Maximum likelihood estimation of object location in diffraction tomography

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Abstract
The problem is formulated within the context of diffraction tomography, where the complex phase of the diffracted wavefield is modeled using the Rytov approximation and the measurements consist of noisy renditions of this complex phase at a single frequency. The log likelihood function is computed for the case of additive zero mean Gaussian white noise and shown to be expressible in the form of the filtered backpropagation algorithm of diffraction tomography. In this form however, the filter function is no longer the rho filter appropriate to least square reconstruction but is now the generalized projection (propagation) of the object (centered at the origin) onto the line(s) parallel to the measurement line(s), but passing through the origin. This result allows the estimation problem to be solved via a diffraction tomographic imaging procedure where the noisy data is filtered and backpropagated in a first step, and the point of maximum value of the resulting image is then the maximum likelihood (ML) estimate of the object's location. The authors include a calculation of the Cramer-Rao bound for the estimation error and a computer simulation study illustrating the estimation procedure