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.

scholarly journals Nonlocal Tensor Sparse Representation and Low-Rank Regularization for Hyperspectral Image Compressive Sensing Reconstruction

2019 ◽  
Vol 11 (2) ◽  
pp. 193 ◽  
Author(s):  
Jize Xue ◽  
Yongqiang Zhao ◽  
Wenzhi Liao ◽  
Jonathan Chan
Keyword(s):  
Remote Sensing ◽  
Compressive Sensing ◽  
Implementation Strategy ◽  
Hyperspectral Image ◽  
State Of The Art ◽  
Low Rank ◽  
Structured Sparsity ◽  
Spectral Correlation ◽  
Tensor Nuclear Norm ◽  
Nonlocal Structure

Hyperspectral image compressive sensing reconstruction (HSI-CSR) is an important issue in remote sensing, and has recently been investigated increasingly by the sparsity prior based approaches. However, most of the available HSI-CSR methods consider the sparsity prior in spatial and spectral vector domains via vectorizing hyperspectral cubes along a certain dimension. Besides, in most previous works, little attention has been paid to exploiting the underlying nonlocal structure in spatial domain of the HSI. In this paper, we propose a nonlocal tensor sparse and low-rank regularization (NTSRLR) approach, which can encode essential structured sparsity of an HSI and explore its advantages for HSI-CSR task. Specifically, we study how to utilize reasonably the l 1 -based sparsity of core tensor and tensor nuclear norm function as tensor sparse and low-rank regularization, respectively, to describe the nonlocal spatial-spectral correlation hidden in an HSI. To study the minimization problem of the proposed algorithm, we design a fast implementation strategy based on the alternative direction multiplier method (ADMM) technique. Experimental results on various HSI datasets verify that the proposed HSI-CSR algorithm can significantly outperform existing state-of-the-art CSR techniques for HSI recovery.

scholarly journals Matrix completion with Preference Ranking for Top-N Recommendation

2018 ◽  
Author(s):  
Zengmao Wang ◽  
Yuhong Guo ◽  
Bo Du
Keyword(s):  
Minimization Problem ◽  
State Of The Art ◽  
Matrix Completion ◽  
Experimental Results ◽  
Rank Function ◽  
Low Rank ◽  
Preference Ranking ◽  
Recovery Model ◽  
Popular Method ◽  
Admm Algorithm

Matrix completion has become a popular method for top-N recommendation due to the low rank nature of sparse rating matrices. However, many existing methods produce top-N recommendations by recovering a user-item matrix solely based on a low rank function or its relaxations, while ignoring other important intrinsic characteristics of the top-N recommendation tasks such as preference ranking over the items. In this paper, we propose a novel matrix completion method that integrates the low rank and preference ranking characteristics of recommendation matrix under a self-recovery model for top-N recommendation. The proposed method is formulated as a joint minimization problem and solved using an ADMM algorithm. We conduct experiments on E-commerce datasets. The experimental results show the proposed approach outperforms several state-of-the-art methods.

Nonconvex Nonsmooth Low-Rank Minimization for Peneralized Image Compressed Sensing via Group Sparse Representation

2020 ◽  
Author(s):  
Yunyi Li ◽  
Li Liu ◽  
Yu Zhao ◽  
Xiefeng Cheng ◽  
Guan Gui
Keyword(s):  
Sparse Representation ◽  
Minimization Problem ◽  
Singular Values ◽  
Nuclear Norm ◽  
Low Rank ◽  
Rank Minimization ◽  
Group Matrix ◽  
Reconstruction Performance ◽  
Generalized Framework ◽  
Surrogate Function

Group sparse representation (GSR) based method has led to great successes in various image recovery tasks, which can be converted into a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear norm based convex surrogate usually leads to over-shrinking problem, since the standard soft-thresholding operator shrinks all singular values equally. To improve traditional sparse representation based image compressive sensing (CS) performance, we propose a generalized CS framework based on GSR model, leading to a nonconvex nonsmooth low-rank minimization problem. The popular -norm and M-estimator are employed for standard image CS and robust CS problem to fit the data respectively. For the better approximation of the rank of group-matrix, a family of nuclear norms are employed to address the over-shrinking problem. Moreover, we also propose a flexible and effective iteratively-weighting strategy to control the weighting and contribution of each singular value. Then we develop an iteratively reweighted nuclear norm algorithm for our generalized framework via an alternating direction method of multipliers framework, namely, GSR-ADMM-IRNN. Experimental results demonstrate that our proposed CS framework can achieve favorable reconstruction performance compared with current state-of-the-art methods and the RCS framework can suppress the outliers effectively.

