31 citations · 118 across the 11 of their papers we have counts for
13 papers
On the rank of quaternion Hankel matrices
Philippe Flores, Julien Flamant, Nicolas Le Bihan
This paper discusses the left and right ranks of quaternion matrices with Hankel structure. While they are in general different for arbitrary quaternion matrices, we show that the…
Time and covariance smoothing for restoration of bivariate signals
Yusuf Yigit Pilavci, Pierre Palud, Julien Flamant +3
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two component…
Multilinear analysis of quaternion arrays: theory and computation
Julien Flamant, Xavier Luciani, Sebastian Miron +1
Multidimensional quaternion arrays (often referred to as "quaternion tensors") and their decompositions have recently gained increasing attention in various fields such as color an…
On factorization of rank-one auto-correlation matrix polynomials
Konstantin Usevich, Julien Flamant, Marianne Clausel +1
This article characterizes the rank-one factorization of auto-correlation matrix polynomials. We establish a sufficient and necessary uniqueness condition for uniqueness of the fac…
Polarimetric phase retrieval: uniqueness and algorithms
Julien Flamant, Konstantin Usevich, Marianne Clausel +1
This work introduces a novel Fourier phase retrieval model, called polarimetric phase retrieval that enables a systematic use of polarization information in Fourier phase retrieval…
A general framework for constrained convex quaternion optimization
Julien Flamant, Sebastian Miron, David Brie
This paper introduces a general framework for solving constrained convex quaternion optimization problems in the quaternion domain. To soundly derive these new results, the propose…
Quaternion Non-negative Matrix Factorization: definition, uniqueness and algorithm
Julien Flamant, Sebastian Miron, David Brie
This article introduces quaternion non-negative matrix factorization (QNMF), which generalizes the usual non-negative matrix factorization (NMF) to the case of polarized signals. P…
A complete framework for linear filtering of bivariate signals
Julien Flamant, Pierre Chainais, Nicolas Le Bihan
A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on a tailored quaternion Fourier transform. This framework features…
On the zeros of the spectrogram of white noise
Rémi Bardenet, Julien Flamant, Pierre Chainais
In a recent paper, Flandrin [2015] has proposed filtering based on the zeros of a spectrogram, using the short-time Fourier transform and a Gaussian window. His results are based o…
Spectral analysis of stationary random bivariate signals
Julien Flamant, Nicolas Le Bihan, Pierre Chainais
A novel approach towards the spectral analysis of stationary random bivariate signals is proposed. Using the Quaternion Fourier Transform, we introduce a quaternion-valued spectral…
Time-frequency analysis of bivariate signals
Julien Flamant, Nicolas Le Bihan, Pierre Chainais
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivari…
Expansion-maximization-compression algorithm with spherical harmonics for single particle imaging with X-ray lasers
Julien Flamant, Nicolas Le Bihan, Andrew V. Martin +1
In 3D single particle imaging with X-ray free-electron lasers, particle orientation is not recorded during measurement but is instead recovered as a necessary step in the reconstru…
Density estimation on the rotation group using diffusive wavelets
Nicolas Le Bihan, Julien Flamant, Jonathan H. Manton
This paper considers the problem of estimating probability density functions on the rotation group . Two distinct approaches are proposed, one based on characteristic functi…