Related papers: Duality in reconstruction systems
Advances in image super-resolution (SR) have recently benefited significantly from rapid developments in deep neural networks. Inspired by these recent discoveries, we note that many state-of-the-art deep SR architectures can be…
This paper considers different facets of the interplay between reproducing kernel Hilbert spaces (RKHS) and stable analysis/synthesis processes: First, we analyze the structure of the reproducing kernel of a RKHS using frames and…
We define the notion of "projective" multiresolution analyses, for which, by definition, the initial space corresponds to a finitely generated projective module over the algebra $C(\btn)$ of continuous complex-valued functions on an…
In this paper, we study design of deep neural networks for tasks of image restoration. We propose a novel style of residual connections dubbed "dual residual connection", which exploits the potential of paired operations, e.g., up- and…
We provide a pedagogical introduction to some aspects of integrability, dualities and deformations of physical systems in 0+1 and in 1+1 dimensions. In particular, we concentrate on the T-duality of point particles and strings as well as on…
We give a summary on spectral techniques for finite dimensional algebras and study its link to singularity theory. In particular, we offer a contribution to the categorification of the Milnor lattice of two-dimensional singularities through…
This paper extends the concepts of Minimal Redundancy Condition (MRC) and robustness of erasures for infinite frames in Hilbert spaces. We begin by establishing a comprehensive framework for the MRC, emphasizing its importance in ensuring…
By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with…
Given a channel with additive noise and adversarial erasures, the task is to design a frame that allows for stable signal reconstruction from transmitted frame coefficients. To meet these specifications, we introduce numerically…
Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may…
Recent works in image inpainting have shown that structural information plays an important role in recovering visually pleasing results. In this paper, we propose an end-to-end architecture composed of two parallel UNet-based streams: a…
The notion of geometrical duality is discussed in the context of both Brans-Dicke theory and general relativity. It is shown that, in some particular solutions, the spacetime singularities that arise in usual Riemannian general relativity…
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…
We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals, considered as elements in a Hilbert space…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
We simulate the performance of a gravitational wave interferometer in the Dual Recycling (DR) configuration, as will be used for systems like Advanced-LIGO. Our grid-based simulation program models complex interferometric detectors with…
Forward modeling of wave scattering and radar imaging mechanisms is the key to information extraction from synthetic aperture radar (SAR) images. Like inverse graphics in optical domain, an inherently-integrated forward-inverse approach…
Various theoretical and algorithmic aspects of inverse problems in discrete tomography of planar Penrose model sets are discussed. These are motivated by the demand of materials science for the reconstruction of quasicrystalline structures…
We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system having some property at all resolutions coarser than a given…
In this paper, we present a general framework to construct recurrent fractal interpolation surfaces (RFISs) on rectangular grids. Then we introduce bilinear RFISs, which are easy to be generated while there are no restrictions on…