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

Several variations of the Heisenberg uncertainty inequality are derived on the basis of "noise-resolution duality" recently proposed by the authors. 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 can be 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

Complementary aspects of spatial resolution and signal-to-noise ratio in computational imaging

A generic computational imaging setup is considered which assumes sequential illumination of a semi-transparent object by an arbitrary set of structured illumination patterns. For each incident illumination pattern, all transmitted light is collected by a photon-counting bucket (single-pixel) detector. The transmission coefficients measured in this way are then used to reconstruct the spatial distribution of the object's projected transmission. It is demonstrated that the squared spatial resolution of such a setup is usually equal to the ratio of the image area to the number of linearly independent illumination patterns. If the noise in the measured transmission coefficients is dominated by photon shot noise, then the ratio of the spatially-averaged squared mean signal to the spatially-averaged noise variance in the "flat" distribution reconstructed in the absence of the object, is equal to the average number of registered photons when the illumination patterns are orthogonal. The signal-to-noise ratio in a reconstructed transmission distribution is always lower in the case of non-orthogonal illumination patterns due to spatial correlations in the measured data. Examples of imaging methods relevant to the presented analysis include conventional imaging with a pixelated detector, computational ghost imaging, compressive sensing, super-resolution imaging and computed tomography