Sparse multidimensional representation using shearlets

Labate, Demetrio; Lim, Wang-Q; Kutyniok, Gitta; Weiss, Guido

doi:10.1117/12.613494

Cited by 355 publications

(268 citation statements)

References 13 publications

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“…Examples include Gabor filters [45], wavelets [13,15,47], curvelets [5], or shearlets [34,44]. More recently, Riesz-Laplace wavelets have been proposed for multiresolution monogenic signal analysis [69].…”

Section: Recent and Related Workmentioning

confidence: 99%

Two-Dimensional Compact Variational Mode Decomposition

et al. 2017

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Decomposing multidimensional signals, such as images, into spatially compact, potentially overlapping modes of essentially wavelike nature makes these components accessible for further downstream analysis. This decomposition enables space-frequency analysis, demodulation, estimation of local orientation, edge and corner detection, texture analysis, denoising, inpainting, or curvature estimation. Our model decomposes the input signal into modes with narrow Fourier bandwidth; to cope with sharp region boundaries, incompatible with narrow bandwidth, we introduce binary support functions that act as masks on the narrow-band mode for image recomposition. L 1 and TV terms promote sparsity and spatial compactness. Constraining the support functions to partitions of the signal domain, we effectively get an image segmentation model based on spectral homogeneity. By coupling several submodes together with a single support function, we are able to decompose an image into several crystal grains. Our efficient algorithm is based on variable splitting and alternate direction optimization; we employ Merriman-Bence-Osher-like threshold dynamics to handle efficiently the motion by mean curvature of the support function boundaries under the sparsity promoting terms. The versatility and effectiveness of our proposed model is demonstrated on a broad variety of example images from different modalities. These demonstrations include the decomposition of images into overlapping modes with smooth or sharp boundaries, segmentation of images of crystal grains, and inpainting of damaged image regions through artifact detection.

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Section: Recent and Related Workmentioning

confidence: 99%

Two-Dimensional Compact Variational Mode Decomposition

et al. 2017

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“…As a result, one can define systems of wavelets with composite dilations containing elements that are "long and narrow" and range over many locations, scales, shapes and directions. Building on this idea [26,34], shearlets are able to provide a nearly optimally sparse representation for a general class of images [24,25].…”

Section: Wavelets With Composite Dilationsmentioning

confidence: 99%

“…However, except for some very special cases, no satisfactory method for designing efficient numerical implementations of wavelets with composite dilations was developed so far, due to the difficulty of adapting the standard wavelet implementation algorithms to this more general setting. The goal of this paper is to introduce a 1 Even though the shearlet system is not exactly an example of wavelets with composite dilations, it is closely related to this framework being defined as a union of two such systems [26,34].…”

Section: Introductionmentioning

confidence: 99%

“…The most notable of these representations are the curvelets [42,8], the contourlets [13] and the shearlets [26,34], which are constructed by defining systems of analyzing waveforms ranging not only at various scales and locations, like traditional wavelets, but also at various orientations, with the number of orientations increasing at finer scales.…”

Section: Introductionmentioning

confidence: 99%

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Directional Multiscale Processing of Images Using Wavelets with Composite Dilations

2012

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“…But the computational efficiency of NSCT is low. In 2005, Labate et al [10] proposed a new multi-scale geometric analysis tools: shearlet which is optimally sparse in representing images. The decomposition of shearlet is similar to Contourlet transform, but an important advantage of shearlet over Contourlet transform is that there are no restrictions on the number of directions for the shearing.…”

Section: Introductionmentioning

confidence: 99%

Image Retrieval by Using Non-subsampled Shearlet Transform and Krawtchouk Moment Invariants

Wan

2015

Computer Vision - ACCV 2014 Workshops

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Abstract. In this paper, we use non-subsampled shearlet transform (NSST) and Krawtchouk Moment Invariants (KMI) to realize image retrieval based on texture and shape features. Shearlet is a new sparse representation tool of multidimensional function, which provides a simple and efficient mathematical framework. We decompose the images by NSST. The directional subband coefficients are modeled by Generalized Gaussian Distribution (GGD). The distribution parameters are used to build texture feature vectorswhich are measured by Kullback-Leibler distance (KLD). Meanwhile, low-order KMI are employed to extract shape features which are measured by Euclidean distance (ED). Finally, the image retrieval is achieved based on weighted distance measurement. Experimental results show the proposed retrieval system can obtain the highest retrieval rate comparing with the methods based on DWT, Contourlet, NSCT and DT-CWT.

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Sparse multidimensional representation using shearlets

Cited by 355 publications

References 13 publications

Two-Dimensional Compact Variational Mode Decomposition

Two-Dimensional Compact Variational Mode Decomposition

Directional Multiscale Processing of Images Using Wavelets with Composite Dilations

Image Retrieval by Using Non-subsampled Shearlet Transform and Krawtchouk Moment Invariants

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