Gamma-ray energy-imaging integrated deconvolution

The maximum likelihood expectation maximization (MLEM) algorithm is an important method in gamma-ray Compton imaging. In conventional Compton camera systems, the image reconstruction is performed only in 2D or 3D spatial coordinates for a specific gamma-ray energy. In this paper, we describe a new energy-imaging integrated deconvolution algorithm in which a source pixel is defined in a combined spatial and energy space. Therefore, the reconstructed source distribution using this technique gives the original incident gamma-ray intensity and energy spectrum as a function of incident angle. By employing this energy-imaging integrated deconvolution algorithm, a Compton camera can provide the image at any specific energy, as well as the spectrum at any specific direction. Since the ML solution estimates the true incident gamma-ray intensity, the deconvolved energy spectrum at the source location is free of Compton continuum. To reconstruct truthfully the source distribution from the observation data, the accuracy of the system response function t_ij, i.e. the probability for a photon from source pixel j to be observed as event i, is the most crucial information. Because the large number of pixels in the energy-imaging integrated space, and the very large number of possible measurement events, it is impossible to pre-calculate the system response function t_ij by simulations. In this paper, an analytical approach to estimate the system response function for Compton camera systems is introduced to allow the calculation of the system response function during the reconstruction process. The energy-imaging integrated deconvolution algorithm is applied to a 3-dimensional position-sensitive CdZnTe gamma-ray imaging spectrometer.