Non-informative Bayesian dispersion particle filter
Article Sidebar
Main Article Content
Abstract
In this research paper, we attempt to introduce a new algorithm for filtering a state-space model. The observations of this algorithm follow an exponential dispersion model. The paper focuses here on the inclusion of non-informative prior knowledge in parameter estimation on nonlinear state-space models using an improper uniform prior measure. Therefore, a new particle filter is introduced. A conventional particle filter (PF) produces an incorrect sample from a discrete approximation distribution. This new algorithm is a regularized continuous distribution method that is obtained with the exponential dispersion model. A necessary and sufficient condition for the existence and convergence of the non-informative Bayesian estimator of dispersion parameters is established. This methodology extends the classical PF implemented by this new estimation method for the exponential dispersion model framework using a non-informative Bayesian approach. In order to evaluate the performance of the proposed algorithm, a case study with simulations and microscopic image restoration is carried out. The results exhibit a great performance improvement from the proposed approach
Downloads
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
- Authors keep the rights and guarantee the Journal of Innovative Applied Mathematics and Computational Sciences the right to be the first publication of the document, licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License that allows others to share the work with an acknowledgement of authorship and publication in the journal.
- Authors are allowed and encouraged to spread their work through electronic means using personal or institutional websites (institutional open archives, personal websites or professional and academic networks profiles) once the text has been published.
References
Alenlöv, J., & Olsson, J. (2019). Particle-based adaptive-lag online marginal smoothing in general state-space models. IEEE Transactions on Signal Processing, 67(21), 5571-5582. https://doi.org/10.1109/TSP.2019.2941066
Allen, R., David, G., & Nomarski, G. (1969). The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy. Zeitschrift Fur Wissenschaftliche Mikroskopie Und Mikroskopische Technik, 69(4), 193-221.
Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. A. (2002). A tutorial on particle filters for online nonlinear non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50(2), 174-188. https://doi.org/10.1109/78.978374
Booth, M. J. (2014). Adaptive optical microscopy, the ongoing quest for a perfect image. Light, Science and Applications, 3, 165-165. https://doi.org/10.1038/lsa.2014.46
Campillo, F. (2006). Modèles de Markov cachés et filtrage particulaire. DEA. Université Du Sud Toulon-Var.
Charnes, A., Frome, E. L., & Yu, P. L. (1976). The Equivalence of Generalized Least Squares and Maximum Likelihood Estimates in the Exponential Family. Journal of the American Statistical Association, 71(353), 469-171. https://doi.org/10.1080/01621459.1976.10481508
Chang, C. W., & Mycek, M. A. (2012). Total variation versus wavelet-based methods for image denoising in fluorescence lifetime imaging microscopy. Journal of Biophotonics, 5, 449-457. https://doi.org/10.1002/jbio.201100137
Chen, S. Y., Zhao, M. Z., Wu, G., Yao, C. Y., & Zhang, J. W. (2012). Recent Advances in Morphological Cell Image Analysis. Computational and Mathematical Methods in Medicine, 1-10. https://doi.org/10.1155/2012/101536
Chen, Z. (2003). Bayesian filtering: from Kalman filters to particle filters, and Beyond. Hamilton: McMaster University, Statistics, 182(1), 1-69.
Doucet, A., Godsill, S., & Anderieu, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10, 197-208. https://doi.org/10.1023/A:1008935410038
Frigault, M. M., Lacoste, J., Swift, J. L., & Brown, C. M. (2009). Live-cell microscopy, tips and tools. Journal of Cell Science, 122(6), 753-767. https://doi.org/10.1242/jcs.033837
Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.
Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82(4), 711-732. https://doi.org/10.1093/biomet/82.4.711
Hobbs, N. T., & Hooten, M. B. (2015). Bayesian models: a statistical primer for ecologists. Princeton Univ. Press.
