It is known that the Continuous Wavelet Transform of a distribution f decays rapidly near the points where f is smooth, while it decays slowly near the irregular points. This property allows the identification of the singular support of f . However, the Continuous Wavelet Transform is unable to describe the geometry of the set of singularities of f and, in particular, identify the wavefront set...

In compressive sensing, it is challenging to reconstruct image of high quality from very few noisy linear projections. Existing methods mostly work well on piecewise constant images but not so well on piecewise smooth images such as natural images, medical images that contain a lot of details. We propose a twostage method called GeoCS to recover images with rich geometric information from very ...

Nowadays many MRI scans can give 3D volume data with different contrasts, but the observers may want to view various contrasts in the same 3D volume. The conventional 2D medical fusion methods can only fuse the 3D volume data layer by layer, which may lead to the loss of interframe correlative information. In this paper, a novel 3D medical volume fusion method based on 3D band limited shearlet ...

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...

A weakly admissible mesh (WAM) on a continuum real-valued domain is sequence of discrete grids such that the maximum norm polynomials grid comparable to supremum domain. The asymptotic rate growth sizes and comparability constants must grow in controlled manner. In this paper, we recognize notion WAM can be generalized hierarchical subspaces not necessarily polynomial functions, analyze particu...