Simultaneous 3dx-Ray Ptycho-Tomography With Gradient Descent

The acquisition model of a 3Dx-ray imaging system can be understood as the combination of two known techniques: tomography and ptychography. First, x-rays go through a 3D object producing a set of 2D tomographic projections at different angles. Then, a detector captures the magnitude of a diffraction pattern produced by the interaction of these projections with a finite-sized coherent beam spot (also called probe). In 2D ptychography, in order to solve this phase retrieval problem, the observations have to be captured with a large overlap between them. However, this constraint can be relaxed in 3Dx-ray imaging, due to the fact that most of the required redundant information is acquired thanks to the combination of tomography and ptychography. In this work, we address the so-called ptycho-tomography problem and introduce a 3D reconstruction method that uses the gradient descent algorithm. In the experimental section, the proposed method is evaluated and compared against state-of-art-methods.