Hua, J., & Li, C. (2018). Distributed Outlier-Robust Bayesian Filtering for State Estimation. IEEE Transactions on Signal and Information Processing over Networks, 3(5), 428-441. https://doi.org/10.1109/TSIPN.2018.2889579
Jørgensen, B., Martinez, J. R., & Tsao, M. (1994). Asymptotic Behaviour of the Variance Function . Scandinavian Journal of Statistics, 21(3), 223-243.
Jørgensen, B. (1991). Exponential Dispersion Models. Monograph of IMPA, Rio De Janeiro.
Kalman, R. E. (1960). A New Approach to Linear Filtering and Prediction Problems. Transactions of the ASME–Journal of Basic Engineering, 82, 35-45. https://doi.org/10.1115/1.3662552
Lemoine, N. P. (2019). Moving beyond noninformative priors: Why and how to choose weakly informative priors in Bayesian analyses. Oikos, 128(7), 912-928. https://doi.org/10.1111/oik.05985
Letac, G., & Mora, M. (1990). Natural real exponential families with cubic variance functions. The Annals of Statistics, 18(1), 1-37. https://doi.org/10.1214/aos/1176347491
Mannam, V., Zhang, Y., Zhu, Y., Nichols, E., Wang, Q., Sundaresan, V., & Howard, S. S. (2022). Real-time image denoising of mixed Poisson–Gaussian noise in fluorescence microscopy images using ImageJ. Optica, 9(4), 335-345. https://doi.org/10.1364/OPTICA.448287
Marhaba, B., & Zribi, M. (2018). The bootstrap Kernel-Diffeomorphism Filter for Satellite Image Restoration. IEEE 22nd International Symposium on Consumer Technologies, Russia, 80-84. https://doi.org/10.1109/ISCE.2018.8408924
van Munster, E. B., van Vliet, L. J., & Aten, J. A. (1997). Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope. Journal of Microscopy, 188(2), 149-157. https://doi.org/10.1046/j.1365-2818.1997.2570815.x
Papini, A. (2012). A new algorithm to reduce noise in microscopy images implemented with a simple program in Pytho. Microscopy Research and Technique, 75(3), 334-342. https://doi.org/10.1002/jemt.21062
Sadok, I., Masmoudi, A., & Zribi, M. (2023). Integrating the EM algorithm with particle filter for image restoration with exponential dispersion noise. Communications in Statistics-Theory and Methods, 52(2), 446-462. https://doi.org/10.1080/03610926.2021.1915336
Sadok, I., & Masmoudi, A. (2022). New parametrization of stochastic volatility models. Communications in Statistics-Theory and Methods, 51(7), 1936-1953. https://doi.org/10.1080/03610926.2021.1934031
Sadok , I., & Zribi, M. (2022). Image Restoration Using Weibull Particle Filters. IEEE 4th International Conference on Pattern Analysis and Intelligent Systems (PAIS), 1-6. https://doi.org/10.1109/PAIS56586.2022.9946893
Sadok, I., Zribi, M., & Masmoudi, A. (2023). Non-informative Bayesian estimation in dispersion models. Hacettepe Journal of Mathematics and Statistics, 1-18. https://doi.org/10.15672/hujms.1053432
Satpathy, S. K., Panda, S., Nagwanshi, K. K., & Ardil, C. (2022). Image restoration in non-linear filtering domain using MDB approach. International Journal of Computer and Information Engineering, 7(2), 328-332. https://doi.org/10.48550/arXiv.2204.09296
Shechtman, Y., Eldar, Y. C., Cohen, O., Chapman, H. N., Miao, J., & Segev, M. (2015). Phase Retrieval with Application to Optical Imaging. IEEE Signal Processing Magazine, 32(3), 87-101. https://doi.org/ 10.1109/MSP.2014.2352673
Van der Merwe, R., Doucet, A., Freitas, J. F. G., & Wan, E. (2000). The unscented particle filter. Advances in Neural Information Processing Systems, 13.
Wang, Y. L. (2003). Computational restoration of fluorescence images: noise reduction, deconvolution, and pattern recognition. Methods in Cell Biology, 72, 337-348. https://doi.org/10.1016/S0091-679X(03)72016-0