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A likelihood ratio formula for two-dimensional random fields

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1 Author(s)

This paper is concerned with the detection of a random signal in white Gaussian noise when both the signal and the noise are two-dimensional random fields. The principal result is the derivation of a recursive formula for the likelihood ratio relating it to certain conditional moments of the signal. It is also shown that, except for some relatively uninteresting cases, a simple exponential formula for the likelihood ratio, such as one has in one dimension, is not possible.

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Information Theory, IEEE Transactions on  (Volume:20 ,  Issue: 4 )