Related papers: Duality in reconstruction systems
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…
Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…
We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension.…
The state-of-the-art in discriminative unsupervised surface anomaly detection relies on external datasets for synthesizing anomaly-augmented training images. Such approaches are prone to failure on near-in-distribution anomalies since these…
We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a…
In this paper we characterize sums of CR functions from competing CR structures in two scenarios. In one scenario the structures are conjugate and we are adding to the theory of pluriharmonic boundary values. In the second scenario the…
Physically accurate and mathematically tractable models are presented to characterize scattering and reflection properties of reconfigurable intelligent surfaces (RISs). We take continuous and discrete strategies to model a single patch and…
Dimensionality reduction (DR) is characterized by two longstanding trade-offs. First, there is a global-local preservation tension: methods such as t-SNE and UMAP prioritize local neighborhood preservation, yet may distort global manifold…
We consider estimating a random vector from its noisy projections onto low dimensional subspaces constituting a fusion frame. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is…
The property of quantum many-body systems under spatial reflection and the relevant physics of renormalization group (RG) procedure are revealed. By virtue of the matrix product state (MPS) representation, various attributes for…
In this paper we provide explicit dual Ramsey statements for several classes of finite relational structures (such as finite linearly ordered graphs, finite linearly ordered metric spaces and finite posets with a linear extension) and…
Despite its wide use in medicine, ultrasound imaging faces several challenges related to its poor signal-to-noise ratio and several sources of noise and artefacts. Enhancing ultrasound image quality involves balancing concurrent factors…
We present a mathematical model: dynamical systems over finite sets (DSF), and we show that Boolean and discrete genetic models are special cases of DFS. In this paper, we prove that a function defined over finite sets with different number…
In computer vision and image processing tasks, image fusion has evolved into an attractive research field. However, recent existing image fusion methods are mostly built on pixel-level operations, which may produce unacceptable artifacts…
This paper studies properties of dual probabilistic frames -- in particular in relation to redundancy -- and introduces both approximately dual probabilistic frames and pseudo-dual probabilistic frames. We show that the canonical dual…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
We present 3D Surface Splatting (3DSS), the first differentiable surface splatting renderer for physically-based inverse rendering from multi-view images. Our central insight is that the surface separation problem at the heart of surface…
Finding the optimal dual frame and optimal dual pair for signal reconstruction, which can minimize the reconstruction error when erasure occurs during data transmission, is a deep rooted problem from the perspective of frame theory. In this…
Remote sensing (RS) images are important to monitor and survey earth at varying spatial scales. Continuous observations from various RS sources complement single observations to improve applications. Fusion into single or multiple images…
Collimated beam ultrasound systems are a novel technology for imaging inside multi-layered structures such as geothermal wells. Such systems include a transmitter and multiple receivers to capture reflected signals. Common algorithms for…