We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as ĝ(ξ) = ∏n j=1(1 + 2πiδjξ) −1 e 2 for δ1, . . . , δn ∈ R, c > 0 (in which case g is called totally positive of Gaussian type). In analogy to Beurling’s sampling theorem for the Paley-Wiener space of entire functions...

Abstract. Starting from a general operator representation in the time-frequency domain, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A characterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of (Hilbert-Schmidt) optimal Gabor mul...

We study Weyl-Heisenberg (=Gabor) expansions for either L 2 (IR d) or a subspace of it. These are expansions in terms of the spanning set where K and L are some discrete lattices in IR d , L 2 (IR d) is nite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the \basis" properties of WH systems (e.g. being a frame or a Riesz ba...

The problem of reconstructing a function from the magnitudes its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous [2]. On other hand, is always finite-dimensional settings. A prominent example such phase retrieval recovery signal modulus Gabor transform. In this paper, we st...

We study Weyl-Heisenberg (=Gabor) expansions for either L2(IR ) or a subspace of it. These are expansions in terms of the spanning set X = (EM φ : k ∈ K, l ∈ L,φ ∈ Φ), where K and L are some discrete lattices in IR, Φ ⊂ L2(IR ) is finite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the “basis” properties of WH systems (e....

We study Weyl-Heisenberg (=Gabor) expansions for either L 2 (IR d) or a subspace of it. These are expansions in terms of the spanning set where K and L are some discrete lattices in IR d , L 2 (IR d) is nite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the \basis" properties of WH systems (e.g. being a frame or a Riesz ba...

Preface Application-oriented mathematics develops theoretical results and new mathematical concepts, motivated by application, in contrast to " applied mathematics " focusing just on providing and applying mathematical tools for the applied sciences. The application-oriented approach produces results significant both for mathematics and the applied sciences. In this context we developed new con...

Human skin color distribution is relatively compact in a color space, and it changes from frame to frame following illumination variations, also it is subject to camouflage interruption in complicated background for skin segmentation. This paper mainly talks about face detection based on skin color feature in complicated background. We assume that skin pixels in each frame are closed together a...