Least squares algorithm for region-of-interest evaluation in emission tomography

Abstract

An accurate model of the nonstationary geometrical response of a camera-collimator system is discussed. The algorithm is compared to three other algorithms that are specialized for region-of-interest evaluation, as well as to the conventional method for summing the reconstructed quantity over the regions of interest. For noise-free data and for regions of accurate shape, least-squares estimates were unbiased within roundoff errors. For noisy data, estimates were still unbiased but precision worsened for regions smaller than resolution: simulating typical statistics of brain perfusion studies performed with a collimated camera, the estimated standard deviation for a 1-cm-square region was 10% with an ultra-high-resolution collimator and 7% with a low-energy all-purpose collimator. Conventional region-of-interest estimates show comparable precision but are heavily biased if filtered backprojection is used for image reconstruction. Using the conjugate-gradient iterative algorithm and the model of nonstationary geometrical response, bias of estimates decreased on increasing the number of iterations, but precision worsened, thus achieving an estimated standard deviation of more than 25% for the same 1-cm region.

Partial Volume Correction Strategies in PET

“…Reconstruction methods that improve the effective resolution of the scanner (at a given noise level) can be considered as PVC methods. In this sense, there are numerous approaches to reconstruction that attempt to achieve the aforementioned goals [46,47]; the use of statistical iterative reconstructions has been an important step in this direction both for voxel-based [11,48] and ROI-based [49][50][51][52] reconstructions. Within the context of these algorithms (and building on them), a number of recent methods deserve to be highlighted.…”

Time‐varying reconstruction in single photon emission computed tomography

“…In emission tomography this summation is usually done after the reconstruction. It is, however, possible to select the ROIs before the reconstruction and reduce the dimensions of the problem by assuming that the activity is constant within each ROI (Carson, 1986;Formiconi, 1993). Let vector w [ R q denote the total activities of q nonintersecting ROIs whose union covers the whole slice…”

Iterative region of interest reconstruction in emission tomography

“…We must emphasize the important different between our interest in this paper and the focus of region of interest evaluation, for example, in [1] and [2]. Their aim is to conduct ROI evaluation due to concerns in the quanti cation of emission tomographic data [2]. In this context, the FOV is divided into several ROIs, namely…”