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There been a renewed interest in the technique of coincidence Doppler broadening spectroscopy (CDBS) in which one-dimensional electronic momenta in materials are studied by means of the energies of the two gamma-rays emitted in the process of positron annihilation. Advantages of CDBS over conventional positron Doppler spectroscopy are its 40% improved resolution and its much reduced background noise at high momenta. The present work capitalizes on the fact that CDBS raw data is in the form of a very large two-dimensional image, with excellent prospects for designing parallel deconvolution algorithms for the removal of the instrumental error of measurement that arises from the availability of an accurate point spread function in the reference gamma-ray line of Sr at 514 keV. The generalized least-square method with Tikhonov-Miller regularization is developed by incorporating a priori information of non-negativity into the mathematical regularization technique for the solution of blurring matrix equations. The paper reports the performance of the parallel image deconvolution algorithm on the IBM SP2 computer.