Analytical deconvolution for improvement in spatial resolution of the In-111 coincidence camera

The In-111 coincidence camera we previously proposed can significantly increase detection efficiency because collimators are no longer needed. However, the initial simulations indicated that spatial resolution was too poor for medical imaging. To improve the resolution, we derived an analytical deconvolution algorithm in this study. In the derivation, 1-D Fourier transform for the shift-invariant point spread function (PSF) with respect to the detector bin location t was carried out analytically. The Fourier transform is approximately a linear function of the source-to-detector distance s when s is greater than 5 cm and its variation over s is much slower than that of any extensive source. The Fourier transform of the PSF can thus be taken out of the integration over s with reasonable accuracy and its inversion is the deconvolution kernel. A low-pass filter was applied to the deconvolved Fourier transform to suppress high-frequency oscillation. Applying the derived deconvolution algorithm to computer simulated phantoms, we achieved a resolution of 2 cm for s = 10 cm. Compared to the pre-deconvolution resolution of 19 cm, this is a huge improvement but is still poor. The errors caused by the approximations made in the derivation can be further reduced and also the high-frequency behavior of the deconvolved Fourier transform can be improved using better deconvolution techniques. Monte Carlo simulations for more realistic sources with image noise should be performed for further evaluation.