Solutions to the Reconstruction Problem

2019 ◽  
pp. 29-55
Author(s):  
Zoë H. Slade
Keyword(s):  
Reconstruction Problem

scholarly journals Quantum Polar Duality and the Symplectic Camel: A New Geometric Approach to Quantization

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Uncertainty Principle ◽  
Convex Geometry ◽  
Geometric Approach ◽  
Point Of View ◽  
Reconstruction Problem ◽  
Orthogonal Projections ◽  
Topological Version ◽  
Mahler Conjecture ◽  
Quantum Indeterminacy ◽  
Dual Quantum

AbstractWe define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what we call a dual quantum pair. We thereafter show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. The notion of quantum polarity exhibits a strong interplay between the uncertainty principle and symplectic and convex geometry and our approach could therefore pave the way for a geometric and topological version of quantum indeterminacy. We relate our results to the Blaschke–Santaló inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty principle and the less-known Donoho–Stark principle from the point of view of quantum polarity.

scholarly journals On a Reconstruction Problem for Sequences

1997 ◽  
Vol 77 (2) ◽  
pp. 344-348 ◽  
Author(s):  
I. Krasikov ◽  
Y. Roditty
Keyword(s):  
Reconstruction Problem

scholarly journals COMBINATORIAL RECONSTRUCTION OF HALF-SIBLING GROUPS FROM MICROSATELLITE DATA

2010 ◽  
Vol 08 (02) ◽  
pp. 337-356 ◽  
Author(s):  
SAAD I. SHEIKH ◽  
TANYA Y. BERGER-WOLF ◽  
ASHFAQ A. KHOKHAR ◽  
ISABEL C. CABALLERO ◽  
MARY V. ASHLEY ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Experimental Results ◽  
Microsatellite Data ◽  
Reconstruction Problem ◽  
Full Sibling ◽  
Synthetic Datasets ◽  
Sibling Group ◽  
Half Sibling ◽  
Sibling Groups

While full-sibling group reconstruction from microsatellite data is a well-studied problem, reconstruction of half-sibling groups is much less studied, theoretically challenging, and computationally demanding. In this paper, we present a formulation of the half-sibling reconstruction problem and prove its APX-hardness. We also present exact solutions for this formulation and develop heuristics. Using biological and synthetic datasets we present experimental results and compare them with the leading alternative software COLONY. We show that our results are competitive and allow half-sibling group reconstruction in the presence of polygamy, which is prevalent in nature.

Implementation and evaluation of an analytical solution to the photon attenuation and nonstationary resolution reconstruction problem in SPECT

1993 ◽  
Vol 40 (4) ◽  
pp. 1231-1237 ◽  
Author(s):  
Edward J. Soares ◽  
Charles L. Byrne ◽  
Stephen J. Glick ◽  
C. Robert Appledorn ◽  
Michael A. King
Keyword(s):  
Analytical Solution ◽  
Reconstruction Problem ◽  
Photon Attenuation

scholarly journals Compressed Sensing-Based DOA Estimation with Unknown Mutual Coupling Effect

Electronics ◽  
2018 ◽  
Vol 7 (12) ◽  
pp. 424 ◽  
Author(s):  
Peng Chen ◽  
Zhenxin Cao ◽  
Zhimin Chen ◽  
Linxi Liu ◽  
Man Feng
Keyword(s):  
Compressed Sensing ◽  
Mutual Coupling ◽  
Linear Array ◽  
State Of The Art ◽  
Coupling Effect ◽  
Estimation Method ◽  
Doa Estimation ◽  
System Model ◽  
Reconstruction Problem ◽  
Uniform Linear Array

The performance of a direction-finding system is significantly degraded by the imperfection of an array. In this paper, the direction-of-arrival (DOA) estimation problem is investigated in the uniform linear array (ULA) system with the unknown mutual coupling (MC) effect. The system model with MC effect is formulated. Then, by exploiting the signal sparsity in the spatial domain, a compressed-sensing (CS)-based system model is proposed with the MC coefficients, and the problem of DOA estimation is converted into that of a sparse reconstruction. To solve the reconstruction problem efficiently, a novel DOA estimation method, named sparse-based DOA estimation with unknown MC effect (SDMC), is proposed, where both the sparse signal and the MC coefficients are estimated iteratively. Simulation results show that the proposed method can achieve better performance of DOA estimation in the scenario with MC effect than the state-of-the-art methods, and improve the DOA estimation performance about 31.64 % by reducing the MC effect by about 4 dB.

scholarly journals Shearlet-based regularized reconstruction in region-of-interest computed tomography

