Gradient-Domain PET Reconstruction

This work adapts the concept of gradient-domain reconstruction to iterative positron emission tomography (PET). We apply separate iterative PET reconstructions to recover the partial derivatives, expressed as finite differences, of the objective radio-tracer density. The final reconstruction is then obtained by integrating the reconstructed partial derivatives using a Poisson solver. The motivation behind this method is that the sparsity of the individual partial derivatives often exceeds the sparsity in the image domain or in the field of gradient magnitudes, which may lead to improved quality compared to traditional methods and the total variation regularization. Additionally, working directly in the gradient domain, we believe it will be easier to integrate gradient domain approaches for particle simulation, image filtering, or regularization to the reconstruction loop. We demonstrate the gradient domain approach on a hypothetical 2D PET scanner and show that results are comparable to that of the ML-EM reconstruction.