Transmission matrix inference via pseudolikelihood decimation. (English) Zbl 1510.78055
Summary: Recently, significant efforts in medical imaging are towards the exploitation of disordered media as optics tools. Among several approaches, the transmission matrix description is promising for characterizing complex structures and, currently, has enabled imaging and focusing through disorder. In the present work, we report a statistical mechanics description of the transmission problem. We convert a linear input-output transmission recovery into the statistical inference of an effective interaction matrix. We do this by relying on a pseudolikelihood maximization process based on random intensity observations. Our aim is to bridge results from spin-glass theory to the field of disordered photonics, uncovering insights from the scattering problem and encouraging the development of novel imaging techniques for better medical investigations.
MSC:
| 78A70 | Biological applications of optics and electromagnetic theory |
| 78A45 | Diffraction, scattering |
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 92C55 | Biomedical imaging and signal processing |
| 62P30 | Applications of statistics in engineering and industry; control charts |
| 62F15 | Bayesian inference |
| 62C10 | Bayesian problems; characterization of Bayes procedures |
| 65K10 | Numerical optimization and variational techniques |
Software:
minFuncReferences:
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