7 accepted papers
This paper considers the analysis of bivariate signals using complex Singular Spectrum Analysis (SSA). It introduces a pseudo-correlation based criterion in the grouping step of complex SSA. The advantage of using pseudo-correlation rather than correlation measures when analyzing polarized signals w…
The article introduces an elementary cost and storage reduction method for spectral clustering and principal component analysis. The method consists in randomly “puncturing” both the data matrix $X\in\mathbb{C}^{p\times n}$ (or $\mathbb{R}^{p\times n}$) and its corresponding kernel (Gram) matrix $K$…
The filtering estimation problem under uncertainty conditions is addressed for a class of improper quaternion signals, called widely factorizable, characterized because their augmented correlation function is a factorizable kernel. From the knowledge of the correlation functions involved, a recursiv…
Improperness testing for complex-valued vectors and processes has been of interest lately due to the potential applications of complex-valued time series analysis in several research areas. This paper provides exact distribution characterization of the GLRT (Generalized Likelihood Ratio Test) statis…
Bivariate signals are commonly processed with the usual Fourier transform, using methods such as the rotary spectrum analysis. We show that bivariate signals can be efficiently processed using the Quaternion Fourier transform. A bivariate counterpart of the analytic signal is introduced, the quatern…
Single-particle imaging experiments using X-ray Free-Electron Lasers (XFEL) belong to a new generation of X-ray imaging techniques potentially allowing high resolution images of non-crystallizable molecules to be obtained. One of the challenges of single-particle imaging is the reconstruction of the…
This paper considers the problem of parameter estimation for multiple scattering process on the sphere. Using harmonic analysis, a Fourier expansion of the pdf of the process is obtained. Based on the Fourier coefficient statistics, we consider the problem of estimating the parameter of the process…