On the noise-resolution duality, Heisenberg uncertainty and Shannon's information

Timur Gureyev, Frank de Hoog, Yakov Nesterets, David Paganin

Abstract


Several variations of the Heisenberg uncertainty inequality are derived on the basis of `noise-resolution duality' recently proposed by us. The same approach leads to a related inequality that provides an upper limit for the information capacity of imaging systems in terms of the number of imaging quanta (particles) used in the experiment. These results are useful in the context of biomedical imaging constrained by the radiation dose delivered to the sample, or in imaging (e.g., astronomical) problems under low light conditions.

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Keywords


uncertainty inequalities; Heisenberg uncertainty; Shannon information; noise; spatial resolution

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DOI: http://dx.doi.org/10.21914/anziamj.v56i0.9414



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