June 2015
Spotlight Summary by Brynmor Davis
Finite sampling corrected 3D noise with confidence intervals
Imaging devices are subject to degradation by noise from a variety of sources. Differing physical origins result in differing spatio-temporal characteristics of the noise terms that combine to degrade a video stream. For example, an uncorrected dark noise non-uniformity will result in a change in offset between pixels, and so will produce a noise signal with spatial, but not temporal, variation. By contrast, thermal noise will vary in time, in addition to both spatial dimensions.
While the sources of imaging noise are complex, and in many cases scene dependent, approximations can be made to develop useful quantitative noise models. In this work, the authors consider a noise model consisting of a sum of Gaussian random processes with differing spatio-temporal dependencies (e.g., one term has variation only in time; another varies in the horizontal and temporal axes, but not vertically; etc.). This sort of reasonable model can be used to investigate how a hypothetical imager performs. But more practically, it can be employed to rigorously characterize a real camera using experimental data. Here the authors present work that can be used to answer important questions such as: how much data do I need to collect in order to define the noise model with a desired precision?; and which noise components can I most accurately characterize?
Measurable statistical quantities, calculated from collected data, are shown to be related to combinations of the defining model variances. This paper makes the important contribution of quantifying this relationship, while taking into account the finite extent (both in space and time) of any real-world measurement. Further, a framework is provided for calculating confidence intervals in the estimated model parameters. That is, once the noise model has been estimated, it is known how accurate the model can be expected to be.
In addition to providing a clear and comprehensive analysis in this article, the authors have made available well organized and clearly commented code on the Matlab file exchange (http://www.mathworks.com/matlabcentral/fileexchange/49657-finite-sampling-corrected-3d-noise-with-confidence-intervals). This open-source approach makes it significantly easier for scientists and engineers to employ these useful and rigorous methods in the characterization of their imaging systems.
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While the sources of imaging noise are complex, and in many cases scene dependent, approximations can be made to develop useful quantitative noise models. In this work, the authors consider a noise model consisting of a sum of Gaussian random processes with differing spatio-temporal dependencies (e.g., one term has variation only in time; another varies in the horizontal and temporal axes, but not vertically; etc.). This sort of reasonable model can be used to investigate how a hypothetical imager performs. But more practically, it can be employed to rigorously characterize a real camera using experimental data. Here the authors present work that can be used to answer important questions such as: how much data do I need to collect in order to define the noise model with a desired precision?; and which noise components can I most accurately characterize?
Measurable statistical quantities, calculated from collected data, are shown to be related to combinations of the defining model variances. This paper makes the important contribution of quantifying this relationship, while taking into account the finite extent (both in space and time) of any real-world measurement. Further, a framework is provided for calculating confidence intervals in the estimated model parameters. That is, once the noise model has been estimated, it is known how accurate the model can be expected to be.
In addition to providing a clear and comprehensive analysis in this article, the authors have made available well organized and clearly commented code on the Matlab file exchange (http://www.mathworks.com/matlabcentral/fileexchange/49657-finite-sampling-corrected-3d-noise-with-confidence-intervals). This open-source approach makes it significantly easier for scientists and engineers to employ these useful and rigorous methods in the characterization of their imaging systems.
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Article Information
Finite sampling corrected 3D noise with confidence intervals
David P. Haefner and Stephen D. Burks
Appl. Opt. 54(15) 4907-4915 (2015) View: Abstract | HTML | PDF