Bayesian Methods in Nonlinear Digital Image Restoration

Hunt,

doi:10.1109/tc.1977.1674810

Cited by 172 publications

(78 citation statements)

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“…Measurements that are nonlinearly related to the desired image can be easily dealt with in the Bayesian framework. [16][17][18] Given the data g, the posterior probability of any image f is given by Bayes's law (6) in terms of the proportionality…”

Section: Posterior Probabilitymentioning

confidence: 99%

<title>Introduction to Bayesian image analysis</title>

Hanson

1993

SPIE Proceedings

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The basic concepts in the application of Bayesian methods to image analysis are introduced. The Bayesian approach has benefits in image analysis and interpretation because it permits the use of prior knowledge concerning the situation under study. The fundamental ideas are illustrated with a number of examples ranging from a problem in one and two dimensions to large problems in image reconstruction that make use of sophisticated prior information.

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Section: Posterior Probabilitymentioning

confidence: 99%

<title>Introduction to Bayesian image analysis</title>

Hanson

1993

SPIE Proceedings

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“…In the standard Bayesian approach introduced to image reconstruction by Hunt (1977), these quantities are assumed to be known a priori. Hunt called this method, based on a Gaussian prior, simply MAP for maximum a posteriori reconstruction.…”

Section: Bayesian Reconstructionmentioning

confidence: 99%

Rayleigh Task Performance as a Method to Evaluate Image Reconstruction Algorithms

Hanson

Myers

1991

Maximum Entropy and Bayesian Methods

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ABSTRACT. We evaluate several tomographic reconstruction algorithms on the basis of how well one can perform the Rayleigh discrimination task using the reconstructed images. The Rayleigh task is defined here as deciding whether a perceived object is either a pair of neighboring points or a line, both convolved with a 2D Gaussian. The method of evaluation is based on the results of a numerical testing procedure in which the stated discrimination task is carried out on reconstructions of a randomly generated sequence of images. The ability to perform the Rayleigh task is summarized in terms of a discriminability index that is derived from the area under the receiver-operating characteristic (ROC) curve. Reconstruction algorithms employing a nonnegativity constraint are compared, including maximum a posteriori (MAP) estimation based on the Bayesian method with entropy and Gaussian priors as well as the additive and multiplicative versions of the algebraic reconstruction technique (ART and MART). The performance of all four algorithms tested is found to be similar for complete noisy data. However, for sparse noiseless data, the MAP algorithm based on the Gaussian prior does not perform as well as the others.

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“…Considering the fact that for a given g, the variation in b is due to the noise n, Hunt (1977), together with the above definitions, non-blind image restoration problem can be recast as seeking the unknown GTI, g(i, j), that minimizes the functional…”

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confidence: 99%