The shearlet representation has gained increasingly more prominence in recent years as a flexible mathematical framework which enables the efficient analysis of anisotropic phenomena by combining multiscale analysis with the ability to handle directional information. In this paper, we introduce a class of shearlet smoothness spaces which is derived from the theory of decomposition spaces recent...

Microseismic noise suppression is widely used in the exploration of unconventional oil and gas resources. The effective microseismic downhole signals have extremely weak energy are contaminated by strong interference, making data processing interpretation difficult. need for high-frequency signal reservation presents a basic problem design methods. represent as continuous reflection event more ...

Model-based image denoising methods are well suited for use as processors in remote sensing systems such satellites due to their well-developed mathematical theory and low computational cost, but these can often only deal with a single type of random noise. In this paper, based on the model-based techniques, mixed noise algorithm using Gaussian curvature surface shearlet transform is proposed. ...

In this paper we introduce a new localization framework for wavelet transforms, such as the 1D wavelet transform and the Shearlet transform. Our goal is to design nonadaptive window functions that promote sparsity in some sense. For that, we introduce a framework for analyzing localization aspects of window functions. Our localization theory diverges from the conventional theory in two ways. Fi...