 2. Medical Image by J. Michael Fitzpatrick, Milan Sonka

By J. Michael Fitzpatrick, Milan Sonka

...a vintage textual content meant to supply a finished evaluate of the idea and present perform of clinical Imaging.

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Example text

This depends on the scan duration, the source strength, and the detector efficiency at the source photon energy ¼ . The dependence on reflects the fact that in modern systems there are multiple detectors, each of which 1 Some gamma emitting radioisotopes produce photons at two or more distinct energies. If the detector has adequate energy resolution, then it can separate photons at the energy of interest from other photons, or bin the various energies separately. 6 Statistical Image Reconstruction Methods can have its own efficiency.

There are The problem 9 many possible choices for the basis functions. We would like to choose basis func¼. 9) below. The conventional basis is just the “pixel” or “voxel” basis, which satisfies both of these requirements. The voxel basis ´Üµ is 1 inside the th voxel, and is 0 everywhere else. 6) ¡ where ´Ü Ý µ is the center of the th pixel and ¡ is the pixel width. This basis gives a piecewise-constant approximation to ¼ , as illustrated in Fig. 2. 5), the problem of estimating ¼ ´Üµ is reduced to ¼ from the simpler problem of estimating the parameter vector ½ ÆÔ ¼ where “¼ ” denotes vector and matrix the measurement vector ½ Æ transpose.

One effective remedy to this problem is to modify the objective function by including a penalty function that favors reconstructed images that are piecewise smooth. This process is called regularization since the penalty function improves the conditioning of the problem 7 . 15) where the objective function ¨ includes a roughness penalty Ê´ µ discussed in more detail below. The parameter ¬ controls the tradeoff between spatial resolution and noise: larger values of ¬ generally lead to reduced noise at the price of reduced spatial resolution.

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