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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 15 — Jul. 29, 2013
  • pp: 18125–18137

Sparse ACEKF for phase reconstruction

Zhong Jingshan, Justin Dauwels, Manuel A. Vázquez, and Laura Waller  »View Author Affiliations

Optics Express, Vol. 21, Issue 15, pp. 18125-18137 (2013)

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We propose a novel low-complexity recursive filter to efficiently recover quantitative phase from a series of noisy intensity images taken through focus. We first transform the wave propagation equation and nonlinear observation model (intensity measurement) into a complex augmented state space model. From the state space model, we derive a sparse augmented complex extended Kalman filter (ACEKF) to infer the complex optical field (amplitude and phase), and find that it converges under mild conditions. Our proposed method has a computational complexity of NzN logN and storage requirement of 𝒪(N), compared with the original ACEKF method, which has a computational complexity of 𝒪(NzN3) and storage requirement of 𝒪(N2), where Nz is the number of images and N is the number of pixels in each image. Thus, it is efficient, robust and recursive, and may be feasible for real-time phase recovery applications with high resolution images.

© 2013 OSA

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.5070) Image processing : Phase retrieval

ToC Category:
Image Processing

Original Manuscript: April 4, 2013
Revised Manuscript: June 6, 2013
Manuscript Accepted: July 2, 2013
Published: July 22, 2013

Zhong Jingshan, Justin Dauwels, Manuel A. Vázquez, and Laura Waller, "Sparse ACEKF for phase reconstruction," Opt. Express 21, 18125-18137 (2013)

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