Image Processing Using Shearlets

Easley, Glenn R.; Labate, Demetrio

doi:10.1007/978-0-8176-8316-0_8

Cited by 26 publications

(11 citation statements)

References 89 publications

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“…The excellent denoising performance of this algorithm takes advantage of the sparsity properties of shearlets, that have optimally sparse representation properties for a large class of images [ 18 , 26 ]. Thanks to these sparsity properties, this method is particularly efficient at removing noise without blurring edges [ 24 , 27 ]. Overall, the boundaries of the structures in an image look sharper after the application of this denoising method.…”

Section: Methodsmentioning

confidence: 99%

Automated Detection of Soma Location and Morphology in Neuronal Network Cultures

et al. 2015

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Automated identification of the primary components of a neuron and extraction of its sub-cellular features are essential steps in many quantitative studies of neuronal networks. The focus of this paper is the development of an algorithm for the automated detection of the location and morphology of somas in confocal images of neuronal network cultures. This problem is motivated by applications in high-content screenings (HCS), where the extraction of multiple morphological features of neurons on large data sets is required. Existing algorithms are not very efficient when applied to the analysis of confocal image stacks of neuronal cultures. In addition to the usual difficulties associated with the processing of fluorescent images, these types of stacks contain a small number of images so that only a small number of pixels are available along the z-direction and it is challenging to apply conventional 3D filters. The algorithm we present in this paper applies a number of innovative ideas from the theory of directional multiscale representations and involves the following steps: (i) image segmentation based on support vector machines with specially designed multiscale filters; (ii) soma extraction and separation of contiguous somas, using a combination of level set method and directional multiscale filters. We also present an approach to extract the soma’s surface morphology using the 3D shearlet transform. Extensive numerical experiments show that our algorithms are computationally efficient and highly accurate in segmenting the somas and separating contiguous ones. The algorithms presented in this paper will facilitate the development of a high-throughput quantitative platform for the study of neuronal networks for HCS applications.

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Section: Methodsmentioning

confidence: 99%

Automated Detection of Soma Location and Morphology in Neuronal Network Cultures

et al. 2015

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“…However, the traditional wavelet transform (WT) is inefficient to provide significant geometrical information of the objects or distribution due to wavelets are isotropic and are incapable of accommodating edges in images (anisotropic features) [27]. On the contrary, an extension of wavelets, namely shearlets can accommodate anisotropic features [28]. Shearlet transform is designed to combine the geometric features and the multi-scale analysis by creating a non-isotropic form of WT.…”

Section: Shearlet Transformmentioning

confidence: 99%

“…Thus, shearlet transform is mainly well adapted to signify edges and other anisotropic objects that considered the most dominant features in typical microscopic images. It provides approximately optimally sparse depictions for a large class of functions that are convenient to model images [28].…”

Section: Shearlet Transformmentioning

confidence: 99%

A novel glomerular basement membrane segmentation using neutrsophic set and shearlet transform on microscopic images

Guo

Ashour

Sun

2017

Health Inf Sci Syst

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“…In order to prove the estimate (20) for S, we first study the different terms of the summand independently. Let λ = (d, j, ℓ, k) ∈ Λ d and recall the matrix M λ from (16). It holds…”

Section: This However Is Obviously True Sincementioning

confidence: 99%

Multivariate α-molecules

Flinth

Schäfer

2016

Journal of Approximation Theory

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The suboptimal performance of wavelets with regard to the approximation of multivariate data gave rise to new representation systems, specifically designed for data with anisotropic features. Some prominent examples of these are given by ridgelets, curvelets, and shearlets, to name a few.The great variety of such so-called directional systems motivated the search for a common framework, which unites many under one roof and enables a simultaneous analysis, for example with respect to approximation properties. Building on the concept of parabolic molecules, the recently introduced framework of α-molecules does in fact include the previous mentioned systems. Until now however it is confined to the bivariate setting, whereas nowadays one often deals with higher dimensional data. This motivates the extension of this unifying theory to dimensions larger than 2, put forward in this work. In particular, we generalize the central result that the cross-Gramian of any two systems of α-molecules will to some extent be localized.As an exemplary application, we investigate the sparse approximation of video signals, which are instances of 3D data. The multivariate theory allows us to derive almost optimal approximation rates for a large class of representation systems.Suitable representation systems are provided e.g. by so-called frame systems [6], which ensure stable measurement of the coefficients and also stable reconstruction. A system (m λ ) λ∈Λ in H forms a frame if there exist constants A, B > 0, called the frame bounds, such that A f 2 ≤ λ∈Λ | f, m λ | 2 ≤ B f 2 for all f ∈ H.

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Image Processing Using Shearlets

Cited by 26 publications

References 89 publications

Automated Detection of Soma Location and Morphology in Neuronal Network Cultures

Automated Detection of Soma Location and Morphology in Neuronal Network Cultures

A novel glomerular basement membrane segmentation using neutrsophic set and shearlet transform on microscopic images

Multivariate α-molecules

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