Comparison between parallel hole and rotating slat collimation: analytical noise propagation models

Efficient determination of the uncertainty for the optimization of SPECT system design: a subsampled fisher information matrix

System designs in single photon emission tomography (SPECT) can be evaluated based on the fundamental trade-off between bias and variance that can be achieved in the reconstruction of emission tomograms. This trade off can be derived analytically using the Cramer-Rao type bounds, which imply the calculation and the inversion of the Fisher information matrix (FIM). The inverse of the FIM expresses the uncertainty associated to the tomogram, enabling the comparison of system designs. However, computing, storing and inverting the FIM is not practical with 3-D imaging systems. In order to tackle the problem of the computational load in calculating the inverse of the FIM, a method based on the calculation of the local impulse response and the variance, in a single point, from a single row of the FIM, has been previously proposed for system design. However this approximation (circulant approximation) does not capture the global interdependence between the variables in shift-variant systems such as SPECT, and cannot account e.g., for data truncation or missing data. Our new formulation relies on subsampling the FIM. The FIM is calculated over a subset of voxels arranged in a grid that covers the whole volume. Every element of the FIM at the grid points is calculated exactly, accounting for the acquisition geometry and for the object. This new formulation reduces the computational complexity in estimating the uncertainty, but nevertheless accounts for the global interdependence between the variables, enabling the exploration of design spaces hindered by the circulant approximation. The graphics processing unit accelerated implementation of the algorithm reduces further the computation times, making the algorithm a good candidate for real-time optimization of adaptive imaging systems. This paper describes the subsampled FIM formulation and implementation details. The advantages and limitations of the new approximation are explored, in comparison with the circulant approximation, in the context of design optimization of a parallel-hole collimator SPECT system and of an adaptive imaging system (similar to the commercially available D-SPECT).

Tomographic image quality of rotating slat versus parallel hole-collimated SPECT

Parallel and converging hole collimators are most frequently used in nuclear medicine. Less common is the use of rotating slat collimators for single photon emission computed tomography (SPECT). The higher photon collection efficiency, inherent to the geometry of rotating slat collimators, results in much lower noise in the data. However, plane integrals contain spatial information in only one direction, whereas line integrals provide two-dimensional information. It is not a trivial question whether the initial gain in efficiency will compensate for the lower information content in the plane integrals. Therefore, a comparison of the performance of parallel hole and rotating slat collimation is needed. This study compares SPECT with rotating slat and parallel hole collimation in combination with MLEM reconstruction with accurate system modeling and correction for scatter and attenuation. A contrast-to-noise study revealed an improvement of a factor 2-3 for hot lesions and more than a factor of 4 for cold lesion. Furthermore, a clinically relevant case of heart lesion detection is simulated for rotating slat and parallel hole collimators. In this case, rotating slat collimators outperform the traditional parallel hole collimators. We conclude that rotating slat collimators are a valuable alternative for parallel hole collimators.