2018 ◽  
Vol 13 (4) ◽  
pp. 34
Author(s):  
T.A. Bubba ◽  
D. Labate ◽  
G. Zanghirati ◽  
S. Bonettini
Keyword(s):  
Optimization Problem ◽  
Ad Hoc ◽  
Iterative Scheme ◽  
Tomographic Reconstruction ◽  
Region Of Interest ◽  
Projection Data ◽  
Reconstruction Problem ◽  
Convex Optimization Problem ◽  
Scanning Time ◽  
Novel Approach

Region of interest (ROI) tomography has gained increasing attention in recent years due to its potential to reducing radiation exposure and shortening the scanning time. However, tomographic reconstruction from ROI-focused illumination involves truncated projection data and typically results in higher numerical instability even when the reconstruction problem has unique solution. To address this problem, bothad hocanalytic formulas and iterative numerical schemes have been proposed in the literature. In this paper, we introduce a novel approach for ROI tomographic reconstruction, formulated as a convex optimization problem with a regularized term based on shearlets. Our numerical implementation consists of an iterative scheme based on the scaled gradient projection method and it is tested in the context of fan-beam CT. Our results show that our approach is essentially insensitive to the location of the ROI and remains very stable also when the ROI size is rather small.

scholarly journals X-rays Image reconstruction using Proximal Algorithm and adapted TV Regularization

2021 ◽  
Vol 348 ◽  
pp. 01011
Author(s):  
Aicha Allag ◽  
Redouane Drai ◽  
Tarek Boutkedjirt ◽  
Abdessalam Benammar ◽  
Wahiba Djerir
Keyword(s):  
Structural Information ◽  
X Rays ◽  
Reconstruction Algorithms ◽  
Reconstruction Problem ◽  
Tv Regularization ◽  
Object Based ◽  
Suggested Technique ◽  
Reconstruction Image ◽  
Ill Posed

Computed tomography (CT) aims to reconstruct an internal distribution of an object based on projection measurements. In the case of a limited number of projections, the reconstruction problem becomes significantly ill-posed. Practically, reconstruction algorithms play a crucial role in overcoming this problem. In the case of missing or incomplete data, and in order to improve the quality of the reconstruction image, the choice of a sparse regularisation by adding l1 norm is needed. The reconstruction problem is then based on using proximal operators. We are interested in the Douglas-Rachford method and employ total variation (TV) regularization. An efficient technique based on these concepts is proposed in this study. The primary goal is to achieve high-quality reconstructed images in terms of PSNR parameter and relative error. The numerical simulation results demonstrate that the suggested technique minimizes noise and artifacts while preserving structural information. The results are encouraging and indicate the effectiveness of the proposed strategy.

scholarly journals Neighborhood Reconstruction and Cancellation of Graphs

10.37236/6676 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Richard H. Hammack ◽  
Cristina Mullican
Keyword(s):  
Direct Product ◽  
Structural Characterization ◽  
Unsolved Problem ◽  
Reconstruction Problem ◽  
Cancellation Problem ◽  
Open Vertex ◽  
Isomorphic Graphs ◽  
Product Of Graphs

We connect two seemingly unrelated problems in graph theory.Any graph $G$ has a neighborhood multiset $\mathscr{N}(G)= \{N(x) \mid x\in V(G)\}$ whose elements are precisely the open vertex-neighborhoods of $G$. In general there exist non-isomorphic graphs $G$ and $H$ for which $\mathscr{N}(G)=\mathscr{N}(H)$. The neighborhood reconstruction problem asks the conditions under which $G$ is uniquely reconstructible from its neighborhood multiset, that is, the conditions under which $\mathscr{N}(G)=\mathscr{N}(H)$ implies $G\cong H$. Such a graph is said to be neighborhood-reconstructible.The cancellation problem for the direct product of graphs seeks the conditions under which $G\times K\cong H\times K$ implies $G\cong H$. Lovász proved that this is indeed the case if $K$ is not bipartite. A second instance of the cancellation problem asks for conditions on $G$ that assure $G\times K\cong H\times K$ implies $G\cong H$ for any bipartite~$K$ with $E(K)\neq \emptyset$. A graph $G$ for which this is true is called a cancellation graph.We prove that the neighborhood-reconstructible graphs are precisely the cancellation graphs. We also present some new results on cancellation graphs, which have corresponding implications for neighborhood reconstruction. We are particularly interested in the (yet-unsolved) problem of finding a simple structural characterization of cancellation graphs (equivalently, neighborhood-reconstructible graphs).

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