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 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...

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.

In this paper, we first briefly review the directional properties of the Dual-Tree complex wavelet transform and we investigate how the directional selectivity of the transform can be increased (i.e., to obtain more than 6 orientations per scale). To this end, we describe a new augmented Lagrangian optimization algorithm to jointly perform the 2D spectral factorization of a set of 2D directiona...

The fast digital shearlet transform (FDST) was recently introduced as a means to analyze natural images efficiently, owing to the fact that those are typically governed by cartoon-like structures. In this paper, we introduce and discuss a first-order hybrid sigma-delta quantization algorithm for coarsely quantizing the shearlet coefficients generated by the FDST. Radial oversampling in the freq...

Volumetric data acquisition and increasingly massive data storage have increased the need to develop better analysis tools for three-dimensional data sets. These volumetric data sets can provide information beyond that contained in standard two-dimensional images. Common strategies to deal with such data sets have been based on sequential use of two-dimensional analysis tools. In this work, we ...

This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Similar to the two-dimensional case, our approach is based on translations, anisotropic dilations and specific shear matrices. We show that the associated integral transform again originates from a square-integrable representation of a specific group, the full n-variate shearlet group. More...