Abstract
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 N(z)N logN and storage requirement of O(N), compared with the original ACEKF method, which has a computational complexity of O(NzN(3)) and storage requirement of O(N(2)), 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.
Highlights
When light propagates, its amplitude and phase evolve according to the wave equation
From the state space model, we derive a sparse augmented complex extended Kalman filter (ACEKF) to infer the complex optical field, 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(N2), where Nz is the number of images and N is the number of pixels in each image
Summary
Its amplitude and phase evolve according to the wave equation. We solve these problems by developing efficient inference methods for recovering the phase from a set of defocus intensity images, which can be captured either sequentially by moving camera along the optical axis, or all at once by using various focal stack collection methods [2, 3]. Such methods can be useful for applications in medical imaging, neuroscience, and materials science, where low noise images are difficult to obtain. Since our proposed method is recursive (not iterative), it has the ability to estimate phase in real-time during the measurement sequence, progressively improving the estimate as each new image is captured
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