Related papers: Microlocal Analysis of the Geometric Separation Pr…
Modern data is customarily of multimodal nature, and analysis tasks typically require separation into the single components. Although a highly ill-posed problem, the morphological difference of these components sometimes allow a very…
In this paper, we present an image separation method for separating images into point- and curvelike parts by employing a combined dictionary consisting of wavelets and compactly supported shearlets utilizing the fact that they sparsely…
Natural images are typically a composition of cartoon and texture structures. A medical image might, for instance, show a mixture of gray matter and the skull cap. One common task is to separate such an image into two single images, one…
In this paper, we present a theoretical analysis of separating images consisting of pointlike and $C^{ \beta}$-curvelike structures, where $\beta \in (1,2] $. Our approach is based on $l_1$-minimization, in which the sparsity of the desired…
In image processing, problems of separation and reconstruction of missing pixels from incomplete digital images have been far more advanced in past decades. Many empirical results have produced very good results, however, providing a…
Recently, compressed sensing techniques in combination with both wavelet and directional representation systems have been very effectively applied to the problem of image inpainting. However, a mathematical analysis of these techniques…
Consider a high-dimensional data set, in which for every data-point there is incomplete information. Each object in the data set represents a real entity, which is described by a point in high-dimensional space. We model the lack of…
This paper presents a co-clustering technique that, given a collection of images and their hierarchies, clusters nodes from these hierarchies to obtain a coherent multiresolution representation of the image collection. We formalize the…
We present an efficient method for image segmentation in the presence of strong inhomogeneities. The approach can be interpreted as a two-level clustering procedure: pixels are first grouped into superpixels via a linear least-squares…
Segmentation of ultra-high resolution images is increasingly demanded, yet poses significant challenges for algorithm efficiency, in particular considering the (GPU) memory limits. Current approaches either downsample an ultra-high…
Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure…
We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are…
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…
Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However,…
Image segmentation aims at identifying regions of interest within an image, by grouping pixels according to their properties. This task resembles the statistical one of clustering, yet many standard clustering methods fail to meet the basic…
Scientific and commercial data is often incomplete. Recovery of the missing information is an important pre-processing step in data analysis. Real-world data can in many cases be represented as a superposition of two or more different types…
Hyperspectral imaging is a powerful technology that is plagued by large dimensionality. Herein, we explore a way to combat that hindrance via non-contiguous and contiguous (simpler to realize sensor) band grouping for dimensionality…
This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system in which the elements are highly…
An algorithm is proposed for the segmentation of image into multiple levels using mean and standard deviation in the wavelet domain. The procedure provides for variable size segmentation with bigger block size around the mean, and having…
Superpixel segmentation aims at dividing the input image into some representative regions containing pixels with similar and consistent intrinsic properties, without any prior knowledge about the shape and size of each superpixel. In this…