Focus on the phase reconstruction from three phase-shifting interferograms with unknown phase shifts, an advanced principal component analysis method is proposed. First, use a simple subtraction operation among interferograms, two intensity difference images are obtained easily. Second, set the center region of the data of intensity difference images to zero, and then construct a covariance matrix to obtain a transformation matrix. Third, two principal components of interferograms can be determined by the Hotelling transform and then phase can be calculated from the two normalized principal components by an arctangent function. By means of the simulation calculation and the experimental research, it is proved that the phase with high precision can be obtained rapidly by the proposed algorithm.
This article investigates the distributed maximum correntropy unscented Kalman filtering problem for nonlinear systems via a sensor network. The system dynamics is subject to state equality constraints and non-Gaussian noise. By utilizing the maximum correntropy criterion to handle non-Gaussian noise, a centralized maximum correntropy constrained unscented Kalman filter is first proposed. Then, two novel distributed maximum correntropy constrained unscented Kalman filters with special features are designed. Specifically, the first one is developed by approximating the centralized filter with each sensor's own and its neighbors' measurements. The other one is designed by fusing state estimates. It is worth mentioning that these two distributed algorithms only need finite steps to fuse information over the sensor network rather than infinite steps to achieve the average consensus. Finally, the validity of the proposed algorithms is demonstrated by simulation experiments, with a detailed comparison.
This article addresses the distributed state estimation problem for uncertain time-varying dynamic systems with state constraints over a sensor network. By using a null space method, the distributed state estimation problem for uncertain dynamic systems with state constraints can be cast into a new unconstrained distributed state estimation problem for reduced uncertain dynamic systems. A constrained distributed Kalman filter is proposed, and it is shown that the full state estimates can be recovered at any time and satisfy the constraints. An optimized upper bound of the estimation error covariance of each sensor is obtained, and the corresponding gains are designed. The application conditions of the proposed algorithm are mild, and they can be off-line checked. Furthermore, the computational requirements in this article are also reduced compared with the existing results. Finally, the performance of the proposed filter algorithm is demonstrated through numerical simulations.
Structured illumination digital holographic microscopy (SI-DHM) is a high-resolution, label-free technique enabling us to image unstained biological samples. SI-DHM has high requirements on the stability of the experimental setup and needs long exposure time. Furthermore, image synthesizing and phase correcting in the reconstruction process are both challenging tasks. We propose a deep-learning-based method called DL-SI-DHM to improve the recording, the reconstruction efficiency and the accuracy of SI-DHM and to provide high-resolution phase imaging. In the training process, high-resolution amplitude and phase images obtained by phase-shifting SI-DHM together with wide-field amplitudes are used as inputs of DL-SI-DHM. The well-trained network can reconstruct both the high-resolution amplitude and phase images from a single wide-field amplitude image. Compared with the traditional SI-DHM, this method significantly shortens the recording time and simplifies the reconstruction process and complex phase correction, and frequency synthesizing are not required anymore. By comparsion, with other learning-based reconstruction schemes, the proposed network has better response to high frequencies. The possibility of using the proposed method for the investigation of different biological samples has been experimentally verified, and the low-noise characteristics were also proved.
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