Universal bounds for imaging in scattering media

Abstract

In this work we establish universal ensemble independent bounds on the mean and variance of the mutual information and channel capacity for imaging through a complex medium. Both upper and lower bounds are derived and are solely dependent on the mean transmittance of the medium and the number of degrees of freedom $N$. In the asymptotic limit of large $N$, upper bounds on the channel capacity are shown to be well approximated by that of a bimodal channel with independent identically Bernoulli distributed transmission eigenvalues. Reflection based imaging modalities are also considered and permitted regions in the transmission-reflection information plane defined. Numerical examples drawn from the circular and DMPK random matrix ensembles are used to illustrate the validity of the derived bounds. Finally, although the mutual information and channel capacity are shown to be non-linear statistics of the transmission eigenvalues, the existence of central limit theorems is demonstrated and discussed.

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Cited by in corpus (4)

• Single Pixel Polarimetric Imaging through Scattering Media
• Symmetry constraints for vector scattering and transfer matrices containing evanescent components: energy conservation, reciprocity and time reversal
• Random matrix theory of polarized light scattering in disordered media
• Extended scattering channels for random matrix simulations of polarized light transport