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- Adler, Jeremy, et al.
(författare)
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Noise and colocalization in fluorescence microscopy: solving a problem
- 2008
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Ingår i: Microscopy and Analysis. ; 22:5, s. 7-10
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Forskningsöversikt (övrigt vetenskapligt/konstnärligt)abstract
- The Pearson correlation coefficient (PCC) is regularly used in colocalization measurements, but it is sensitive to image noise. Images of fluorophores are usually degraded by Poisson and background noise and we have found that, even with apparently high quality images, the measured PCC is substantially understated, to the extent that the numbers become misleading. This means that ostensibly significant differences in the PCC between two populations may just reflect differing image quality while dissimilar levels of noise may mask significant differences. A new correction, based on measurements of image quality, derived from a pair of images for each fluorophore, aligns the measured PCC with the true PCC. Our method, the Replicate Based Noise Corrected Correlation (RBNCC), generates an accurate PCC even from poor images. It is highly photon efficient and therefore well suited for use in live cell fluorescence imaging or with rapidly bleaching fluorophores.
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- Bergholm, Fredrik, et al.
(författare)
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Analysis of Bias in the Apparent Correlation Coefficient Between Image Pairs Corrupted by Severe Noise
- 2010
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 0924-9907 .- 1573-7683. ; 37:3, s. 204-219
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Tidskriftsartikel (refereegranskat)abstract
- The correlation coefficient r is a measure of similarity used to compare regions of interest in image pairs. In fluorescence microscopy there is a basic tradeoff between the degree of image noise and the frequency with which images can be acquired and therefore the ability to follow dynamic events. The correlation coefficient r is commonly used in fluorescence microscopy for colocalization measurements, when the relative distributions of two fluorophores are of interest. Unfortunately, r is known to be biased understating the true correlation when noise is present. A better measure of correlation is needed. This article analyses the expected value of r and comes up with a procedure for evaluating the bias of r, expected value formulas. A Taylor series of so-called invariant factors is analyzed in detail. These formulas indicate ways to correct r and thereby obtain a corrected value free from the influence of noise that is on average accurate (unbiased). One possible correction is the attenuated corrected correlation coefficient R, introduced heuristically by Spearman (in Am. J. Psychol. 15:72-101, 1904). An ideal correction formula in terms of expected values is derived. For large samples R tends towards the ideal correction formula and the true noise-free correlation. Correlation measurements using simulation based on the types of noise found in fluorescence microscopy images illustrate both the power of the method and the variance of R. We conclude that the correction formula is valid and is particularly useful for making correct analyses from very noisy datasets.
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- Bergholm, Fredrik
(författare)
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Intermittent Open Boundaries for Shallow Water Equations
- 2006
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Shallow water equations are used in oceanography, acoustics and electromagnetics. This report (to be submitted as article) focuses on quickly moving shallow water waves in oceanography (also Coriolis force). In wave propagation modelling, it is very often attractive to split up a numerical model into smaller pieces. For barotropic wave modelling, in oceanography, this is almost a necessity. Wave propagation in a submodel communicates with adjacent region(s) by open boundaries. An open boundary is always a half measure, but there are interesting ways of making the open boundaries “softer” – a kind of half-open boundaries. In this article, we investigate the usefulness of having \emphintermittent open boundaries. They tend to produce less errors, and may be analyzed analytically, also. The basic principle is to have both an open boundary condition and a suitable so–called transition condition.
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