نتایج جستجو برای: shearlet group

تعداد نتایج: 979538  

2009
Gitta Kutyniok Morteza Shahram David L. Donoho

Shearlab is a Matlab toolbox for digital shearlet transformation of two-D (image) data we developed following a rational design process. The Pseudo-Polar FFT fits very naturally with the continuum theory of the Shearlet transform and allows us to translate Shearlet ideas naturally into a digital framework. However, there are still windows and weights which must be chosen. We developed more than...

2014
Gitta Kutyniok Philipp Petersen

We analyze the detection and classification of singularities of functions f = χB , where B ⊂ R and d = 2, 3. It will be shown how the set ∂B can be extracted by a continuous shearlet transform associated with compactly supported shearlets. Furthermore, if ∂S is a d−1 dimensional piecewise smooth manifold with d = 2 or 3, we will classify smooth and non-smooth components of ∂S. This improves pre...

2014
Chang Duan Qihong Huang Xuegang Wang Hong Wang

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...

Journal: :SIAM J. Imaging Sciences 2014
Martin Genzel Gitta Kutyniok

Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides (optimally) sparse approximations of the original image. Due to the common assumption that images are typically governed by anisotropic features, directional represen...

2012
S. Häuser G. Steidl

Segmentation plays an important role in many preprocessing stages in image processing. Recently, convex relaxation methods for image multi-labeling were proposed in the literature. Often these models involve the total variation (TV) semi-norm as regularizing term. However, it is well-known that the TV functional is not optimal for the segmentation of textured regions. In recent years directiona...

Journal: :Journal of Fourier Analysis and Applications 2013

2009
Philipp Grohs

Based on the shearlet transform we present a general construction of continuous tight frames for L(R) from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems, piecewise polynomial systems, or both. From the results in [5] it follows that these systems enjoy the same desirable approximation properties for directional data as the bandl...

2009
Glenn Easley Kanghui Guo Demetrio Labate

The continuous curvelet and shearlet transforms have recently been shown to be much more effective than the traditional wavelet transform in dealing with the set of discontinuities of functions and distributions. In particular, the continuous shearlet transform has the ability to provide a very precise geometrical characterization of general discontinuity curves occurring in images. In this pap...

2009
Philipp Grohs

In recent years directional multiscale transformations like the curveletor shearlet transformation have gained considerable attention. The reason for this is that these transforms are unlike more traditional transforms like wavelets able to efficiently handle data with features along edges. The main result confirming this property for shearlets is contained in [21] where it is shown that for ve...

Journal: :SIAM J. Math. Analysis 2012
Gitta Kutyniok Jakob Lemvig Wang-Q Lim

Abstract. We study efficient and reliable methods of capturing and sparsely representing anisotropic structures in 3D data. As a model class for multidimensional data with anisotropic features, we introduce generalized three-dimensional cartoon-like images. This function class will have two smoothness parameters: one parameter β controlling classical smoothness and one parameter α controlling a...

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