A Statistical Model for Imaging Systems

TL;DR

This paper introduces a new statistical model for imaging systems based on a variance-based statistic, revealing new laws and enabling the imaging of the $Z$ quantity of objects, which extends traditional flux density imaging.

Contribution

The paper develops a novel statistical model using the $Z$ statistic, establishing three fundamental imaging formulas that connect object and noise properties with image characteristics.

Findings

The $Z$ statistic links object and noise properties with image data.

Three fundamental imaging formulas are derived, including a classic convolution equation.

The $Z$ quantity of an object can be imaged, opening new research avenues.

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.