Finite sampling corrected 3D noise with confidence intervals

Abstract

When evaluated with a spatially uniform irradiance, an imaging sensor exhibits both spatial and temporal variations, which can be described as a three-dimensional (3D) random process considered as noise. In the 1990s, NVESD engineers developed an approximation to the 3D power spectral density for noise in imaging systems known as 3D noise. The goal was to decompose the 3D noise process into spatial and temporal components identify potential sources of origin. To characterize a sensor in terms of its 3D noise values, a finite number of samples in each of the three dimensions (two spatial, one temporal) were performed. In this correspondence, we developed the full sampling corrected 3D noise measurement and the corresponding confidence bounds. The accuracy of these methods was demonstrated through Monte Carlo simulations. Both the sampling correction as well as the confidence intervals can be applied a posteriori to the classic 3D noise calculation. The Matlab functions associated with this work can be found on the Mathworks file exchange ["Finite sampling corrected 3D noise with confidence intervals," https://www.mathworks.com/matlabcentral/fileexchange/49657-finite-sampling-corrected-3d-noise-with-confidence-intervals.].

Modeling demosaicing of color corrected cameras in the NV-IPM

“…The noise on each channel is treated as independent (fully uncorrelated) and instead add in power spectral density [10].…”

Spatially resolved 3D noise

“…To obtain the variance of the independent random processes, statistics following directional averaging are calculated. The required seven equations for each of the unknown variances can be found by calculating the variance for each of: three orthogonal directional averages applied across one dimension, three different two dimensional directional averages, and the total variance [6]. As the individual random processes are independent, the effects of directional averages on each random process can be assessed independently.…”

“…As the individual random processes are independent, the effects of directional averages on each random process can be assessed independently. The complete details and derivation for calculating the individual variances is described in reference [6]. The seven variances (following different directional averaging) are calculated and related to the variance of the independent underlying random process through a mixing matrix in Eq(2).…”

“…If this measurement were to be repeated, a different value would likely be found, and the total variability would be determined by a governing distribution. In [6], expressions for the confidence intervals of the 3D noise measurement were derived, further the Matlab functions associated with this publication are available in [7]. If the entirety of the possible noise sampling were used to calculate 3D noise, the results can then be used to determine an appropriately sized sub-cube to conduct further calculations.…”

“…In a recent correspondence, efforts have been made to correct for cases with finite sampling [6]. In addition to correcting for the finite sampling of a measurement, the corresponding confidence intervals were also derived.…”