Sparse ACEKF for phase reconstruction Articles uri icon

publication date

  • July 2013

start page

  • 18125

end page

  • 18137


  • 15


  • 21

International Standard Serial Number (ISSN)

  • 1094-4087


  • 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 log N 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 (N-2), where N-z 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.


  • image processing; image reconstruction techniques; image processing: phase retrieval