Optimization of Greedy Pursuit Algorithms Based on Probability Analysis

2013 ◽  
Vol 433-435 ◽  
pp. 621-625
Author(s):  
Yi Zheng ◽  
Ti Jian Cai
Keyword(s):  
Compressed Sensing ◽  
Conditional Probability ◽  
Signal Reconstruction ◽  
Probability Analysis ◽  
Improved Method

Through analyzing prior conditional probability of signal reconstruction in compressed sensing, the paper puts forward an improved method toward serials greedy pursuit algorithms. This method can achieve more accurate selection when select columns in perception matrix that is the most correlated with the residual. Meanwhile, this paper reviews most of greedy pursuit algorithms, and simulations validate the efficacy of the proposed method.

An Algorithm Combining Analysis-based Blind Compressed Sensing and Nonlocal Low-rank Constraints for MRI Reconstruction

2019 ◽  
Vol 15 (3) ◽  
pp. 281-291 ◽  
Author(s):  
Mei Sun ◽  
Jinxu Tao ◽  
Zhongfu Ye ◽  
Bensheng Qiu ◽  
Jinzhang Xu ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Signal Reconstruction ◽  
Low Rank ◽  
Mr Images ◽  
Scanning Time ◽  
Previous State ◽  
Rank Approximation ◽  
Mri Reconstruction ◽  
Magnetic Resonance Imaging Mri ◽  
Rank Constraints

Background: In order to overcome the limitation of long scanning time, compressive sensing (CS) technology exploits the sparsity of image in some transform domain to reduce the amount of acquired data. Therefore, CS has been widely used in magnetic resonance imaging (MRI) reconstruction. </P><P> Discussion: Blind compressed sensing enables to recover the image successfully from highly under- sampled measurements, because of the data-driven adaption of the unknown transform basis priori. Moreover, analysis-based blind compressed sensing often leads to more efficient signal reconstruction with less time than synthesis-based blind compressed sensing. Recently, some experiments have shown that nonlocal low-rank property has the ability to preserve the details of the image for MRI reconstruction. Methods: Here, we focus on analysis-based blind compressed sensing, and combine it with additional nonlocal low-rank constraint to achieve better MR images from fewer measurements. Instead of nuclear norm, we exploit non-convex Schatten p-functionals for the rank approximation. </P><P> Results & Conclusion: Simulation results indicate that the proposed approach performs better than the previous state-of-the-art algorithms.

Quantifying electron transit in donor-bridge-acceptor systems using probabilistic confidence

2018 ◽  
Vol 17 (07) ◽  
pp. 1850046 ◽  
Author(s):  
Evan Curtin ◽  
Gloria Bazargan ◽  
Karl Sohlberg
Keyword(s):  
Charge Transport ◽  
Conditional Probability ◽  
Probabilistic Approach ◽  
Probability Analysis ◽  
Time Dependent ◽  
Quantum Particles ◽  
Transit Times ◽  
Conditional Probability Analysis ◽  
Insight Into ◽  
Dependent Probability

A probabilistic approach to characterizing transit times for quantum particles is generalized to a system of more than two spatial regions and applied to the transport of charge in donor-bridge-acceptor systems. The approach is based on applying conditional probability analysis to a discrete representation of the time-dependent probability density as generated by numerical solution of the time-dependent Schrödinger equation for an initially localized electron. To carry out this analysis, it is first necessary to cast the conditional probability analysis approach in matrix form. The results afford a quantification of the electron transit time and may provide a tool to gain insight into the mechanism of charge transport.

scholarly journals Gradient Projection with Approximate L0 Norm Minimization for Sparse Reconstruction in Compressed Sensing

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3373 ◽  
Author(s):  
Ziran Wei ◽  
Jianlin Zhang ◽  
Zhiyong Xu ◽  
Yongmei Huang ◽  
Yong Liu ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Objective Function ◽  
Signal Reconstruction ◽  
Reconstruction Error ◽  
Sparse Signal ◽  
Reconstruction Accuracy ◽  
L1 Norm ◽  
Function Model ◽  
L2 Norm

