Abstract
Deconvolution consists of reconstructing a signal from blurred (and usually noisy) sensory observations. It requires perfect knowledge of the impulse response of the sensor. Relevant works in the litterature propose methods with improved precision and robustness. But those methods are not able to account for a partial knowledge of the impulse response of the sensor. In this article, we experimentally show that inverting a Choquet capacity-based model of an imprecise knowledge of this impulse response allows to robustly recover the measured signal. The method we use is an interval valued extension of the well known Schultz procedure.
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References
Campos, L., Huete, J., Moral, S.: Probabilities intervals: a tool for uncertain reasoning. Int. J. Uncertain. Fuzz. 2, 167–196 (1994)
Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1953)
Denneberg, D.: Non-Additive Measure and Integral. Kluwer Academic Publishers, Dordrecht (1994)
Eggermont, P., Herman, G.: Iterative algorithms for large partitioned linear systems with applications to image reconstruction. Linear Algebra Appl. 40, 37–67 (1981)
Grabisch, M., Labreuche, C.: The symmetric and asymmetric Choquet integral on finite spaces for decision making. Stat. Pap. 43, 37–52 (2002)
Herzberger, J., Petkovi, L.: Efficient iterative algorithms for bounding the inverse of a matrix. Computing 44, 237–244 (1990)
Hudson, M., Lee, T.: Maximum likelihood restoration and choice of smoothing parameter in deconvolution of image data subject to poisson noise. Comput. Stat. Data Anal. 26(4), 393–410 (1998)
Jalobeanu, A., Blanc-Ferraud, L., Zerubia, J.: Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method. Pattern Recogn. 35(2), 341–352 (2002)
Kaaresen, K.F.: Deconvolution of sparse spike trains by iterated window maximization. IEEE Trans. Signal Process. 45(5), 1173–1183 (1997)
Kalifa, J., Mallat, S.: Thresholding estimators for linear inverse problems and deconvolutions. Ann. Stat. 1, 58–109 (2003)
Loquin, K., Strauss, O.: On the granularity of summative kernels. Fuzzy Set. Syst. 159(15), 1952–1972 (2008)
Poree, F., Bansard, J.-Y., Kervio, G., Carrault, G.: Stability analysis of the 12-lead ECG morphology in different physiological conditions of interest for biometric applications. In: Proc. of the Int. Conf. on Computers in Cardiology 2009, Park City, UT, USA, vol. 36, pp. 285–288 (2009)
Rice, J.: Choice of smoothing parameter in deconvolution problems. Contemp Math. 59, 137–151 (1986)
Rico, A., Strauss, O.: Imprecise expectations for imprecise linear filtering. Int. J. Approx. Reason. 51, 933–947 (2010)
Sainz, M., Herrero, P., Armengol, J., Vehí, J.: Continuous minimax optimization using modal intervals. J. Math. Anal. Appl. 339, 18–30 (2008)
Strauss, O., Rico, A.: Towards interval-based non-additive deconvolution in signal processing. Soft Comput. 16(5), 809–820 (2012)
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Strauss, O., Rico, A. (2013). Towards a Robust Imprecise Linear Deconvolution. In: Kruse, R., Berthold, M., Moewes, C., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33042-1_7
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DOI: https://doi.org/10.1007/978-3-642-33042-1_7
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