Related papers: Algebraic Image Processing
The analysis of digital images using homological procedures is an outstanding topic in the area of Computational Algebraic Topology. In this paper, we describe a certified reduction strategy to deal with digital images, but preserving their…
A description of the real, complete modules over the Clifford algebra of a Hilbert space, with the elements of the latter acting by skew-symmetric operators.
We initiate an investigation into how much the existing theory of (nonselfadjoint) operator algebras on a Hilbert space generalizes to algebras acting on L^p spaces. In particular we investigate the applicability of the theory of real…
We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
Image processing is one of the most immerging and widely growing techniques making it a lively research field. Image processing is converting an image to a digital format and then doing different operations on it, such as improving the…
In this paper, we give a multiplication operator representation of bounded self-adjoint operators T on a Hilbert space H such that -- is a frame for H, for some -- . We state a necessary condition in order for a frame -- to have a…
In this note one tries to venture into a study of some notions, in the context of a (unital) normed algebra, in particular the algebra of operators on a Hilbert space. Namely, one considers ``moving norms'', i.e.\ norming an element minus a…
A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…
Consider the Plancherel decomposition of the tensor product of a highest weight and a lowest weight unitary representations of $SL_2$. We construct explicitly the action of the Lie algebra $sl_2 + sl_2$ in the direct integral of Hilbert…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…
Image Processing, Optimization and Prediction of an Image play a key role in Computer Science. Image processing provides a way to analyze and identify an image .Many areas like medical image processing, Satellite images, natural images and…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision. The subject has given new insights in multiple view geometry and its application…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
The purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, following the classical example of divided power algebras. We…
Operator-valued frames (or g-frames) are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this paper, we give a new formula for operator-valued…
Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with a^2 in A for all a in A. In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory…
For finding the numerical solution of operator equations in many applications a decomposition in subspaces is needed. Therefore, it is necessary to extend the known method of matrix representation to the utilization of fusion frames. In…