In the reconstruction of sparse signals in compressed sensing, the reconstruction algorithm is required to reconstruct the sparsest form of signal. In order to minimize the objective function, minimal norm algorithm and greedy pursuit algorithm are most commonly used. The minimum L1 norm algorithm has very high reconstruction accuracy, but this convex optimization algorithm cannot get the sparsest signal like the minimum L0 norm algorithm. However, because the L0 norm method is a non-convex problem, it is difficult to get the global optimal solution and the amount of calculation required is huge. In this paper, a new algorithm is proposed to approximate the smooth L0 norm from the approximate L2 norm. First we set up an approximation function model of the sparse term, then the minimum value of the objective function is solved by the gradient projection, and the weight of the function model of the sparse term in the objective function is adjusted adaptively by the reconstruction error value to reconstruct the sparse signal more accurately. Compared with the pseudo inverse of L2 norm and the L1 norm algorithm, this new algorithm has a lower reconstruction error in one-dimensional sparse signal reconstruction. In simulation experiments of two-dimensional image signal reconstruction, the new algorithm has shorter image reconstruction time and higher image reconstruction accuracy compared with the usually used greedy algorithm and the minimum norm algorithm.

Distributed Compressed Sensing Based Channel Parameter Estimation for MIMO-FBMC Communications

2021 ◽  
Author(s):  
Han Wang ◽  
Xianpeng Wang
Keyword(s):  
Channel Estimation ◽  
Compressed Sensing ◽  
Signal Reconstruction ◽  
Estimation Method ◽  
Sparse Signal ◽  
Weak Selection ◽  
Sparse Signal Reconstruction ◽  
Distributed Compressed Sensing ◽  
Time Frequency ◽  
Selection Threshold

Abstract For the sparse correlation between channels in multiple input multiple output filter bank multicarrier with offset quadrature amplitude modulation (MIMO-FBMC/OQAM) systems, the distributed compressed sensing (DCS)-based channel estimation approach is studied. A sparse adaptive distributed sparse channel estimation method based on weak selection threshold is proposed. Firstly, the correlation between MIMO channels is utilized to represent a joint sparse model, and channel estimation is transformed into a joint sparse signal reconstruction problem. Then, the number of correlation atoms for inner product operation is optimized by weak selection threshold, and sparse signal reconstruction is realized by sparse adaptation. The experiment results show that proposed DCS-based method not only estimates the multipath channel components accurately but also achieves higher channel estimation performance than classical orthogonal matching pursuit (OMP) method and other traditional DCS methods in the time-frequency dual selective channels.

Compressed Sensing and Its Application in CT and EEG

2017 ◽  
pp. 1126-1149
Author(s):  
Sajib Saha ◽  
Murat Tahtali
Keyword(s):  
Compressed Sensing ◽  
Applied Mathematics ◽  
Signal Reconstruction ◽  
Optimization Technique ◽  
Linear Measurements ◽  
Reconstruction Procedure ◽  
Sparsity Constraints ◽  
Ill Posed ◽  
X Ray Computed ◽  
A New Technique

Compressed sensing, also known as compressive sampling is a new technique being rapidly developed over the last few years. The theory states that when some prior information about the signal is available and appropriately incorporated into the signal reconstruction procedure, a signal can be accurately reconstructed even if the Shannon/ Nyquest sampling requirement is violated. The key idea of compressed sensing is to recover a sparse signal from very few non-adaptive, linear measurements by optimization technique. Following the discovery by Donoho in (2006), that sparsity could enable exact solution of ill-posed problems under certain conditions, there has been a tremendous growth on efficient application of sparsity constraints for solving ill-posed problems. The theoretical foundation of compressed sensing has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. In this chapter we will detail the application of compressed sensing in X-ray computed tomography (CT) and Electroencephalography. Starting from the very basic principles we will provide theoretical justifications on why and how sparsity prior is used in CT and in EEG.

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