scholarly journals On a Gradient-Based Algorithm for Sparse Signal Reconstruction in the Signal/Measurements Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Ljubiša Stanković ◽  
Miloš Daković
Keyword(s):  
Compressive Sensing ◽  
Statistical Study ◽  
Signal Reconstruction ◽  
Sparse Signals ◽  
Step Size ◽  
Gradient Algorithms ◽  
Gradient Based ◽  
Complete Set ◽  
The Time Domain ◽  
Adaptive Step

Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common compressive sensing methods the signal is recovered in the sparsity domain. A method for the reconstruction of sparse signals which reconstructs the missing/unavailable samples/measurements is recently proposed. This method can be efficiently used in signal processing applications where a complete set of signal samples exists. The missing samples are considered as the minimization variables, while the available samples are fixed. Reconstruction of the unavailable signal samples/measurements is preformed using a gradient-based algorithm in the time domain, with an adaptive step. Performance of this algorithm with respect to the step-size and convergence are analyzed and a criterion for the step-size adaptation is proposed in this paper. The step adaptation is based on the gradient direction angles. Illustrative examples and statistical study are presented. Computational efficiency of this algorithm is compared with other two commonly used gradient algorithms that reconstruct signal in the sparsity domain. Uniqueness of the recovered signal is checked using a recently introduced theorem. The algorithm application to the reconstruction of highly corrupted images is presented as well.

scholarly journals An analog hardware solution for compressive sensing reconstruction using gradient-based method

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Irena Orović ◽  
Nedjeljko Lekić ◽  
Marko Beko ◽  
Srdjan Stanković
Keyword(s):  
Compressive Sensing ◽  
Signal Reconstruction ◽  
Optimal Choice ◽  
Sparse Signals ◽  
Reconstruction Algorithms ◽  
Hardware Implementations ◽  
Nested Iterations ◽  
Gradient Based ◽  
Analog Implementation ◽  
Lower Complexity

AbstractThis work proposes an analog implementation of gradient-based algorithm for compressive sensing signal reconstruction. Compressive sensing has appeared as a promising technique for efficient acquisition and reconstruction of sparse signals in many real-world applications. It starts from the assumption that sparse signals can be exactly reconstructed using far less samples than in standard signal processing. In this paper, we consider the gradient-based algorithm as the optimal choice that provides lower complexity and competitive accuracy compared with existing methods. Since the efficient hardware implementations of reconstruction algorithms are still an emerging topic, this work is focused on the design of hardware that will provide fast parallel algorithm execution for real-time applications, overcoming the limitations imposed by the large number of nested iterations during the signal reconstruction. The proposed implementation is simple and fast, executing 400 iterations in 1 ms which is sufficient to obtain highly accurate reconstruction results.

scholarly journals Analysis of Low Complexity Adaptive Step-size Orthogonal Gradient-based FEQ for OFDM Systems

1970 ◽  
Vol 5 (2) ◽  
pp. 134-145
Author(s):  
Suchada Sitjongsataporn
Keyword(s):  
Orthogonal Frequency Division Multiplexing ◽  
Weighted Least Squares ◽  
Low Complexity ◽  
Gradient Algorithm ◽  
Frequency Division ◽  
Ofdm Systems ◽  
Step Size ◽  
Adaptive Step Size ◽  
Gradient Based ◽  
Adaptive Step

We propose two low complexity adaptive step-size mechanisms based on the normalised orthogonal gradient algorithm for frequency-domain equalisation in orthogonal frequency division multiplexing (OFDM) systems. These algorithms are derived from employing a mixed-subcarrier exponentially weighted least squares criterion. Two low complexity adaptive stepsizeapproaches are investigated by exploiting an estimate of autocorrelation between previous and present weight-estimated mixed-subcarrier errors. We compare our approaches with a previously fixed stepsize normalised orthogonal gradient adaptive algorithm and other existing algorithm for implementation. Simulation results demonstrate that the proposed algorithms can achieve good performance for involving an OFDM receiver.

scholarly journals Noises in randomly sampled sparse signals

2014 ◽  
Vol 27 (3) ◽  
pp. 359-373 ◽  
Author(s):  
Ljubisa Stankovic
Keyword(s):  
Compressive Sensing ◽  
Random Sampling ◽  
Domain Analysis ◽  
External Noise ◽  
Sampling Theorem ◽  
Sparse Signals ◽  
Gradient Based

Sparse signals can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Two main reconstruction directions are in the sparse transformation domain analysis of signals and the gradient based algorithms. In the transformation domain analysis, that will be considered here, the estimation of nonzero signal coefficients is based on the signal transform calculated using available samples only. The missing samples manifest themselves as a noise. This kind of noise is analyzed in the case of random sampling, when the sampling instants do not coincide with the sampling theorem instants. Analysis of the external noise influence to the results, with randomly sampled sparse signals, is done as well. Theory is illustrated and checked on statistical examples.

scholarly journals Filtering-Based Regularized Sparsity Variable Step-Size Matching Pursuit and Its Applications in Vehicle Health Monitoring

2021 ◽  
Vol 11 (11) ◽  
pp. 4816
Author(s):  
Haoqiang Liu ◽  
Hongbo Zhao ◽  
Wenquan Feng
Keyword(s):  
Health Monitoring ◽  
Matching Pursuit ◽  
Signal Reconstruction ◽  
Superior Performance ◽  
Sparse Signal ◽  
Variable Step Size ◽  
Step Size ◽  
Signal Sampling ◽  
Reconstruction Performance ◽  
Sparsity Level

Recent years have witnessed that real-time health monitoring for vehicles is gaining importance. Conventional monitoring scheme faces formidable challenges imposed by the massive signals generated with extremely heavy burden on storage and transmission. To address issues of signal sampling and transmission, compressed sensing (CS) has served as a promising solution in vehicle health monitoring, which performs signal sampling and compression simultaneously. Signal reconstruction is regarded as the most critical part of CS, while greedy reconstruction has been a research hotspot. However, the existing approaches either require prior knowledge of the sparse signal or perform with expensive computational complexity. To exploit the structure of the sparse signal, in this paper, we introduce an initial estimation approach for signal sparsity level firstly. Then, a novel greedy reconstruction algorithm that relies on no prior information of sparsity level while maintaining a good reconstruction performance is presented. The proposed algorithm integrates strategies of regularization and variable adaptive step size and further performs filtration. To verify the efficiency of the algorithm, typical voltage disturbance signals generated by the vehicle power system are taken as trial data. Preliminary simulation results demonstrate that the proposed algorithm achieves superior performance compared to the existing methods.

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