scholarly journals Compressed Sensing of Multichannel EEG Signals: The Simultaneous Cosparsity and Low-Rank Optimization

2015 ◽  
Vol 62 (8) ◽  
pp. 2055-2061 ◽  
Author(s):  
Yipeng Liu ◽  
Maarten De Vos ◽  
Sabine Van Huffel
Keyword(s):  
Compressed Sensing ◽  
Low Rank ◽  
Eeg Signals ◽  
Multichannel Eeg

scholarly journals Compressive Sensing of Multichannel EEG Signals via lq Norm and Schatten-p Norm Regularization

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Jun Zhu ◽  
Changwei Chen ◽  
Shoubao Su ◽  
Zinan Chang
Keyword(s):  
Compressive Sensing ◽  
Optimization Model ◽  
State Of The Art ◽  
Rank Function ◽  
Nuclear Norm ◽  
Low Rank ◽  
Eeg Signals ◽  
Regularization Problem ◽  
Surrogate Function ◽  
Multichannel Eeg

In Wireless Body Area Networks (WBAN) the energy consumption is dominated by sensing and communication. Recently, a simultaneous cosparsity and low-rank (SCLR) optimization model has shown the state-of-the-art performance in compressive sensing (CS) recovery of multichannel EEG signals. How to solve the resulting regularization problem, involving l0 norm and rank function which is known as an NP-hard problem, is critical to the recovery results. SCLR takes use of l1 norm and nuclear norm as a convex surrogate function for l0 norm and rank function. However, l1 norm and nuclear norm cannot well approximate the l0 norm and rank because there exist irreparable gaps between them. In this paper, an optimization model with lq norm and schatten-p norm is proposed to enforce cosparsity and low-rank property in the reconstructed multichannel EEG signals. An efficient iterative scheme is used to solve the resulting nonconvex optimization problem. Experimental results have demonstrated that the proposed algorithm can significantly outperform existing state-of-the-art CS methods for compressive sensing of multichannel EEG channels.

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.

scholarly journals Quantization for low-rank matrix recovery

2018 ◽  
Vol 8 (1) ◽  
pp. 161-180
Author(s):  
Eric Lybrand ◽  
Rayan Saab
Keyword(s):  
Compressed Sensing ◽  
Reconstruction Error ◽  
Linear Operators ◽  
Low Rank ◽  
Quantization Scheme ◽  
Reconstruction Algorithms ◽  
Finite Frame ◽  
Rank Matrix ◽  
Band Limited ◽  
Low Rank Matrix

Abstract We study Sigma–Delta $(\varSigma\!\varDelta) $ quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the oversampling factor, and we leverage our results to obtain root-exponential accuracy by optimizing over the choice of quantization scheme. Additionally, we show that a random encoding scheme, applied to the quantized measurements, yields a near-optimal exponential bit rate. As an added benefit, our schemes are robust both to noise and to deviations from the low-rank assumption. In short, we provide a full generalization of analogous results, obtained in the classical setup of band-limited function acquisition, and more recently, in the finite frame and compressed sensing setups to the case of low-rank matrices sampled with sub-Gaussian linear operators. Finally, we believe our techniques for generalizing results from the compressed sensing setup to the analogous low-rank matrix setup is applicable to other quantization schemes.

Robust Multichannel EEG Compressed Sensing in the Presence of Mixed Noise

2019 ◽  
Vol 19 (22) ◽  
pp. 10574-10583 ◽  
Author(s):  
Chang Li ◽  
Wei Tao ◽  
Juan Cheng ◽  
Yu Liu ◽  
Xun Chen
Keyword(s):  
Compressed Sensing ◽  
Mixed Noise ◽  
Multichannel Eeg

scholarly journals Generalized notions of sparsity and restricted isometry property. Part I: a unified framework

2019 ◽  
Vol 9 (1) ◽  
pp. 157-193 ◽  
Author(s):  
Marius Junge ◽  
Kiryung Lee
Keyword(s):  
Banach Space ◽  
Inverse Problems ◽  
Compressed Sensing ◽  
Dimensionality Reduction ◽  
Group Actions ◽  
Function Spaces ◽  
Restricted Isometry Property ◽  
Low Rank ◽  
Unified Framework ◽  
Order Tensor

Abstract The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose generalized notions of sparsity and provide a unified framework for the corresponding RIP, in particular when combined with isotropic group actions. Our results extend an approach by Rudelson and Vershynin to a much broader context including commutative and non-commutative function spaces. Moreover, our Banach space notion of sparsity applies to affine group actions. The generalized approach in particular applies to high-order tensor products.

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