Related papers: A Frame Decomposition of the Atmospheric Tomograph…
Motivated by recent work in Dynamical Sampling, we prove a necessary and sufficient condition for a frame in a separable and infinite-dimensional Hilbert space to admit the form $\{T^{n} \varphi \}_{n \geq 0}$ with $T \in B(H)$. Also, a…
Fusion frames are a convenient tool in applications where we deal with a large amount of data or when a combination of local data is needed. Oblique dual fusion frames are suitable in situations where the analysis for the data and its…
The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency…
In the recent work arXiv:2112.10289 we introduced a geometric decomposition of meanders. In the present paper, we generalize this approach to the case of singular meanders and give a more algebraic description of this decomposition.
Comparison of stellar catalogues with position and proper motion components using a decomposition on a set of orthogonal vector spherical harmonics. We show the theoretical and practical advantages of this technique as a result of…
Deconvolution of the telescope Point Spread Function (PSF) is necessary for even moderate dynamic range imaging with interferometric telescopes. The process of deconvolution can be treated as a search for a model image such that the…
Sparse decomposition has been extensively used for different applications including signal compression and denoising and document analysis. In this paper, sparse decomposition is used for image segmentation. The proposed algorithm separates…
We consider three-dimensional elastic frames constructed out of Euler--Bernoulli beams and describe a simple process of generating joint conditions out of the geometric description of the frame. The corresponding differential operator is…
The core of quantum tomography is the possibility of writing a generally unbounded complex operator in form of an expansion over operators that are generally nonlinear functions of a generally continuous set of spectral densities--the…
A novel approach is presented to recover an image degraded by atmospheric turbulence. Given a sequence of frames affected by turbulence, we construct a variational model to characterize the static image. The optimization problem is solved…
A novel approach is presented in this paper to improve images which are altered by atmospheric turbulence. Two new algorithms are presented based on two combinations of a blind deconvolution block, an elastic registration block and a…
X-ray radiography is the most readily available imaging modality and has a broad range of applications that spans from diagnosis to intra-operative guidance in cardiac, orthopedics, and trauma procedures. Proper interpretation of the hidden…
Unsupervised localization and segmentation are long-standing computer vision challenges that involve decomposing an image into semantically-meaningful segments without any labeled data. These tasks are particularly interesting in an…
Sparse decomposition has been widely used for different applications, such as source separation, image classification and image denoising. This paper presents a new algorithm for segmentation of an image into background and foreground text…
Adaptive Optics is a prime example of how progress in observational astronomy can be driven by technological developments. At many observatories it is now considered to be part of a standard instrumentation suite, enabling ground-based…
The problem of detecting anomalies in time series from network measurements has been widely studied and is a topic of fundamental importance. Many anomaly detection methods are based on packet inspection collected at the network core…
This paper gives a geometric description of functional spaces related to Domain Decomposition techniques for computing solutions of Laplace and Helmholtz equations. Understanding the geometric structure of these spaces leads to algorithms…
Let~$X=\Po/\Gamma$ be an~$n$-punctured sphere, $n>3$. We introduce and study~$n-3$ deformation operators on the space of modular forms~$M_*(\Gamma)$ based on the classical theory of uniformizing differential equations and accessory…
This is the announcement, and the long summary, of a series of articles on the algorithmic study of Thurston maps. We describe branched coverings of the sphere in terms of group-theoretical objects called bisets, and develop a theory of…
Composition is an important feature of a specification language, as it enables the design of a complex system in terms of a product of its parts. Decomposition is equally important in order to reason about structural properties of a system.…