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Choosing a noise model for Electrical Impedance Tomography

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One medical imaging technique is electrical impedance tomography, involving measuring voltages corresponding to different current profiles to infer conductivity. The associated inverse problem, the Calderon problem, has been widely studied. In inverse problems literature, the measurement error is assumed to be deterministic and small. For statisticians, a more satisfactory approach allows large noise according to a specified noise model. But what should the noise model be in this case? A natural candidate would be white noise in a Hilbert space, but the appropriate Hilbert space to use is not obvious. I will walk through the steps required to reach such a Hilbert space.

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