  In this work, we present the Deep Newton Reconstruction Network (DNR-Net), a
hybrid data-driven reconstruction technique for emission tomography inspired by
Newton's method, a well-known iterative optimization algorithm. The DNR-Net
employs prior information about the tomographic problem provided by the
projection operator while utilizing deep learning approaches to a) imitate
Newton's method by approximating the Newton descent direction and b) provide
data-driven regularisation. We demonstrate that DNR-Net is capable of providing
high-quality image reconstructions using data from SPECT phantom simulations by
applying it to reconstruct images from noisy sinograms, each one containing 24
projections. The Structural Similarity Index (SSIM) and the Contrast-to-Noise
ratio (CNR) were used to quantify the image quality. We also compare our
results to those obtained by the OSEM method. According to the quantitative
results, the DNR-Net produces reconstructions comparable to the ones produced
by OSEM while featuring higher contrast and less noise.
