Sparse ACEKF for phase reconstruction
Vazquez, Manuel A.
Date of Issue2013
School of Electrical and Electronic Engineering
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.
DRNTU::Engineering::Electrical and electronic engineering
© 2013 OSA. This paper was published in Optics Express and is made available as an electronic reprint (preprint) with permission of OSA. The paper can be found at the following official DOI: [http://dx.doi.org/10.1364/OE.21.018125]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.