PCH-EM: A Solution to Information Loss in the Photon Transfer Method

Working from a Poisson-Gaussian noise model, a multi-sample extension of thePhoton Counting Histogram Expectation Maximization (PCH-EM) algorithm isderived as a general-purpose alternative to the Photon Transfer (PT) method.This algorithm is derived from the same model, requires the same experimentaldata, and estimates the same sensor performance parameters as the time-testedPT method, all while obtaining lower uncertainty estimates. It is shown that asread noise becomes large, multiple data samples are necessary to capture enoughinformation about the parameters of a device under test, justifying the needfor a multi-sample extension. An estimation procedure is devised consisting ofinitial PT characterization followed by repeated iteration of PCH-EM todemonstrate the improvement in estimate uncertainty achievable with PCH-EM;particularly in the regime of Deep Sub-Electron Read Noise (DSERN). Astatistical argument based on the information theoretic concept of sufficiencyis formulated to explain how PT data reduction procedures discard informationcontained in raw sensor data, thus explaining why the proposed algorithm isable to obtain lower uncertainty estimates of key sensor performance parameterssuch as read noise and conversion gain. Experimental data captured from a CMOSquanta image sensor with DSERN is then used to demonstrate the algorithm'susage and validate the underlying theory and statistical model. In support ofthe reproducible research effort, the code associated with this work can beobtained on the MathWorks File Exchange (Hendrickson et al., 2024).