background traditional digital subtraction angiography (dsa) is currently the gold standard diagnostic method for the diagnosis and evaluation of cerebral arteriovenous malformation (avm) and dural arteriovenous fistulas (davf). objectives the aim of this study was to analyze different less invasive magnetic resonance angiography (mra) images, time-resolved mra (tr-mra) and three-dimensional ti...

Phase retrieval has become a very active area of research. We will classify when phase retrieval by Parseval frames passes to the Naimark complement and when phase retrieval by projections passes to the orthogonal complements. We introduce a new concept we call norm retrieval and show that this is what is necessary for passing phase retrieval to complements. This leads to a detailed study of no...

Multiwavelets are generated from refinable function vectors by using multiresolution analysis. In this paper we investigate the approximation properties of a multivariate refinable function vector associated with a general dilation matrix in terms of both the subdivision operator and the order of sum rules satisfied by the matrix refinement mask. Based on a fact about the sum rules of biorthogo...

In this paper multiwavelets based on two scaling functions are discussed. They exhibit the following properties: compact support, symmetry and orthogonality as well as a good frequency resolution. Lattice structures do not only o er the possibility to implement these multiwavelet transforms, the lattice rotation angles also can be used in order to parameterize all multiwavelets of a certain len...

Multiwavelets, wavelets with several scaling functions, offer simultaneous orthogonality, symmetry, and short support, which is not possible with ordinary (scalar) wavelets. These properties make multiwavelets promising for signal processing applications, such as image denoising. The common approach for image denoising is to get the multiwavelet decomposition of a noisy image and apply a common...

If B < ∞ we call F = {fi}i∈I a Bessel sequence with Bessel bound B. If 0 < A ≤ B < ∞, then {fi}i∈I is a frame for K. If K 6= H we call {fi}i∈I a frame sequence in H. The largest A and the smallest B satisfying the above inequalities are called the optimal lower and upper frame bound and will be denoted A(F) and B(F) respectively. If A = B = λ we call this a λ-tight frame and if λ = 1 it is call...

We examine relations between popular variational methods in image processing and classical operator splitting methods in convex analysis. We focus on a gradient descent reprojection algorithm for image denoising and the recently proposed Split Bregman and alternating Split Bregman methods. By identifying the latter with the so-called DouglasRachford splitting algorithm we can guarantee its conv...

‎A numerical technique based on the collocation method using Legendre multiwavelets are‎ ‎presented for the solution of forced Duffing equation‎. ‎The operational matrix of integration for ‎Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation‎ ‎to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate‎ ‎the valid...