Two-dimensional Bayesian estimate of images

Proceedings of the IEEEPublished 1 January 1972

A. Habibi

DOI10.1109/proc.1972.8787

Source URL

Citations231

SJR quartileQ1

SJR score6.25

SNIP11.38

TL;DR

A dynamic model for pictorial data that can be represented by a random field of an exponential autocorrelation function is developed and is used to realize a two-dimensional recursive filter that gives a Bayesian-estimate of the pictorialData from a noisy observation of the data.

Abstract

A dynamic model for pictorial data that can be represented by a random field of an exponential autocorrelation function is developed. A partial difference equation describes the dynamic model and is used to realize a two-dimensional recursive filter that gives a Bayesian-estimate of the pictorial data from a noisy observation of the data. It is assumed that the noise is additive, white, and uncorrelated with the signal. Practical application of the estimation technique is illustrated by applying the results to enhance several pictures. A comparison of this technique and its one-dimensional counterpart (Kalman filter) is made, and generalization of the estimation technique to other autoregressive sources is considered.

Keywords

Computer Science

Journal of Basic EngineeringA New Approach to Linear Filtering and Prediction Problems

30,999 Citations1960R. E. Kalman

Journal of Basic EngineeringNew Results in Linear Filtering and Prediction Theory

6,330 Citations1961R. E. Kalman, R. S. Bucy

The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results and properties of the variance equation are of great interest in the theory of adaptive systems.

IEEE Transactions on Information TheoryTwo-dimensional discrete Markovian fields

380 Citations1972J. Woods

A definition of discrete Markovian random fields is formulated analogously to a definition for the continuous case given by Levy, and this theory is applied to the problem of obtaining spectral estimates of a two-dimensional field, given observation over a limited aperture.

Bell System Technical JournalStatistics of Television Signals

222 Citations1952E. R. Kretzmer

The results are used to estimate the amount by which the channel capacity required for television transmission may be reduced through exploitation of the statistics measured.

Proceedings of the IEEEImage processing

164 Citations1971Thomas S. Huang, William F. Schreiber +1 more

Parts of image processing are discussed--specifically: the mathematical operations one is likely to encounter, and ways of implementing them by optics and on digital computers; image description; and image quality evaluation.

IRE Transactions on Communications SystemsImage Coding by Linear Transformation and Block Quantization

156 Citations1971A. Habibi, P. A. Wintz

The feasibility of coding two-dimensional data arrays by first performing a two- dimensional linear transformation on the data and then block quantizing the transformed data is investigated.

Proceedings of the IEEEImage processing

127 Citations1971Thomas S. Huang, William F. Schreiber +1 more

Proceedings of the IEEERole of recursive estimation in statistical image enhancement

100 Citations1972N. Nahi

Bell System Technical JournalA Model for the Random Video Process

83 Citations1966L. Franks

A model for the random picture is proposed and derives expressions for second-order statistical properties of the video signal obtained from a conventional scanning operation on the picture, which will satisfactorily characterize the power spectral density of the random video signal.

IEEE Transactions on Information TheoryThe subjective effect of two-dimensional pictorial noise

24 Citations1965Thomas S. Huang

It is deduced that for the class of noises whose spectra are symmetrical with respect to both horizontal and vertical frequencies, the weighting function in the integral representing noise objectionability is similar in shape to these isopreference surfaces.