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...

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...

In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to apply the coorbit space theory can indeed be satisfied for the shearlet group. Consequently, we establish new families of smoothness spaces, the shearlet coorbit spaces. Moreover, our approach yields Banach frames f...

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.

In this chapter, we illustrate the properties of the continuous shearlet transform with respect to its ability to describe the set of singularities of multidimensional functions and distributions. This is of particular interest since singularities and other irregular structures typically carry the most essential information in multidimensional phenomena. Consider, for example, the edges of natu...

Fourier samples are collected in a variety of applications including magnetic resonance imaging (MRI) and synthetic aperture radar (SAR). The data are typically under-sampled and noisy. In recent years, l regularization has received considerable attention in designing image reconstruction algorithms from undersampled and noisy Fourier data. The underlying image is assumed to have some sparsity ...

The inversion of the Radon transform is a classical ill-posed inverse problem where some method of regularization must be applied in order to accurately recover the objects of interest from the observable data. A well-known consequence of the traditional regularization methods is that some important features to be recovered are lost, as evident in imaging applications where the regularized reco...