Matrix completion via minimizing an approximate rank

2019 ◽  
Vol 17 (05) ◽  
pp. 689-713
Author(s):  
Xueying Zeng ◽  
Lixin Shen ◽  
Yuesheng Xu ◽  
Jian Lu
Keyword(s):  
State Of The Art ◽  
Matrix Completion ◽  
Relaxation Parameter ◽  
Rank Function ◽  
Low Rank ◽  
Completion Problem ◽  
Rank Matrix ◽  
Matrix Completion Problem ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix

The low rank matrix completion problem which aims to recover a matrix from that having missing entries has received much attention in many fields such as image processing and machine learning. The rank of a matrix may be measured by the [Formula: see text] norm of the vector of its singular values. Due to the nonconvexity and discontinuity of the [Formula: see text] norm, solving the low rank matrix completion problem which is clearly NP hard suffers from computational challenges. In this paper, we propose a constrained matrix completion model in which a novel nonconvex continuous rank surrogate is used to approximate the rank function of a matrix, promote low rank of the recovered matrix and address the computational challenges. The proposed rank surrogate differs from the convex nuclear norm and other existing state-of-the-art nonconvex surrogates in a way that it alleviates the discontinuity and nonconvexity of the rank function through a local [Formula: see text]-relaxation of the [Formula: see text] norm so that it possesses several desirable properties. These properties ensure that it accurately approximates the rank function by choosing an appropriate relaxation parameter. We moreover develop an efficient iterative algorithm to solve the resulting model. We also propose strategies of automatically updating the relaxation parameter to practically ensure the global convergence and speed up the algorithm. We establish theoretical convergence results for the proposed algorithm. Experimental results are presented to demonstrate significant performance improvements of the proposed model and the associated algorithm as compared to state-of-the-art methods in both recoverability and computational efficiency.

scholarly journals Nonconvex Nonsmooth Low-Rank Minimization for Peneralized Image Compressed Sensing via Group Sparse Representation

2020 ◽  
Author(s):  
Yunyi Li ◽  
Li Liu ◽  
Yu Zhao ◽  
Xiefeng Cheng ◽  
Guan Gui
Keyword(s):  
Sparse Representation ◽  
Minimization Problem ◽  
Singular Values ◽  
Nuclear Norm ◽  
Low Rank ◽  
Rank Minimization ◽  
Group Matrix ◽  
Reconstruction Performance ◽  
Generalized Framework ◽  
Surrogate Function

Group sparse representation (GSR) based method has led to great successes in various image recovery tasks, which can be converted into a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear norm based convex surrogate usually leads to over-shrinking problem, since the standard soft-thresholding operator shrinks all singular values equally. To improve traditional sparse representation based image compressive sensing (CS) performance, we propose a generalized CS framework based on GSR model, leading to a nonconvex nonsmooth low-rank minimization problem. The popular -norm and M-estimator are employed for standard image CS and robust CS problem to fit the data respectively. For the better approximation of the rank of group-matrix, a family of nuclear norms are employed to address the over-shrinking problem. Moreover, we also propose a flexible and effective iteratively-weighting strategy to control the weighting and contribution of each singular value. Then we develop an iteratively reweighted nuclear norm algorithm for our generalized framework via an alternating direction method of multipliers framework, namely, GSR-ADMM-IRNN. Experimental results demonstrate that our proposed CS framework can achieve favorable reconstruction performance compared with current state-of-the-art methods and the RCS framework can suppress the outliers effectively.

scholarly journals A Multi-Timescale Bilinear Model for Optimization and Control of HVAC Systems with Consistency

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 400 ◽  
Author(s):  
Zelin Nie ◽  
Feng Gao ◽  
Chao-Bo Yan
Keyword(s):  
Optimization Model ◽  
Air Conditioning ◽  
State Of The Art ◽  
Hvac Systems ◽  
Practical Significance ◽  
Hvac System ◽  
Bilinear Model ◽  
Optimization And Control ◽  
And Control ◽  
Slow Timescale

Reducing the energy consumption of the heating, ventilation, and air conditioning (HVAC) systems while ensuring users’ comfort is of both academic and practical significance. However, the-state-of-the-art of the optimization model of the HVAC system is that either the thermal dynamic model is simplified as a linear model, or the optimization model of the HVAC system is single-timescale, which leads to heavy computation burden. To balance the practicality and the overhead of computation, in this paper, a multi-timescale bilinear model of HVAC systems is proposed. To guarantee the consistency of models in different timescales, the fast timescale model is built first with a bilinear form, and then the slow timescale model is induced from the fast one, specifically, with a bilinear-like form. After a simplified replacement made for the bilinear-like part, this problem can be solved by a convexification method. Extensive numerical experiments have been conducted to validate the effectiveness of this model.

Computing Robust Principal Components by A* Search

2018 ◽  
Vol 27 (07) ◽  
pp. 1860013 ◽  
Author(s):  
Swair Shah ◽  
Baokun He ◽  
Crystal Maung ◽  
Haim Schweitzer
Keyword(s):  
State Of The Art ◽  
Principal Component ◽  
Low Rank ◽  
A Algorithm ◽  
Running Time ◽  
Current State ◽  
Dimensionality Reduction Technique ◽  
Related Variant ◽  
Low Rank Representation ◽  
The Cost

Principal Component Analysis (PCA) is a classical dimensionality reduction technique that computes a low rank representation of the data. Recent studies have shown how to compute this low rank representation from most of the data, excluding a small amount of outlier data. We show how to convert this problem into graph search, and describe an algorithm that solves this problem optimally by applying a variant of the A* algorithm to search for the outliers. The results obtained by our algorithm are optimal in terms of accuracy, and are shown to be more accurate than results obtained by the current state-of-the- art algorithms which are shown not to be optimal. This comes at the cost of running time, which is typically slower than the current state of the art. We also describe a related variant of the A* algorithm that runs much faster than the optimal variant and produces a solution that is guaranteed to be near the optimal. This variant is shown experimentally to be more accurate than the current state-of-the-art and has a comparable running time.

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