The soft x-ray transform

Several new forward models are introduced as mathematical formalizations of the processes that take place during image formation in transmission soft x-ray microscopy, which has the unique capability of imaging whole cells in their native environment with high resolution. Mathematical solutions of some of the associated inverse problems are provided by deriving closed-form formulas specifying the inverse transforms. Numerical experimental results are presented to demonstrate how the inverse transforms can be used to improve the reconstructions computed from data acquired according to the forward models.