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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 is(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)
Evolutionary spectra were developed by Priestley to extend spectral analysis to some nonstationary time series, in particular semistationary processes, of which the ubiquitous uniformly modulated processes are a subclass. Coherence is well defined for bivariate semistationary processes and can be estimated from such processes. We consider Priestley's(More)
A previous study considered the estimation of wavelet coherence from jointly stationary time series via time-domain smoothing and use of a single Morlet wavelet. The form of the asymptotic (Goodman's) distribution was derived. In this paper we extend this approach to nonstationary time series where the nonstationarity is induced by various types of(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)
Estimating the rate (first-order intensity) of a point process is a task of great interest in the understanding of its nature. In this work we first address the estimation of the rate of an orderly point process on the real line using a multiresolution wavelet expansion approach. Implementing Haar wavelets, we find that in the case of a Poisson process the(More)
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