scholarly journals Tight recovery guarantees for orthogonal matching pursuit under Gaussian noise

2020 ◽  
Author(s):  
Chen Amiraz ◽  
Robert Krauthgamer ◽  
Boaz Nadler
Keyword(s):  
Gaussian Noise ◽  
Noise Level ◽  
High Probability ◽  
Matching Pursuit ◽  
Signal To Noise Ratio ◽  
Orthogonal Matching Pursuit ◽  
Sufficient Condition ◽  
Signal To Noise ◽  
Linear Measurements ◽  
Sparse Vector

Abstract Orthogonal matching pursuit (OMP) is a popular algorithm to estimate an unknown sparse vector from multiple linear measurements of it. Assuming exact sparsity and that the measurements are corrupted by additive Gaussian noise, the success of OMP is often formulated as exactly recovering the support of the sparse vector. Several authors derived a sufficient condition for exact support recovery by OMP with high probability depending on the signal-to-noise ratio, defined as the magnitude of the smallest non-zero coefficient of the vector divided by the noise level. We make two contributions. First, we derive a slightly sharper sufficient condition for two variants of OMP, in which either the sparsity level or the noise level is known. Next, we show that this sharper sufficient condition is tight, in the following sense: for a wide range of problem parameters, there exist a dictionary of linear measurements and a sparse vector with a signal-to-noise ratio slightly below that of the sufficient condition, for which with high probability OMP fails to recover its support. Finally, we present simulations that illustrate that our condition is tight for a much broader range of dictionaries.

scholarly journals Wavelet Compressive Sampling Signal Reconstruction Using Upside-Down Tree Structure

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Yijiu Zhao ◽  
Xiaoyan Zhuang ◽  
Zhijian Dai ◽  
Houjun Wang
Keyword(s):  
Matching Pursuit ◽  
Signal To Noise Ratio ◽  
Signal Reconstruction ◽  
Compressive Sampling ◽  
Tree Structure ◽  
Orthogonal Matching Pursuit ◽  
Reconstruction Method ◽  
Wavelet Domain ◽  
Wavelet Coefficients ◽  
Signal To Noise

This paper suggests an upside-down tree-based orthogonal matching pursuit (UDT-OMP) compressive sampling signal reconstruction method in wavelet domain. An upside-down tree for the wavelet coefficients of signal is constructed, and an improved version of orthogonal matching pursuit is presented. The proposed algorithm reconstructs compressive sampling signal by exploiting the upside-down tree structure of the wavelet coefficients of signal besides its sparsity in wavelet basis. Compared with conventional greedy pursuit algorithms: orthogonal matching pursuit (OMP) and tree-based orthogonal matching pursuit (TOMP), signal-to-noise ratio (SNR) using UDT-OMP is significantly improved.

scholarly journals Minimum Array Elements for Resolution of Several Direction of Arrival Estimation Methods in Various Noise-Level Environments

2018 ◽  
Vol 2 ◽  
pp. 87-94
Author(s):  
Ismail El Ouargui ◽  
Said Safi ◽  
Miloud Frikel
Keyword(s):  
Gaussian Noise ◽  
Noise Level ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Direction Of Arrival ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Estimation Methods ◽  
Minimum Number ◽  
Informative Signals

The resolution of a Direction of Arrival (DOA) estimation algorithm is determined based on its capability to resolve two closely spaced signals. In this paper, authors present and discuss the minimum number of array elements needed for the resolution of nearby sources in several DOA estimation methods. In the real world, the informative signals are corrupted by Additive White Gaussian Noise (AWGN). Thus, a higher signal-to-noise ratio (SNR) offers a better resolution. Therefore, we show the performance of each method by applying the algorithms in different noise level environments.

scholarly journals Fringe Phase-Shifting Field Based Fuzzy Quotient Space-Oriented Partial Differential Equations Filtering Method for Gaussian Noise-Induced Phase Error

Sensors ◽  
2019 ◽  
Vol 19 (23) ◽  
pp. 5202 ◽  
Author(s):  
Yu ◽  
Ji ◽  
Xue ◽  
Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Gaussian Noise ◽  
Quotient Space ◽  
Signal To Noise Ratio ◽  
Phase Error ◽  
Phase Shifting ◽  
Signal To Noise ◽  
Partial Differential ◽  
Filtering Method

Traditional filtering methods only focused on improving the peak signal-to-noise ratio of the single fringe pattern, which ignore the filtering effect on phase extraction. Fringe phase-shifting field based fuzzy quotient space-oriented partial differential equations filtering method is proposed to reduce the phase error caused by Gaussian noise while filtering. First, the phase error distribution that is caused by Gaussian noise is analyzed. Furthermore, by introducing the fringe phase-shifting field and the theory of fuzzy quotient space, the modified filtering direction can be adaptively obtained, which transforms the traditional single image filtering into multi-image filtering. Finally, the improved fourth-order oriented partial differential equations with fidelity item filtering method is established. Experiments demonstrated that the proposed method achieves a higher signal-to-noise ratio and lower phase error caused by noise, while also retaining more edge details.

