Advanced Denoising for X-ray Ptychography

The success of ptychographic imaging experiments strongly depends on achieving high signal-to-noise ratio. This is particularly important in nanoscale imaging experiments when diffraction signals are very weak and the experiments are accompanied by significant parasitic scattering (background), outliers or correlated noise sources. It is also critical when rare events such as cosmic rays, or bad frames caused by electronic glitches or shutter timing malfunction take place. In this paper, we propose a novel iterative algorithm with rigorous analysis that exploits the direct forward model for parasitic noise and sample smoothness to achieve a thorough characterization and removal of structured and random noise. We present a formal description of the proposed algorithm and prove its convergence under mild conditions. Numerical experiments from simulations and real data (both soft and hard X-ray beamlines) demonstrate that the proposed algorithms produce better results when compared to state-of-the-art methods.Comment: 24 pages, 9 figure

Accelerated stationary iterative methods for the numerical solution of electromagnetic wave scattering problems

The main focus of this work is to contribute to the development of iterative solvers applied to the method of moments solution of electromagnetic wave scattering problems. In recent years there has been much focus on current marching iterative methods, such as Gauss-Seidel and others. These methods attempt to march a solution for the unknown basis function amplitudes in a manner that mimics the physical processes which create the current. In particular the forward backward method has been shown to produce solutions that, for some twodimensional scattering problems, converge more rapidly than non-current marching Krylov methods. The buffered block forward backward method extends these techniques in order to solve three-dimensional scattering problems. The convergence properties of the forward backward and buffered block forward backward methods are analysed extensively in this thesis. In conjunction, several means of accelerating these current marching methods are investigated and implemented. The main contributions of this thesis can be summarised as follows: ² An explicit convergence criterion for the buffered block forward backward method is specified. A rigorous numerical comparison of the convergence rate of the buffered block forward backward method, against that of a range of Krylov solvers, is performed for a range of scattering problems. ² The acceleration of the buffered block forward backward method is investigated using relaxation. ² The efficient application of the buffered block forward backward method to problems involving multiple source locations is examined. ² An optimally sized correction step is introduced designed to accelerate the convergence of current marching methods. This step is applied to the forward backward and buffered block forward backward methods, and applied to two and three-dimensional problems respectively. Numerical results demonstrate the significantly improved convergence of the forward backward and buffered block forward backward methods using this step

Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials

Quantum ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). Quantum ESPRESSO stands for "opEn Source Package for Research in Electronic Structure, Simulation, and Optimization". It is freely available to researchers around the world under the terms of the GNU General Public License. Quantum ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively-parallel architectures, and a great effort being devoted to user friendliness. Quantum ESPRESSO is evolving towards a distribution of independent and inter-operable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.Comment: 36 pages, 5 figures, resubmitted to J.Phys.: Condens. Matte

Approximation of the Scattering Amplitude using Nonsymmetric Saddle Point Matrices

In this thesis we look at iterative methods for solving the primal (Ax = b) and dual (AT y = g) systems of linear equations to approximate the scattering amplitude defined by gTx =yTb. We use a conjugate gradient-like iteration for a unsymmetric saddle point matrix that is contructed so as to have a real positive spectrum. We find that this method is more consistent than known methods for computing the scattering amplitude such as GLSQR or QMR. Then, we use techniques from matrices, moments, and quadrature to compute the scattering amplitude without solving the system directly