scholarly journals Deep learning for a space-variant deconvolution in galaxy surveys

2020 ◽  
Vol 641 ◽  
pp. A67
Author(s):  
F. Sureau ◽  
A. Lechat ◽  
J.-L. Starck
Keyword(s):  
Deep Learning ◽  
Network Architecture ◽  
Signal To Noise Ratio ◽  
Closed Form Solution ◽  
Computation Time ◽  
Form Solution ◽  
High Signal ◽  
Galaxy Surveys ◽  
Point Spread ◽  
Space Variant

The deconvolution of large survey images with millions of galaxies requires developing a new generation of methods that can take a space-variant point spread function into account. These methods have also to be accurate and fast. We investigate how deep learning might be used to perform this task. We employed a U-net deep neural network architecture to learn parameters that were adapted for galaxy image processing in a supervised setting and studied two deconvolution strategies. The first approach is a post-processing of a mere Tikhonov deconvolution with closed-form solution, and the second approach is an iterative deconvolution framework based on the alternating direction method of multipliers (ADMM). Our numerical results based on GREAT3 simulations with realistic galaxy images and point spread functions show that our two approaches outperform standard techniques that are based on convex optimization, whether assessed in galaxy image reconstruction or shape recovery. The approach based on a Tikhonov deconvolution leads to the most accurate results, except for ellipticity errors at high signal-to-noise ratio. The ADMM approach performs slightly better in this case. Considering that the Tikhonov approach is also more computation-time efficient in processing a large number of galaxies, we recommend this approach in this scenario.

scholarly journals Approximation of continuous random variables for the evaluation of the reliability parameter of complex stress–strength models

2021 ◽  
Author(s):  
Alessandro Barbiero ◽  
Asmerilda Hitaj
Keyword(s):  
Order Approximation ◽  
Linear Optimization ◽  
Closed Form Solution ◽  
Random Variables ◽  
Discrete Distribution ◽  
Computation Time ◽  
Form Solution ◽  
Engineering Problem ◽  
Approximation Technique ◽  
Reliability Parameter

AbstractIn many management science or economic applications, it is common to represent the key uncertain inputs as continuous random variables. However, when analytic techniques fail to provide a closed-form solution to a problem or when one needs to reduce the computational load, it is often necessary to resort to some problem-specific approximation technique or approximate each given continuous probability distribution by a discrete distribution. Many discretization methods have been proposed so far; in this work, we revise the most popular techniques, highlighting their strengths and weaknesses, and empirically investigate their performance through a comparative study applied to a well-known engineering problem, formulated as a stress–strength model, with the aim of weighting up their feasibility and accuracy in recovering the value of the reliability parameter, also with reference to the number of discrete points. The results overall reward a recently introduced method as the best performer, which derives the discrete approximation as the numerical solution of a constrained non-linear optimization, preserving the first two moments of the original distribution. This method provides more accurate results than an ad-hoc first-order approximation technique. However, it is the most computationally demanding as well and the computation time can get even larger than that required by Monte Carlo approximation if the number of discrete points exceeds a certain threshold.

EEG SOURCE LOCALIZATION: A COMPARATIVE STUDY OF CLASSICAL AND NEURAL NETWORK METHODS

2001 ◽  
Vol 11 (04) ◽  
pp. 349-359 ◽  
Author(s):  
UDANTHA R. ABEYRATNE ◽  
G. ZHANG ◽  
P. SARATCHANDRAN
Keyword(s):  
Neural Network ◽  
Inverse Problem ◽  
Signal To Noise Ratio ◽  
Closed Form Solution ◽  
Form Solution ◽  
Hybrid Technique ◽  
Eeg Signals ◽  
Rbf Network ◽  
Network Methods ◽  
Lm Algorithm

We address the problem of estimating biopotential sources within the brain, based on EEG signals observed on the scalp. This problem, known as the inverse problem of electrophysiology, has no closed-form solution, and requires iterative techniques such as the Levenberg – Marquardt (LM) algorithm. Considering the nonlinear nature of the inverse problem, and the low signal to noise ratio inherent in EEG signals, a backpropagation neural network (BPN) has been recently proposed as a solution. The technique has not been properly compared with classical techniques such as the LM method, or with more recent neural network techniques such as the Radial Basis Function (RBF) network. In this paper, we provide improved strategies based on BPN and consider RBF networks in solving the inverse problem. We compare the performances of BPN, RBF and a hybrid technique with that of the classical LM method.

scholarly journals Compressive Detection Using Sub-Nyquist Radars for Sparse Signals

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Ying Sun ◽  
Jianjun Huang ◽  
Jingxiong Huang ◽  
Li Kang ◽  
Li Lei ◽  
...  
Keyword(s):  
Signal To Noise Ratio ◽  
Computation Time ◽  
Detection Performance ◽  
High Signal ◽  
Sparse Signals ◽  
Ratio Test ◽  
Digital Conversion ◽  
Real Time Processing ◽  
Analog To Digital ◽  
Analog To Digital Conversion

This paper investigates the compression detection problem using sub-Nyquist radars, which is well suited to the scenario of high bandwidths in real-time processing because it would significantly reduce the computational burden and save power consumption and computation time. A compressive generalized likelihood ratio test (GLRT) detector for sparse signals is proposed for sub-Nyquist radars without ever reconstructing the signal involved. The performance of the compressive GLRT detector is analyzed and the theoretical bounds are presented. The compressive GLRT detection performance of sub-Nyquist radars is also compared to the traditional GLRT detection performance of conventional radars, which employ traditional analog-to-digital conversion (ADC) at Nyquist sampling rates. Simulation results demonstrate that the former can perform almost as well as the latter with a very small fraction of the number of measurements required by traditional detection in relatively high signal-to-noise ratio (SNR) cases.

