Low Rank Fourier Ptychography

In this paper, we introduce a principled algorithmic approach for Fourier ptychographic imaging of dynamic, time-varying targets. To the best of our knowledge, this setting has not been explicitly addressed in the ptychography literature. We argue that such a setting is very natural, and that our methods provide an important first step towards helping reduce the sample complexity (and hence acquisition time) of imaging dynamic scenes to managaeble levels. With significantly reduced acquisition times per image, it is conceivable that dynamic ptychographic imaging of fast changing scenes indeeed becomes practical in the near future.

[1]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[2]  R. Horstmeyer,et al.  Wide-field, high-resolution Fourier ptychographic microscopy , 2013, Nature Photonics.

[3]  Ashok Veeraraghavan,et al.  Toward Long-Distance Subdiffraction Imaging Using Coherent Camera Arrays , 2015, IEEE Transactions on Computational Imaging.

[4]  Emmanuel J. Candès,et al.  PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming , 2011, ArXiv.

[5]  Prateek Jain,et al.  Low-rank matrix completion using alternating minimization , 2012, STOC '13.

[6]  Siyuan Dong,et al.  Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging. , 2014, Optics express.

[7]  Yonina C. Eldar,et al.  Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow , 2016, IEEE Transactions on Information Theory.

[8]  Chinmay Hegde,et al.  Sub-Diffraction Imaging Using Fourier Ptychography and Structured Sparsity , 2018, 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[9]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[10]  Rick P. Millane,et al.  Phase retrieval in crystallography and optics , 1990 .

[11]  Yonina C. Eldar,et al.  Simultaneously Structured Models With Application to Sparse and Low-Rank Matrices , 2012, IEEE Transactions on Information Theory.

[12]  Stefano Marchesini,et al.  Phase retrieval and saddle-point optimization. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[13]  Xiaodong Li,et al.  Phase Retrieval via Wirtinger Flow: Theory and Algorithms , 2014, IEEE Transactions on Information Theory.

[14]  Zhang Fe.  Phase retrieval from coded diffraction patterns , 2015 .

[15]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[16]  Yonina C. Eldar,et al.  Low-Rank Phase Retrieval , 2016, IEEE Transactions on Signal Processing.

[17]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2009, Found. Comput. Math..

[18]  J. Rodenburg,et al.  An improved ptychographical phase retrieval algorithm for diffractive imaging. , 2009, Ultramicroscopy.

[19]  Prateek Jain,et al.  Phase Retrieval Using Alternating Minimization , 2013, IEEE Transactions on Signal Processing.

[20]  Yonina C. Eldar,et al.  Uniqueness conditions for low-rank matrix recovery , 2011, Optical Engineering + Applications.

[21]  John Wright,et al.  Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization , 2009, NIPS.

[22]  Fucai Zhang,et al.  Superresolution imaging via ptychography. , 2011, Journal of the Optical Society of America. A, Optics, image science, and vision.

[23]  K. Nugent,et al.  Unique phase recovery for nonperiodic objects. , 2003, Physical review letters.

[24]  Yuxin Chen,et al.  Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems , 2015, NIPS.

[25]  Yonina C. Eldar,et al.  Phase Retrieval with Application to Optical Imaging: A contemporary overview , 2015, IEEE Signal Processing Magazine.