Shearlet as a new multidirectional and multiscale transform is optimally efficient in representing images containing edges. In this paper, a total variation based multivariate shearlet adaptive shrinkage is proposed for discontinuity-preserving image denoising. The multivariate adaptive threshold is employed to reduce the noise. Projected total variation diffusion is used to suppress the pseudo...

Abstract. Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional representation systems which have been proposed to deliver sparse approximations of such features is the utilization of parabolic scaling. One prominent example is the shearlet system. Our objective in this paper is three-fold: We firstly de...

We develop a mathematically-motivated algorithm for image superresolution, based on the discrete shearlet transform. The shearlet transform is strongly directional, and is known to provide nearoptimally sparse representations for a broad class of images. This often leads to superior performance in edge detection and image representation, when compared to other isotropic frames. We justify the u...

This paper introduces a numerical implementation of the 3D shearlet transform, a directional transform which is derived from the theory of shearlets. The shearlet approach belongs to a class of directional multiscale methods emerged during the last 10 years to overcome the limitations of traditional multiscale systems, which also include curvelets and contourlets. Unlike other methods, shearlet...

In this paper we will study the Continuous Shearlet Transform from a wavelet point of view, and show how this perspective can be used to derive a new geometric interpretation of this transform providing the possibility for FFT-based fast methods to compute the Continuous Shearlet Transform.

This paper presents a novel remote sensing image fusion algorithm, which implements the intensity-hue-saturation (IHS) transform on panchromatic sharpening of multispectral data and the dual-tree compactly supported shearlet transform (DT CSST) during fusion. Shearlet transforms can provide almost optimal representation of the anisotropic features of an image. The spatial domain discrete implem...

In this paper, a new bivariate shrinkage denoising method is proposed to model statistics of shearlet coefficients of images. Using Bayesian estimation theory we derive from this model a simple non-linear shrinkage function for shearlet denoising, which generalizes the soft threshold approach. Experimental results show that the proposed method can remove Gaussian white noise while effectively p...

Medical image fusion is a technique that integrates complementary information from multimodality images. The fused image is more suitable for treatment plan strategies. In this paper, an efficient medical image fusion method has been proposed based on shearlet transform and human visibility feature as fusion rule. Image fusion rule is the solution that influences the quality of image fusion. Th...

We prove a Heisenberg type uncertainty principle for the continuous shearlet transform, and study two generalizations of it. Our work extends the shearlet theory. c ©2016 All rights reserved.