As X-ray imaging is pushed further into the nanoscale, the sample deformations due to the increased radiation levels or mechanical instabilities of the microscopes become more apparent, leading to challenges in realizing high-resolution microscopy under these conditions. Here we propose a distributed optimization solver for imaging of samples at the nanoscale. Our approach solves the tomography and ptychography problems jointly with projection data alignment, nonrigid sample deformation correction, and regularization. Applicability of the method is demonstrated on experimental data sets from the Transmission X-ray Microscope, and the hard X-ray nanoprobe.
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