Related papers: Arbitrary decomposition of a Mueller matrix
The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a…
Gaussian blur is a commonly-used method to filter image data. This paper introduces the collapsing sum, a new operator on matrices that provides a combinatorial interpretation of Gaussian blur. We study the combinatorial properties of this…
In this article, we investigate the multi-parametric matroid problem. The weights of the elements of the matroid's ground set depend linearly on an arbitrary but fixed number of parameters, each of which is taken from a real interval. The…
The effect of matrix perturbations on the polar decomposition has been studied by several authors and various results are known. However, for operators between infinite-dimensional spaces the problem has not been considered so far. Here, we…
The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here we develop methods for decomposing a matrix $C$ into a product $X Y$, where the factors $X$ and $Y$ are…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…
In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes-Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
The problem of imaging materials with circular polarization properties is discussed within the framework of vectorial ptychography. We demonstrate, both theoretically and numerically, that using linear polarizations to investigate such…
The principle of the polarimetric imaging method called APSCI (Adapted Polarization State Contrast Imaging) is to maximize the polarimetric contrast between an object and its background using specific polarization states of illumination and…
A new technique based on superposition of two speckle patterns is proposed and demonstrated for controlled modulation of the spatial polarization distribution of the resultant speckle. It is demonstrated both theoretically and…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with…
New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences.…
The polarization decomposition of arbitrary binary-input memoryless channels (BMCs) is studied in this work. By introducing the polarization factor (PF), defined in terms of the conditional entropy of the channel output under various input…
We present a model for molecular materials made up of polar and polarizable molecular units. A simple two state model is adopted for each molecular site and only classical intermolecular interactions are accounted for, neglecting any…
Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…