Static Thresholded Pulse Coupled Neural Networks in Contourlet Domain — A New Framework for Medical Image Denoising

2020 ◽  
Vol 20 (03) ◽  
pp. 2050025
Author(s):  
S. Shajun Nisha ◽  
S. P. Raja ◽  
A. Kasthuri
Keyword(s):  
Image Denoising ◽  
Gaussian Noise ◽  
Medical Image ◽  
Signal To Noise Ratio ◽  
Noise Removal ◽  
Signal To Noise ◽  
Coupled Neural Networks ◽  
Noise Ratio ◽  
Pulse Coupled Neural Networks ◽  
Image Quality Index

Image denoising, a significant research area in the field of medical image processing, makes an effort to recover the original image from its noise corrupted image. The Pulse Coupled Neural Networks (PCNN) works well against denoising a noisy image. Generally, image denoising techniques are directly applied on the pixels. From the literature review, it is reported that denoising after frequency domain transformation is performing better since noise removal is applied over the coefficients. Motivated by this, in this paper, a new technique called the Static Thresholded Pulse Coupled Neural Network (ST-PCNN) is proposed by combining PCNN with traditional filtering or threshold shrinkage technique in Contourlet Transform domain. Four different existing PCNN architectures, such as Neuromime Structure, Intersecting Cortical Model, Unit-Linking Model and Multichannel Model are considered for comparative analysis. The filters such as Wiener, Median, Average, Gaussian and threshold shrinkage techniques such as Sure Shrink, HeurShrink, Neigh Shrink, BayesShrink are used. For noise removal, a mixture of Speckle and Gaussian noise is considered for a CT skull image. A mixture of Rician and Gaussian noise is considered for MRI brain image. A mixture of Speckle and Salt and Pepper noise is considered for a Mammogram image. The Performance Metrics such as Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), Image Quality Index (IQI), Universal Image Quality Index (UQI), Image Enhancement Filter (IEF), Structural Content (SC), Correlation Coefficient (CC), and Weighted Signal-to-Noise Ratio (WSNR) and Visual Signal-to-Noise Ratio (VSNR) are used to evaluate the performance of denoising.

Digital Modulation Recognition in Different Environments

2014 ◽  
Vol 1049-1050 ◽  
pp. 2084-2087 ◽  
Author(s):  
Rong Li
Keyword(s):  
Gaussian Noise ◽  
Signal To Noise Ratio ◽  
Automatic Recognition ◽  
Modulation Recognition ◽  
Signal To Noise ◽  
Digital Modulation ◽  
Multipath Interference ◽  
Modulation Signal ◽  
Simulation Results ◽  
Recognition Success

For the using of multi-modulation, the precondition of receiving and demodulating signal is to determine the type of the modulation, so automatic recognition of modulation signal has significant influence on the analysis of the signals. In this paper, digital modulation recognition is studied respectively in different environment of White Gaussian Noise (WGN), stationary interference and multipath interference. The simulation results show that the recognition success rate is the highest in stationary interference environment and the lowest in multipath interference environment with the same signal to noise ratio (SNR).

Problem ot the energy transfer for radio paths near single-hop limiting distance for low solar activity

2020 ◽  
Author(s):  
Barbara Atamaniuk ◽  
Igor V. Krasheninnikov ◽  
Alexei Popov ◽  
Barbara Matyjasiak
Keyword(s):  
Solar Activity ◽  
Frequency Dependence ◽  
Wave Field ◽  
High Probability ◽  
Signal To Noise Ratio ◽  
Qualitative Description ◽  
Field Energy ◽  
Signal To Noise ◽  
Iri Model ◽  
Model Calculations

<pre>Formation the feature, in a form of deep trough, in frequency dependence of the wave field strength for single-hop paths with distances near classical limiting distance 3000 km at low level of solar activity was considered. Model calculations within the framework of the extended global ionospheric IRI model show high probability for appearing such situation in the local daytime with a developed regular E-layer of the ionosphere. Some experimental results in multifrequency radio sounding of the ionosphere with a registration of the deep trough in frequency dependence of signal-to-noise ratio (SNR) were analyzed. It is shown that the IRI model, in principle, makes it possible to reproduce this peculiarity in the wave field energy parameters, but in some cases of experimental data, to a large extent, is able to provide only a qualitative description of this effect. Possible reasons for the quantitative discrepancy between experimental and model results are discussed.</pre>

scholarly journals A Novel Sufficient Condition for Generalized Orthogonal Matching Pursuit

2017 ◽  
Vol 21 (4) ◽  
pp. 805-808 ◽  
Author(s):  
Jinming Wen ◽  
Zhengchun Zhou ◽  
Dongfang Li ◽  
Xiaohu Tang
Keyword(s):  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Sufficient Condition ◽  
Generalized Orthogonal
Sign in / Sign up

Export Citation Format

Share Document