Handbook of Computer Vision and Applications Volume 1 Sensors and Imaging Nevertheless, the wider acce- ability of these methodsand, to some extent, Bayesian signal processing itself has been undermined by the large computational demands they typically make.HANDBOOK OF COMPUTER VISION AND APPLICATIONS Volume 1 Sensors and Imaging Bernd Jähne Horst Haußecker Peter Geißler More recently, the particle ?ltering - proach has addressed on-line stochastic simulation. Markov Chain Monte Carlo (MCMC) sampling, and - lated methods, are appreciated for their ability to simulate possibly high-dimensional distributions to arbitrary levels of accuracy. Since the 1990s, stochastic simulation methods have come to dominate Bayesian signal processing. The Expectation-Maximization (EM) algorithm and Laplace approximation, for ex- ple, are standard approaches to handling dif?cult models, but these approximations (certainty equivalence, and Gaussian, respectively) are often too drastic to handle the high-dimensional, multi-modal and/or strongly correlated problems that are - countered. However, the results are often intractable, and so the area of distributional approximation is of increasing relevance in signal processing. Increasingly, full probability modelling (the so-called Bayesian approach)or partial probability modelling using the likelihood functionis the pathway for - sign of these algorithms. The traditional on-line and data-intensive pre- cupations of signal processing continue to demand that these algorithms be tractable. In their place, diverse principles have been explored, leading to a consequent diversity in the implied computational algorithms. Hence, standard Wiener and Kalman theories no longer enjoy their traditional hegemony in the ?eld, revealing the standard computational engines for these problems. In moderncontexts,suchasIndependentComponentAnalysis(ICA),progresshasbeen made speci?cally by imposing non-Gaussian and/or non-linear assumptions. Gaussian linear modelling cannot address current signal processing demands.
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