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$equation$

Hence, the ‘simple’ inversion of the noisy data is equal to the ML estimator.

In the more general case that A is not invertible, the ML estimator for Poisson distributed random data must be obtained by solving the optimization problem

$equation$

Apart from Poisson distributions, the ML approach can be applied to all kinds of probability functions P(X|μ), including the simple case of Gaussian noise. Of course, the functionals to be minimized will look different from those in the Poisson case.

### 7.1.3Bayesian inference techniques

In the preceding section, we assumed the object to be deterministic and we did not impose any constraints on the object or ...

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