Image quality assessment is an important topic in the field of digital image processing. In this study, a full-reference image quality assessment method called Riesz transform and Visual contrast sensitivity-based feature SIMilarity index (RVSIM) is proposed. More precisely, a Log-Gabor filter is first used to decompose reference and distorted images, and Riesz transform is performed on the dec...

We derive an adaptive solver for random elliptic boundary value problems, using techniques from adaptive wavelet methods. Substituting wavelets by polynomials of the random parameters leads to a modular solver for the parameter dependence, which combines with any discretization on the spatial domain. We show optimality properties of this solver, and present numerical computations. Introduction ...

Abstract. We provide a detailed development of a function valued inner product known as the bracket product and used effectively by de Boor, Devore, Ron and Shen to study translation invariant systems. We develop a version of the bracket product specifically geared to Weyl-Heisenberg frames. This bracket product has all the properties of a standard inner product including Bessel’s inequality, a...

Weaving frames have potential applications in wireless sensor networks that require distributed processing of signals under different frames. In this paper, we study some new properties weaving generalized (or g-frames) and orthonormal bases g-orthonormal bases). It is shown a g-frame its dual are woven. The inter-relation optimal bounds universal studied. Further, present characterization g-fr...

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

The problem of exact null-controllability is considered for a wide class of linear neutral-type systems with distributed delay. The main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families. A complete characterization of this problem is given. The minimal time of controllability is specified. The results are based o...

l j l ZZ r g Then r are called orthogonal wavelets of multiplicity r if B forms an orthonormal basis of L IR We say that r are wavelets prewavelets of multiplicity r if B forms a Riesz basis of L IR and j l is orthogonal to k n f r g l n j k ZZ with j k The general theory of wavelets of multiplicity r is treated in As usual the method is based on a generalization of the notion of multiresolutio...