Nonlinear optimization-driven deep learning framework for medical image reconstruction via partial differential equations

High quality medical imaging is essential to accurate clinical decision-making, but reconstruction of sparse or noisy images especially under CT and MRI is still a major challenge, with traditional reconstruction algorithms vulnerable to artifacts and noise, and unwanted inference typically lacking interpretability.We introduce a new modality of addressing the problem of reconstruction with nonlinear optimization, partial differential equation (PDE) constraints and deep neural networks, where the priors on physical properties should be presented as the network loss function and the architecture of the network so as to build more robust and accurate reconstruction.Having a clear formulation of a nonlinear optimization problem and by using the principles of variational approaches, we are also able to integrate a hardware friendly circuit into our solution that could be used to acquire data in real time.Experiments on benchmark CT and MRI, indicate an increase in peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), more effective noise suppression, and convergence times than state-of-the art baselines.The need of nonlinear optimization and employment of PDEs regularization in work on edges preservation and reduction of artifacts can also be seen regarding