Related papers: Shaped extensions of singular spectrum analysis
Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and…
The multiresolution analysis (MRA) associated with the Special affine Fourier transform (SAFT) provides a structured approach for generating orthonormal bases in \( L^2(\mathbb R) \), making it a powerful tool for advanced signal analysis.…
A novel time-reversal subwavelength transmission technique, based on pulse shaping circuits (PSCs), is proposed. This technique removes the need for complex or electrically large electromagnetic structures by generating channel diversity…
We consider the problem of resolving overlapping pulses from noisy multi-snapshot measurements, which has been a problem central to various applications including medical imaging and array signal processing. ESPRIT algorithm has been used…
We present a technique for spatiotemporal data analysis called nonlinear Laplacian spectral analysis (NLSA), which generalizes singular spectrum analysis (SSA) to take into account the nonlinear manifold structure of complex data sets. The…
Light-based synthetic aperture (SA) imaging methods, such as Fourier Ptychography, have brought breakthrough high-resolution wide-field-of-view imaging capabilities to microscopy. While these technologies promise similar improvements in…
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series of length $N$ whose intermittency can give rise to the divergence of their variance. SSA relies on the…
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…
Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, paintined by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific…
We describe a method of analytic evolution of distribution amplitudes (DA) that have singularities, such as non-zero values at the end-points of the support region, jumps at some points inside the support region and cusps. We illustrate the…
In the standard (classic) approach, galaxy clustering measurements from spectroscopic surveys are compressed into baryon acoustic oscillations and redshift space distortions measurements, which in turn can be compared to cosmological…
The growing use of wide angle image capture devices and the need for fast and accurate image analysis in computer visions have enforced the need for dedicated under-representation approaches. Most recent decomposition methods segment an…
Shapelet-based algorithms are widely used for time series classification because of their ease of interpretation, but they are currently outperformed by recent state-of-the-art approaches. We present a new formulation of time series…
Based on the work done by an electromagnetic field on an atomic or molecular electronic system, a general gauge invariant formulation of transient absorption spectroscopy is presented within the semi-classical approximation. Avoiding…
The paper studies processes defined on time domains structured as oriented spatial graphs (or metric graphs, or oriented branched 1-manifolds). This setting can be used, for example, for forecasting models involving branching scenarios. For…
3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity.…
Single-pixel imaging (SPI) is significant for applications constrained by transmission bandwidth or lighting band, where 3D SPI can be further realized through capturing signals carrying depth. Sampling strategy and reconstruction algorithm…
We present a theoretical model for the power spectrum and bispectrum of galaxy clustering that exploits the complementarity between small-scale power spectrum information and large-scale bispectrum measurements. We extend the FOLPS code by…
Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…