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Accurate sky localization is essential for gravitational-wave (GW) astronomy, particularly for multimessenger follow-up and host galaxy identification. For strongly lensed GW events, achieving localization at the level of $\sim…
The wavelet transform and related techniques are used to analyze singular and fractal signals. The normalized wavelet scalogram is introduced to detect singularities including jumps, cusps and other sharply changing points. The wavelet…
Wavelets have been shown to be effective bases for many classes of natural signals and images. Standard wavelet bases have the entire vector space $\mathbb R^n$ as their natural domain. It is fairly straightforward to adapt these to…
This note introduces a new family of wavelets and a multiresolution analysis, which exploits the relationship between analysing filters and Floquet's solution of Mathieu differential equations. The transfer function of both the detail and…
We introduce an extension of continuous wavelet theory that enables an efficient implementation of multiplicative operators in the coefficient space. In the new theory, the signal space is embedded in a larger abstract signal space -- the…
We consider the problem of distributed feature quantization, where the goal is to enable a pretrained classifier at a central node to carry out its classification on features that are gathered from distributed nodes through communication…
Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
We present the quantum theory of the measurement of bosonic particles by multipixel detectors. For the sake of clarity, we specialize on beams of photons. We study the measurement of different spatial beam characteristics, as position and…
Harmonic generation plays a crucial role in contrast-enhanced ultrasound, both for imaging and therapeutic applications. However, accurately capturing these nonlinear effects is computationally very demanding when using traditional…
This review summarizes popular unsupervised learning methods, and gives an overview of their past, current, and future uses in astronomy. Unsupervised learning aims to organise the information content of a dataset, in such a way that…
We describe new algorithms to compute Whitney stratifications of real algebraic varieties. Using either conormal or polar techniques, these algorithms stratify a complexification of a given real variety. We then show that the resulting…
Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…
The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based…
Astrophysics and cosmology are rich with data. The advent of wide-area digital cameras on large aperture telescopes has led to ever more ambitious surveys of the sky. Data volumes of entire surveys a decade ago can now be acquired in a…
Plasma jets are widely investigated both in the laboratory and in nature. Astrophysical objects such as black holes, active galactic nuclei, and young stellar objects commonly emit plasma jets in various forms. With the availability of data…
Various and different methods can be used to produce high-resolution multispectral images from high-resolution panchromatic image (PAN) and low-resolution multispectral images (MS), mostly on the pixel level. However, the jury is still out…
The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this…
We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained…
It is given an efficient complete parametrization of wavelet matrices of rank $m$, genus $g+1$, and degree $g$, which are naturally identified with corresponding polynomial paraunitary matrix-functions. The parametrization depends on…