Indian Journal of Economics and Development

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Boltzmann and Non-Boltzmann Sampling for Image Processing


Affiliations
1 Presidency College, Kamarajar Salai, Triplicane, Chennai-600 005, Tamil Nadu, India
2 Chennai Mathematical Institute (CMI), Siruseri, Kelambakkam, Chennai-603 103, Tamil Nadu, India
 

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.
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  • Boltzmann and Non-Boltzmann Sampling for Image Processing

Abstract Views: 240  |  PDF Views: 118

Authors

T. Pramananda Perumal
Presidency College, Kamarajar Salai, Triplicane, Chennai-600 005, Tamil Nadu, India
K. R. Srivaishnavi
Presidency College, Kamarajar Salai, Triplicane, Chennai-600 005, Tamil Nadu, India
D. L. Asha Rani
Presidency College, Kamarajar Salai, Triplicane, Chennai-600 005, Tamil Nadu, India
K. P. N. Murthy
Chennai Mathematical Institute (CMI), Siruseri, Kelambakkam, Chennai-603 103, Tamil Nadu, India

Abstract


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.

References