We propose an algorithmic framework based on ADMM/split Bregman that combines a multilevel adapted, iterative reweighting strategy and a second total generalized variation regularizer. The level adapted reweighting strategy is a combination of reweighted `-minimization and additional compensation factors for a uniform treatment of the sparsity structure across all levels. Classical multilscale ...

The analysis and detection of edges and interface boundaries is a fundamental problem in applied mathematics and image processing. In the study of the wave equation, for example, one is interested in the evolution of moving fronts; in image processing and computer vision, the detection and analysis of edges is an essential task for applications such as shape recognition, image enhancement and c...

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. ...