Fast laser scan matching approach based on adaptive curvature estimation for mobile robots

Robotica ◽  
2009 ◽  
Vol 27 (3) ◽  
pp. 469-479 ◽  
Author(s):  
P. Núñez ◽  
R. Vázquez-Martín ◽  
A. Bandera ◽  
F. Sandoval
Keyword(s):  
Dynamic Environment ◽  
Closed Form Solution ◽  
Computation Time ◽  
Form Solution ◽  
Local Alignment ◽  
Curvature Function ◽  
Scan Matching ◽  
Characteristic Points ◽  
Curvature Estimation ◽  
Three Stages

SUMMARYThis paper describes a complete laser-based approach for tracking the pose of a robot in a dynamic environment. The main novelty of this approach is that the matching between consecutively acquired scans is achieved using their associated curvature-based representations. The proposed scan matching algorithm consists of three stages. Firstly, the whole raw laser data is segmented into groups of consecutive range readings using a distance-based criterion and the curvature function for each group is computed. Then, this set of curvature functions is matched to the set of curvature functions associated to the previously acquired laser scan. Finally, characteristic points of pairwise curvature functions are matched and used to correctly obtain the best local alignment between consecutive scans. A closed form solution is employed for computing the optimal transformation and minimizing the robot pose shift error without iterations. Thus, the system is outstanding in terms of accuracy and computation time. The implemented algorithm is evaluated and compared to three state of the art scan matching approaches.

scholarly journals High signal-to-noise ratio reconstruction of low bit-depth optical coherence tomography using deep learning

2020 ◽  
Vol 25 (12) ◽  
Author(s):  
Qiangjiang Hao ◽  
Kang Zhou ◽  
Jianlong Yang ◽  
Yan Hu ◽  
Zhengjie Chai ◽  
...  
Keyword(s):  
Optical Coherence Tomography ◽  
Deep Learning ◽  
Signal To Noise Ratio ◽  
High Signal ◽  
Optical Coherence ◽  
Signal To Noise ◽  
Noise Ratio

scholarly journals Network Enhancement: a general method to denoise weighted biological networks

2018 ◽  
Author(s):  
Bo Wang ◽  
Armin Pourshafeie ◽  
Marinka Zitnik ◽  
Junjie Zhu ◽  
Carlos D. Bustamante ◽  
...  
Keyword(s):  
Biological Networks ◽  
Signal To Noise Ratio ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fine Grained ◽  
Contact Maps ◽  
Novel Method ◽  
Alternative Approaches ◽  
Downstream Analysis ◽  
General Method

Networks are ubiquitous in biology where they encode connectivity patterns at all scales of organization, from molecular to the biome. However, biological networks are noisy due to the limitations of technology used to generate them as well as inherent variation within samples. The presence of high levels of noise can hamper discovery of patterns and dynamics encapsulated by these networks. Here we propose Network Enhancement (NE), a novel method for improving the signal-to-noise ratio of undirected, weighted networks, and thereby improving the performance of downstream analysis. NE applies a novel operator that induces sparsity and leverages higher-order network structures to remove weak edges and enhance real connections. This iterative approach has a closed-form solution at convergence with desirable performance properties. We demonstrate the effectiveness of NE in denoising biological networks for several challenging yet important problems. Our experiments show that NE improves gene function prediction by denoising interaction networks from 22 human tissues. Further, we use NE to interpret noisy Hi-C contact maps from the human genome and demonstrate its utility across varying degrees of data quality. Finally, when applied to fine-grained species identification, NE outperforms alternative approaches by a significant margin. Taken together, our results indicate that NE is widely applicable for denoising weighted biological networks, especially when they contain high levels of noise.

scholarly journals Accurate Photometry of Saturated Stars Using the Point-spread-function Wing Technique with Spitzer

2022 ◽  
Vol 163 (2) ◽  
pp. 46
Author(s):  
Kate Y. L. Su ◽  
G. H. Rieke ◽  
M. Marengo ◽  
Everett Schlawin
Keyword(s):  
Point Spread Function ◽  
Signal To Noise Ratio ◽  
High Signal ◽  
Large Radius ◽  
Point Spread ◽  
Primary Sample ◽  
Spread Function ◽  
Optical Stability ◽  
Flux Calibration ◽  
Better Than

