We show that compactly supported functions with sufficient smoothness and enough vanishing moments can serve as analyzing vectors for shearlet coorbit spaces. We use this approach to prove embedding theorems for subspaces of shearlet coorbit spaces resembling shearlets on the cone into Besov spaces. Furthermore, we show embedding relations of traces of these subspaces with respect to the real a...

The construction of continuous shearlet transform has been extended to higher dimensions. It was generalized a group that is topologically isomorphic semidirect product locally compact groups. In this paper, by unified theoretical linear algebra approach the representation theory, class transforms obtained from quasi-regular presented. order develop such representation, we utilize homogeneous s...

In order to solve storage and computation cost problems for the traditional whole sampling image fusion algorithms, a new method of infrared and visible light image fusion is put forward based on compressed sensing (CS) theory. Nonsubsampled shearlet transform (NSST) is introduced as the sparse transform. Compressed sensing is applied to fuse the high frequency subbands decomposed by NSST. The ...

Synthetic aperture radar (SAR) images are inherently degraded by multiplicative speckle noise where thresholdingbased methods in the transform domain are appropriate. Being sparse, the coefficients in the transformed domain play a key role in the performance of any thresholding methods. It has been shown that the coefficients of nonsubsampled shearlet transform (NSST) are sparser than those of ...

Seismic exploration is a remote-sensing tool applied in great many projects for engineering and resource-exploration purposes. Random noise suppression one of the key steps seismic-signal processing, especially those with important details features. The threshold-shrinkage method based on Shearlet transform has been effectively denoising. However, usually introduces boundary effect, which influ...

In this paper, using shearlet frames, we present a numerical  method  for solving  the wave equation. We define a new shearlet system and by the Plancherel theorem, we calculate the shearlet coefficients.

Nowadays, Deep Neural Networks have been applied to many applications (such as classification, denoising and inpainting) and achieved impressive performance. However, most of these works pay much attention to describe how to construct the relative framework but ignore to provide a clear and intuitive understanding of why their framework performs so well. In this paper, we present a generalpurpo...