Abstract

Inverse problems arise routinely in imaging and structure determination using a variety of experimental modalities. After an overview of numerical aspects of medical imaging, we will consider inverse acoustic scattering and protein structure determination from cryo-electron microscopy data (cryo-EM). These are computationally intensive tasks that are typically formulated as non-convex optimization problems. In cryo-EM, the raw data is extremely noisy and existing methods are generally based on some version of maximum likelihood estimation, with a low resolution starting guess. In inverse acoustic scattering, the underlying physical problem is ill-posed and requires both regularization and high-order methods to solve a sequence of forward scattering problems. We will present some algorithms for accelerating image reconstruction in all these settings, illustrate their performance with several examples, and discuss open problems in the field.