The two-dimensional wavelet transform for magnetic resonance imaging (MRI) images does not sparsely represent curve singularity characteristics, which can only capture the limited direction information. Pointing at this problem, this paper presents a new method based on discrete Shearlet transform for compressed sensing MRI (CS-MRI). Frequency coefficients can be got at all scales and in all di...

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...

The two-dimensional wavelet transform for magnetic resonance imaging (MRI) does not represent sparsely curve singularity characteristics, it can only capture the limited direction information. In order to solve this problem, a new method for compressed sensing MRI (CS-MRI) is presented based on discrete shearlet transform in this paper. Frequency coefficients can be got at all scales and in all...

Finding optimal representations of signals in higher dimensions, in particular directional representations, is currently the subject of intensive research. Since it might be difficult to obtain directional information by means of wavelets, several new representation systems were proposed in the past, including ridgelets, curvelets and, more recently, shearlets. In this paper we study and visual...

The only quadrature operator of order two on L2(R) which covaries with orthogonal transforms, in particular rotations is (up to the sign) the Riesz transform. This property was used for the construction of monogenic wavelets and curvelets. Recently, shearlets were applied for various signal processing tasks. Unfortunately, the Riesz transform does not correspond with the shear operation. In thi...

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...

In this paper, g-dual function-valued frames in L2(0;1) are in- troduced. We can achieve more reconstruction formulas to ob- tain signals in L2(0;1) by applying g-dual function-valued frames in L2(0;1).

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...

This paper introduces a new Parseval frame, based on the 3–D shearlet representation, which is especially designed to capture geometric features such as discontinuous boundaries with very high efficiency. We show that this approach exhibits essentially optimal approximation properties for 3–D functions f which are smooth away from discontinuities along C2 surfaces. In fact, the N term approxima...

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...