Based on the shearlet transform we present a general construction of continuous tight frames for L(R) from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems, piecewise polynomial systems, or both. From the results in [5] it follows that these systems enjoy the same desirable approximation properties for directional data as the bandl...

The continuous curvelet and shearlet transforms have recently been shown to be much more effective than the traditional wavelet transform in dealing with the set of discontinuities of functions and distributions. In particular, the continuous shearlet transform has the ability to provide a very precise geometrical characterization of general discontinuity curves occurring in images. In this pap...

In recent years directional multiscale transformations like the curveletor shearlet transformation have gained considerable attention. The reason for this is that these transforms are unlike more traditional transforms like wavelets able to efficiently handle data with features along edges. The main result confirming this property for shearlets is contained in [21] where it is shown that for ve...

It is now widely acknowledged that traditional wavelets are not very effective in dealing with multidimensional signals containing distributed discontinuities. Shearlet Transform is a new discrete multiscale directional representation, which combines the power of multiscale methods with a unique ability to capture the geometry of multidimensional data and is optimally efficient in representing ...

Description: The process is a method of classifying prostate tumors as cancerous or benign. It classifies the tumors according to the Gleason grading scale to determine the cancerous nature of the tumor. The process utilizes a shearlet transform, as well as three other features, and combines them via multiple kernel learning. The shearlet transform is used to represent the local structure of im...

Based on image sparse representation in the shearlet domain, we proposed a 2 1 L sparsity regularized unconvex variation model for image super-resolution. The 2 1 L regularizer term constrains the underlying image to have a sparse representation in shearlet domain. The fidelity term restricts the consistency with the measured imaged in terms of the data degradation model. Then, the variable spl...

The major limitation in current facial recognition systems is that they do not perform very well in uncontrolled environments, that is, when faces present variations in pose, illumination, facial expressions and environment. This is a serious obstacle in applications such as law enforcement and surveillance systems. To address this limitation, in this paper we introduce an improved approach to ...

The analysis and detection of edges is a central problem in applied mathematics and image processing. A number of results in recent years have shown that directional multiscale methods such as continuous curvelet and shearlet transforms offer a powerful theoretical framework to capture the geometry of edge singularities, going far beyond the capabilities of the conventional wavelet transform. T...

We regard the shearlet group as a semidirect product group and show that its standard representation is,typically, a quasiregu- lar representation. As a result we can characterize irreducible as well as square-integrable subrepresentations of the shearlet group.