A Statistical Model for Imaging Systems
Abstract
The behavior of photons is controlled by quantum mechanics, not as deterministic as classical optics shows. To this end, we defined a new statistic $Z$, which is equal to the variance minus the expectation or mean. Then, we established a statistical model for imaging systems and obtained three fundamental imaging formulas. Among them, the first formula is entirely consistent with the classic convolution equation. The second and third ones link the $Z$ quantities of the object and noise elegantly with the $Z$ image and covariance image, revealing new laws. Consequently, besides the flux density, the $Z$ quantity of an object is also imageable, which opens a new realm for imaging systems to explore the physical world.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 DOI:
 10.48550/arXiv.2005.09644
 arXiv:
 arXiv:2005.09644
 Bibcode:
 2020arXiv200509644Z
 Keywords:

 Electrical Engineering and Systems Science  Image and Video Processing;
 Physics  Data Analysis;
 Statistics and Probability;
 Physics  Optics;
 Statistics  Methodology
 EPrint:
 17 pages, 4 figures, 1 table