Related papers: Multivariate Functional Singular Spectrum Analysis…
Synthesis of single-wavelength temporal phase-shifting algorithms (PSA) for interferometry is well-known and firmly based on the frequency transfer function (FTF) paradigm. Here we extend the single-wavelength FTF-theory to dual and…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
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…
The Mamba architecture has been widely applied to various low-level vision tasks due to its exceptional adaptability and strong performance. Although the Mamba architecture has been adopted for spectral reconstruction, it still faces the…
Functional linear discriminant analysis (FLDA) is a powerful tool that extends LDA-mediated multiclass classification and dimension reduction to univariate time-series functions. However, in the age of large multivariate and incomplete…
This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M$^2$. The problem is posed as solving a finite number of trigonometric moment equations…
Time-series data in application areas such as motion capture and activity recognition is often multi-dimension. In these application areas data typically comes from wearable sensors or is extracted from video. There is a lot of redundancy…
"Single-shot" ultrafast spectroscopy based on the frequency encoding of transient absorbance kinetics using chirped probe pulses is analyzed theoretically. FDSS has an advantage over pump-probe spectroscopy in a situation where the "noise"…
Sometimes, it is of interest to single out the fluctuations associated to a given frequency. We propose a new variant of SSA, Circulant SSA (CiSSA), that allows to extract the signal associated to any frequency specified beforehand. This is…
One-dimensional detrended fluctuation analysis (1D DFA) and multifractal detrended fluctuation analysis (1D MF-DFA) are widely used in the scaling analysis of fractal and multifractal time series because of being accurate and easy to…
Modelling a large collection of functional time series arises in a broad spectral of real applications. Under such a scenario, not only the number of functional variables can be diverging with, or even larger than the number of temporally…
The functional ANOVA expansion of a multivariate mapping plays a fundamental role in statistics. The expansion is unique once a unique distribution is assigned to the covariates. Recent investigations in the environmental and climate…
Aims : We describe MS-MFS, a multi-scale multi-frequency deconvolution algorithm for wide-band synthesis-imaging, and present imaging results that illustrate the capabilities of the algorithm and the conditions under which it is feasible…
We develop a new method for multivariate scalar on multidimensional distribution regression. Traditional approaches typically analyze isolated univariate scalar outcomes or consider unidimensional distributional representations as…
Multifractal analysis (MFA) provides a framework for the global characterization of image textures by describing the spatial fluctuations of their local regularity based on the multifractal spectrum. Several works have shown the interest of…
Spectrum sensing and analysis is crucial for a variety of reasons, including regulatory compliance, interference detection and mitigation, and spectrum resource planning and optimization. Effective, real-time spectrum analysis remains a…
Federated domain generalization aims to learn a generalizable model from multiple decentralized source domains for deploying on the unseen target domain. The style augmentation methods have achieved great progress on domain generalization.…
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to…
In this literature, we carefully investigate the structure of single- and multi-frequency imaging functions, that are usually employed in inverse scattering problems. Based on patterns of the singular vectors of the Multi-Static Response…
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…