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—The use of the wavelet coherence of two series in hypothesis testing relies on some sort of smoothing being carried out in order that the coherence estimator is not simply unity. A previous study considered averaging via the use of multiple Morse wavelets. Here we consider time-domain smoothing and use of a single Morlet wavelet. Since the Morlet wavelet… (More)

—Wavelet coherence computed from two time series has been widely applied in hypothesis testing situations, but has proven resistant to analytic study, with resort to simulations for statistical properties. As part of the null hypothesis being tested, such simulations invariably assume joint stationarity of the series. If estimated using multiple orthogonal… (More)

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both… (More)

Image registration is an important processing step in fluorescence microscopy, for example in tracking or super-resolution methods. Precision localization of single fluorescent molecules from a quantum limited photon detection process, subject to Gaussian readout noise, is key to the use of single molecule microscopy. It is therefore important to know the… (More)

This paper is concerned with assessing localization errors emanating from the image registration of two monochromatic fluorescence microscopy images. Assuming an affine transform exists between images, registration in this setting typically involves using control points to solve a multivariate linear regression problem; however with measurement errors… (More)

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