Phase Retrieval Module

Phase retrieval module based on Python 3.7.4 and PyTorch 1.6.0 with CUDA 10.2

Multi-GPU calculation supported by torch.nn.DataParallel wrapper

pretrained parameters for PRModule.preconditioner.DenoisingNetwork is required for neural-network-based operations (it might show poor performance with a case different from the trained condition)

Notations and Functions

1. Basic Notations

   • u: r-space complex matrix corresponding to object (i.e. electron density)
   • z: k-space complex matrix corresponding to Fourier transform of oversampled object (i.e. diffraction pattern)
   • y: Lagrange multiplier complex matrix for dual formulation of optimization problem

2. Supported Algorithms (with R-factor and Poisson NLL as error metrics)

   • Hybrid input-output (HIO) with boundary push
   • Relaxed averaged alternating reflections (RAAR) with boundary push
   • RAAR with projection operator on denoised constraint by Gaussian smoothing or deep learning (gRAAR, dRAAR)
   • Generalized proximal smoothing (GPS)
   • Deep preconditioned generalized proximal smoothing (dpGPS)

3. Additional Functions

   • Subpixel alignment by phase cross-correlation
   • Pairwise distance
   • Phase retrieval transfer function (PRTF)
   • Power spectral density (PSD)
   • Eigenmode and low-rank approximation by singular value decomposition (SVD)

Citation

https://doi.org/10.1103/PhysRevResearch.3.043066

note that references of each functions are written in docstrings

partial convolution is directly imported from https://github.com/NVIDIA/partialconv