@inproceedings{Zhong2012a,
title = {Efficient Gaussian Inference Algorithms for Phase Imaging},
author = {Zhong, Jingshan and Dauwels, Justin and Vazquez, Manuel A. and Waller, Laura},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6287959},
issn = {1520-6149},
year = {2012},
date = {2012-01-01},
booktitle = {2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
pages = {617--620},
publisher = {IEEE},
address = {Kyoto},
abstract = {Novel efficient algorithms are developed to infer the phase of a complex optical field from a sequence of intensity images taken at different defocus distances. The non-linear observation model is approximated by a linear model. The complex optical field is inferred by iterative Kalman smoothing in the Fourier domain: forward and backward sweeps of Kalman recursions are alternated, and in each such sweep, the approximate linear model is refined. By limiting the number of iterations, one can trade off accuracy vs. complexity. The complexity of each iteration in the proposed algorithm is in the order of N logN, where N is the number of pixels per image. The storage required scales linearly with N. In contrast, the complexity of existing phase inference algorithms scales with N3 and the required storage with N2. The proposed algorithms may enable real-time estimation of optical fields from noisy intensity images.},
keywords = {biomedical optical imaging, complex optical field, computational complexity, defocus distances, Fourier domain, Gaussian inference algorithms, image sequences, inference mechanisms, intensity image sequence, iterative Kalman smoothing, iterative methods, Kalman filter, Kalman filters, Kalman recursions, linear model, Manganese, Mathematical model, medical image processing, Noise, noisy intensity image, nonlinear observation model, Optical imaging, Optical sensors, Phase imaging, phase inference algorithms, smoothing methods},
pubstate = {published},
tppubtype = {inproceedings}
}

Novel efficient algorithms are developed to infer the phase of a complex optical field from a sequence of intensity images taken at different defocus distances. The non-linear observation model is approximated by a linear model. The complex optical field is inferred by iterative Kalman smoothing in the Fourier domain: forward and backward sweeps of Kalman recursions are alternated, and in each such sweep, the approximate linear model is refined. By limiting the number of iterations, one can trade off accuracy vs. complexity. The complexity of each iteration in the proposed algorithm is in the order of N logN, where N is the number of pixels per image. The storage required scales linearly with N. In contrast, the complexity of existing phase inference algorithms scales with N3 and the required storage with N2. The proposed algorithms may enable real-time estimation of optical fields from noisy intensity images.

@inproceedings{Santiago-Mozos2008,
title = {On the Uncertainty in Sequential Hypothesis Testing},
author = {Santiago-Mozos, Ricardo and Fernandez-Lorenzana, R. and Perez-Cruz, Fernando and Artés-Rodríguez, Antonio},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=4541223},
isbn = {978-1-4244-2002-5},
year = {2008},
date = {2008-01-01},
booktitle = {2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro},
pages = {1223--1226},
publisher = {IEEE},
address = {Paris},
abstract = {We consider the problem of sequential hypothesis testing when the exact pdfs are not known but instead a set of iid samples are used to describe the hypotheses. We modify the classical test by introducing a likelihood ratio interval which accommodates the uncertainty in the pdfs. The test finishes when the whole likelihood ratio interval crosses one of the thresholds and reduces to the classical test as the number of samples to describe the hypotheses tend to infinity. We illustrate the performance of this test in a medical image application related to tuberculosis diagnosis. We show in this example how the test confidence level can be accurately determined.},
keywords = {binary hypothesis test, Biomedical imaging, Detectors, H infinity control, likelihood ratio, Medical diagnostic imaging, medical image application, medical image processing, Medical tests, patient diagnosis, Probability, Random variables, Sequential analysis, sequential hypothesis testing, sequential probability ratio test, Signal processing, Testing, tuberculosis diagnosis, Uncertainty},
pubstate = {published},
tppubtype = {inproceedings}
}

We consider the problem of sequential hypothesis testing when the exact pdfs are not known but instead a set of iid samples are used to describe the hypotheses. We modify the classical test by introducing a likelihood ratio interval which accommodates the uncertainty in the pdfs. The test finishes when the whole likelihood ratio interval crosses one of the thresholds and reduces to the classical test as the number of samples to describe the hypotheses tend to infinity. We illustrate the performance of this test in a medical image application related to tuberculosis diagnosis. We show in this example how the test confidence level can be accurately determined.