Rajab Ali Kamyabi-Gol
Department of Pure Mathematics and Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad
[ 1 ] - The X-ray Transform and its Application in Nano Crystallography
In this article a review on the definition of the X- ray transform and some ofits applications in Nano crystallography is presented. We shall show that the X- raytransform is a special case of the Radon transform on homogeneous spaces when thetopological group E(n)- the Euclidean group - acts on ℝ2 transitively. First someproperties of the Radon transform are investigated then the relationship ...
[ 2 ] - On a new G-frame and duality
We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality for some kinds of g-frames. Finally, we illustrate an example which provides a suitable translation from discrete frames to Sun's g-frames.
[ 3 ] - Determination of subrepresentations of the standard higher dimensional shearlet group
This paper is devoted to definition standard higher dimension shearlet group $ mathbb{S} = mathbb{R}^{+} times mathbb {R}^{n-1} times mathbb {R}^{n} $ and determination of square integrable subrepresentations of this group. Also we give a characterisation of admissible vectors associated to the Hilbert spaces corresponding to each su brepresentations.
[ 4 ] - Pseudoframe multiresolution structure on abelian locally compact groups
Let $G$ be a locally compact abelian group. The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$. Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level. Also, the construction of affine frames for $L^2(G)$ bas...
[ 5 ] - ON THE SHEARLET TRANSFORM USING HYPERBOLIC FUNCTIONS
In this paper, we focus on the study of shearlet transform which isdened by using the hyperbolic functions. As a result we check an admissibilitycondition such that implies the reconstruction formula. To this end, we will usethe concept of the classical shearlet, which indicates the position and directionof a singularity.
[ 6 ] - رفع نوفه ویدئو توسط تبدیل قیچک قطعهای
Parabolic scaling and anisotropic dilation form the core of famous multi-resolution transformations such as curvelet and shearlet, which are widely used in signal processing applications like denoising. These non-adaptive geometrical wavelets are commonly used to extract structures and geometrical features of multi-dimensional signals and preserve them in noise removal treatments. In discrete s...
[ 7 ] - On a Metric on Translation Invariant Spaces
In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.
[ 8 ] - Some relations between $L^p$-spaces on locally compact group $G$ and double coset $Ksetminus G/H$
Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate t...
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