RRR
swMATH ID:  34784 
Software Authors:  Elser, Veit; Lan, TiYen; Bendory, Tamir 
Description:  Benchmark problems for phase retrieval. In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be recovered is periodic and comprised of atomic distributions arranged homogeneously in the unit cell of the crystal. The crystallographic problem is both the leading application and one of the hardest forms of phase retrieval. We have constructed a graded set of benchmark problems for evaluating algorithms that perform this type of phase retrieval. The data, publicly available online from https://github.com/veitelser/phaseretrievalbenchmarks, is provided in an easily interpretable format. We also propose a simple and unambiguous success/failure criterion based on the actual needs in crystallography. Baseline runtimes were obtained with an iterative algorithm that is similar but more transparent than those used in crystallography. Empirically, the runtimes grow exponentially with respect to a new hardness parameter: the sparsity of the signal autocorrelation. We also review the algorithms used by the leading software packages. This set of benchmark problems, we hope, will encourage the development of new algorithms for the phase retrieval problem in general, and crystallography in particular. 
Homepage:  https://arxiv.org/abs/1706.00399 
Source Code:  https://github.com/veitelser/phaseretrievalbenchmarks 
Keywords:  phase retrieval; crystallography; periodic signals; reconstruction algorithms; benchmark problems; sparsity 
Related Software:  PhaseLift; Manopt; DnCNN; StyleGAN; PULSE; DeepAdverserialRegulariser; NETT; BigGAN; Adam; MNIST; BlockPR; PhaseMax; Macaulay2; UNLocBoX; BUQO; SROCK; Wirtinger Flow; Superflip; GitHub; PhasePack 
Cited in:  8 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Benchmark problems for phase retrieval. Zbl 1421.82041 Elser, Veit; Lan, TiYen; Bendory, Tamir 
2018

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Cited by 16 Authors
Cited in 5 Serials
3  SIAM Journal on Imaging Sciences 
2  Inverse Problems 
1  Applied and Computational Harmonic Analysis 
1  Journal of the Australian Mathematical Society 
1  SIAM Journal on Mathematics of Data Science 
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