Formiconi A R, Pupi A, Passeri A
Dipartimento di Fisiopatologia Clinica, Unitá di Medicina Nucleare, Firenze, Italy.
Phys Med Biol. 1989 Jan;34(1):69-84. doi: 10.1088/0031-9155/34/1/007.
A procedure for the determination of the system matrix in single photon emission tomography (SPECT) is described which uses the conjugate gradient reconstruction technique in order to take into account the variable system resolution of a camera equipped with parallel-hole collimators. The procedure involves the acquisition of the system line spread functions (LSF) in the region occupied by the object to be studied. Those data are used to generate a set of weighting factors based on the assumption that the LSFs of the collimated camera are of Gaussian shape with the full width at half maximum (FWHM) linearly dependent on the source depth in the span of image space. The factors are stored on a disc file for subsequent use in the reconstruction process. Afterwards the reconstruction is performed using the conjugate gradient method with the system matrix modified by the incorporation of these precalculated factors in order to take into account the variable geometrical system response. The set of weighting factors is regenerated whenever the acquisition conditions are changed (collimator, radius of rotation). In the case of an ultra high resolution (UHR) collimator 2000 weighting factors need to be calculated. The modification of the system matrix for the geometrical response allows the number of iterations to increase, considerably improving image definition without the appearance of noise artifacts. Moreover, phantom studies show that the number of iterations is less critical because of improved stability in the convergence to the solution. For brain studies of patients 10-15 iterations are usually performed. Studies with a single line source give a value between 7 and 8 mm for the FWHM of the point spread function (PSF) when the conjugate gradient method with modified system matrix is used on data acquired with a UHR collimator, whereas without the modification of the system matrix the result is 9 mm FWHM, if filtered backprojection (FBP) is used with the same filter as in the clinical studies the result is 15 mm FWHM. The results of this work show that proper definition of the system matrix using conjugate gradients influences the quality of the reconstruction remarkably. Nevertheless, further work has to be done in order to assess to what extent the system matrix is ill-conditioned and, eventually, to define a suitable regularization technique.
