相关论文: Fourier Theory on the Complex Plane III: Low-Pass …
We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability estimates that grant spectral convergence of the…
By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…
X-ray scattering patterns from emerging single particle experiments have commonly many missing or contaminated pixels. This complicates different analyses including projections on Fourier or other basis functions (for noise suppression,…
We study when low coordinate degree functions (LCDF) -- linear combinations of functions depending on small subsets of entries of a vector -- can hypothesis test between high-dimensional probability measures. These functions are a…
To study singularities on complex varieties we study Poincar\'e series of filtrations that are defined by discrete valuations on the local ring at the singularity. In all previous papers on this topic one poses restrictions on the centers…
We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…
A multiparameter filtration, or a multifiltration, may in many cases be seen as the collection of sublevel sets of a vector function, which we call a multifiltering function. The main objective of this paper is to obtain a better…
In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available.…
Shape- and scale-selective digital-filters, with steerable finite/infinite impulse responses (FIR/IIRs) and non-recursive/recursive realizations, that are separable in both spatial dimensions and adequately isotropic, are derived. The…
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…
We consider divisorial filtration on the rings of functions on hypersurface singularities associated with Newton diagrams and their analogues for plane curve singularities. We compute the multi-variable Poincar\'e series for the latter…
Particle filtering is a standard Monte-Carlo approach for a wide range of sequential inference tasks. The key component of a particle filter is a set of particles with importance weights that serve as a proxy of the true posterior…
We review the notion of (finitary) filter pair as a tool for creating and analyzing logics. A filter pair can be seen as a presentation of a logic, given by presenting its lattice of theories as the image of a lattice homomorphism, with…
Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
We investigate a modified split-step Fourier method (SSFM) by including low-pass filters in the linear steps. This method can simultaneously achieve a higher simulation accuracy and a slightly reduced complexity.
The graph fractional Fourier transform (GFRFT) for unitary graph Fourier transform (GFT) matrices can be interpreted through the scalar function $e^{j\alpha\theta}$ on the unit circle. Under the principal branch, its Fourier-series…
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
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 a direct description of LTI filters in terms of their…