Abstract We report Spitzer 3.6 and 4.5 μm photometry of 11 bright stars relative to Sirius, exploiting the unique optical stability of the Spitzer Space Telescope point-spread function (PSF). Spitzer's extremely stable beryllium optics in its isothermal environment enables precise comparisons in the wings of the PSF from heavily saturated stars. These bright stars stand as the primary sample to improve stellar models, and to transfer the absolute flux calibration of bright standard stars to a sample of fainter standards useful for missions like JWST and for large ground-based telescopes. We demonstrate that better than 1% relative photometry can be achieved using the PSF wing technique in the radial range of 20″–100″ for stars that are fainter than Sirius by 8 mag (from outside the saturated core to a large radius where a high signal-to-noise ratio profile can still be obtained). We test our results by (1) comparing the [3.6]−[4.5] color with that expected between the WISE W1 and W2 bands, (2) comparing with stars where there is accurate K S photometry, and (3) also comparing with relative fluxes obtained with the DIRBE instrument on COBE. These tests confirm that relative photometry is achieved to better than 1%.

scholarly journals An Adiabatic Approximation to the Tissue Homogeneity Model for Water Exchange in the Brain: I. Theoretical Derivation

1998 ◽  
Vol 18 (12) ◽  
pp. 1365-1377 ◽  
Author(s):  
Keith S. St. Lawrence ◽  
Ting-Yim Lee
Keyword(s):  
Adiabatic Approximation ◽  
Signal To Noise Ratio ◽  
Closed Form Solution ◽  
Form Solution ◽  
Model Parameters ◽  
Theoretical Derivation ◽  
Extraction Fraction ◽  
Tissue Changes ◽  
Clearance Rate Constant ◽  
The Brain

Using the adiabatic approximation, which assumes that the tracer concentration in parenchymal tissue changes slowly relative to that in capillaries, we derived a time-domain, closed-form solution of the tissue homogeneity model. This solution, which is called the adiabatic solution, is similar in form to those of two-compartment models, Owing to its simplicity, the adiabatic solution can be used in CBF experiments in which kinetic data with only limited time resolution or signal-to-noise ratio, or both, are obtained. Using computer simulations, we investigated the accuracy and the precision of the parameters in the adiabatic solution for values that reflect 2H-labeled water (D2O) clearance from the brain (see Part II). It was determined that of the three model parameters, (1) the vascular volume ( Vi), (2) the product of extraction fraction and blood flow ( EF), and (3) the clearance rate constant ( kadb), only the last one could be determined accurately, and therefore CBF must be determined from this parameter only. From the error analysis of the adiabatic solution, it was concluded that for the D2O clearance experiments described in Part II, the coefficient of variation of CBF was approximately 7% in gray matter and 22% in white matter.

scholarly journals Energy harvesting and information transmission scheme with UAV relay cooperation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Baofeng Ji ◽  
Zhenzhen Chen ◽  
Yuqi Li ◽  
Sudan Chen ◽  
Guoqiang Zheng ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Information Transmission ◽  
Splitting Method ◽  
Closed Form Solution ◽  
Form Solution ◽  
Lambert W Function ◽  
High Signal ◽  
Power Splitting ◽  
Transmission Scheme ◽  
Architecture Model

AbstractThis paper proposed a system architecture model of two-hop unmanned aerial vehicle (UAV) relay wireless communication and designed an energy harvesting and information transmission algorithm based on the energy harvested by UAV relay node. The energy of nodes except source node can be obtained by energy harvesting and all the UAV relay nodes transmitted signals via power splitting. Under the advance of non-static channel, the information user nodes were configured with multiple antennas and adopted max ratio combination (MRC). Based on the optimization criterion of energy efficiency maximization, the analytical solution of the optimal power allocation scheme for energy harvested and information transmission of multi-user two-UAV relay system was derived in detail. Since the optimization problem was a non-convex problem, this paper adopted the high signal-to-noise ratio approximation method and the power splitting method to realize the closed-form solution expression. The optimal solution of the objective function subjected with constraints can be obtained by Lagrangian algorithm and Lambert W function. Finally, the proposed algorithms and theoretical analysis are verified by simulations.

scholarly journals Optimal Power Constrained Distributed Detection over a Noisy Multiaccess Channel

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Zhiwen Hu ◽  
Zhenhua Xu
Keyword(s):  
Signal To Noise Ratio ◽  
Closed Form Solution ◽  
Form Solution ◽  
Detection Performance ◽  
Distributed Detection ◽  
New Method ◽  
Fusion System ◽  
Robust Detection ◽  
Optimal Power ◽  
Multiaccess Channel

The problem of optimal power constrained distributed detection over a noisy multiaccess channel (MAC) is addressed. Under local power constraints, we define the transformation function for sensor to realize the mapping from local decision to transmitted waveform. The deflection coefficient maximization (DCM) is used to optimize the performance of power constrained fusion system. Using optimality conditions, we derive the closed-form solution to the considered problem. Monte Carlo simulations are carried out to evaluate the performance of the proposed new method. Simulation results show that the proposed method could significantly improve the detection performance of the fusion system with low signal-to-noise ratio (SNR). We also show that the proposed new method has a robust detection performance for broad SNR region.

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