Sparse ACEKF for phase reconstruction

• Main Authors: Vazquez, Manuel A., Zhong, Jingshan, Dauwels, Justin, Waller, Laura
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Engineering::Electrical and electronic engineering
• Online Access: https://hdl.handle.net/10356/98619; http://hdl.handle.net/10220/13307
• Institution: Nanyang Technological University

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 ?(N), compared with the original ACEKF method, which has a computational complexity of ?(NzN3) and storage requirement of ?(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.