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Murthy, K. P. N.
- Boltzmann and Non-Boltzmann Sampling for Image Processing
Authors
1 Presidency College, Kamarajar Salai, Triplicane, Chennai-600 005, Tamil Nadu, IN
2 Chennai Mathematical Institute (CMI), Siruseri, Kelambakkam, Chennai-603 103, Tamil Nadu, IN
Source
Indian Journal of Economics and Development, Vol 5, No 9 (2017), Pagination: 1-8Abstract
Objectives: We present two algorithms for image processing; the first is based on Boltzmann sampling and the second on entropic sampling.
Methods: These algorithms come within the Bayesian framework which has three components: 1. Likelihood: a conditional density - the probability of a noisy image given a clean image, 2. A Prior and, 3. A Posterior: a conditional density - the probability of a clean image given a noisy image. The Likelihood provides a model for the degradation process; the Prior models what we consider as a clean image; it also provides a means of incorporating whatever data we have of the image; the Posterior combines the Prior and Likelihood and provides an estimate of the clean counterpart of the given noisy image. The algorithm sets a competition between: 1. The Likelihood that tries to anchor the image to the given noisy image so that the features present can be retained including perhaps the noisy ones and, 2. The Prior which tries to make the image smooth, even at the risk of eliminating some genuine features of the image other than the noise.
Findings: A proper choice of the prior and the likelihood functions would lead to good image processing. We need also good estimators of the clean image.
Application: The choice of estimators is somewhat straight forward for image processing employing Boltzmann algorithm. For non-Boltzmann algorithm we need efficient estimators that make full use of the entropic ensemble generated.
Keywords
Image Processing, Prior, Posterior, Boltzmann Sampling, Entropic Sampling, Bayesian.Full Text
References
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Authors
1 Presidency College, Kamarajar Salai, Triplicane, Chennai 600 005, Tamilnadu, IN
2 Chennai Mathematical Institute (CMI), H1, SIPCOT IT Park, Siruseri, Kelambakkam, Chennai 603 103, Tamilnadu, IN
Source
Indian Journal of Economics and Development, Vol 6, No 2 (2018), Pagination: 1-16Abstract
Objectives: We review two algorithms developed for simulating macroscopic systems. The first is the Metropolis and the second is the Wang-Landau algorithm.
Methods: Metropolis algorithm has been extensively employed for simulating a canonical ensemble and estimating macroscopic properties of a closed system at any desired temperature. A mechanical property, like energy can be calculated by averaging over a large number of micro states of the stationary Markov chain generated by the Metropolis algorithm. However thermal properties like entropy, and free energies are not easily accessible. A method called umbrella sampling was proposed some forty years ago for this purpose. Ever since, umbrella sampling has undergone several metamorphoses and we have now multi canonical Monte Carlo, entropic sampling, flat histogram methods, Wang-Landau algorithm etc.
Findings: In this paper we review Metropolis algorithm for estimating mechanical properties and Wang-Landau algorithm for estimating both mechanical and thermal properties of an equilibrium system.
Applications: We shall make the review as pedagogical and as self-contained as possible. These algorithms can be applied to a variety of problems in physics, astrophysics, chemistry, biology, soft matter, computer science, etc.
Keywords
Monte Carlo Simulation, Metropolis Algorithm, Entropic Sampling, Flathistogram Methods, Detailed Balance, Markov Chain.Full Text
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