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 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.

Bayesian feature learning for seismic compressive sensing and denoising

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. O91-O104 ◽  
Author(s):  
Georgios Pilikos ◽  
A. C. Faul
Keyword(s):  
Compressive Sensing ◽  
State Of The Art ◽  
Feature Learning ◽  
Seismic Signal ◽  
Basis Functions ◽  
Sparse Signals ◽  
Seismic Signals ◽  
Process Factor ◽  
Learned Features ◽  
Fixed Basis

Extracting the maximum possible information from the available measurements is a challenging task but is required when sensing seismic signals in inaccessible locations. Compressive sensing (CS) is a framework that allows reconstruction of sparse signals from fewer measurements than conventional sampling rates. In seismic CS, the use of sparse transforms has some success; however, defining fixed basis functions is not trivial given the plethora of possibilities. Furthermore, the assumption that every instance of a seismic signal is sparse in any acquisition domain under the same transformation is limiting. We use beta process factor analysis (BPFA) to learn sparse transforms for seismic signals in the time slice and shot record domains from available data, and we use them as dictionaries for CS and denoising. Algorithms that use predefined basis functions are compared against BPFA, with BPFA obtaining state-of-the-art reconstructions, illustrating the importance of decomposing seismic signals into learned features.

Random Acquisition in Compressive Sensing

2021 ◽  
Vol 12 (3) ◽  
pp. 140-165
Author(s):  
Mahdi Khosravy ◽  
Thales Wulfert Cabral ◽  
Max Mateus Luiz ◽  
Neeraj Gupta ◽  
Ruben Gonzalez Crespo
Keyword(s):  
Compressive Sensing ◽  
Sampling Theorem ◽  
Lower Number ◽  
Compressive Sampling ◽  
Minimum Requirement ◽  
Random Modulation ◽  
Random Demodulator ◽  
Modulated Wideband Converter ◽  
Signal Image ◽  
Sparsity Structure

Compressive sensing has the ability of reconstruction of signal/image from the compressive measurements which are sensed with a much lower number of samples than a minimum requirement by Nyquist sampling theorem. The random acquisition is widely suggested and used for compressive sensing. In the random acquisition, the randomness of the sparsity structure has been deployed for compressive sampling of the signal/image. The article goes through all the literature up to date and collects the main methods, and simply described the way each of them randomly applies the compressive sensing. This article is a comprehensive review of random acquisition techniques in compressive sensing. Theses techniques have reviews under the main categories of (1) random demodulator, (2) random convolution, (3) modulated wideband converter model, (4) compressive multiplexer diagram, (5) random equivalent sampling, (6) random modulation pre-integration, (7) quadrature analog-to-information converter, (8) randomly triggered modulated-wideband compressive sensing (RT-MWCS).

scholarly journals Bayesian Compressive Sensing of Sparse Signals with Unknown Clustering Patterns

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 247 ◽  
Author(s):  
Mohammad Shekaramiz ◽  
Todd Moon ◽  
Jacob Gunther
Keyword(s):  
Compressive Sensing ◽  
Bayesian Learning ◽  
Sparse Signals ◽  
Sparsity Pattern ◽  
Multiple Measurement Vectors ◽  
Measurement Vector ◽  
Clustering Pattern ◽  
Clustering Patterns ◽  
Recovery Problem ◽  
Solution Matrix

We consider the sparse recovery problem of signals with an unknown clustering pattern in the context of multiple measurement vectors (MMVs) using the compressive sensing (CS) technique. For many MMVs in practice, the solution matrix exhibits some sort of clustered sparsity pattern, or clumpy behavior, along each column, as well as joint sparsity across the columns. In this paper, we propose a new sparse Bayesian learning (SBL) method that incorporates a total variation-like prior as a measure of the overall clustering pattern in the solution. We further incorporate a parameter in this prior to account for the emphasis on the amount of clumpiness in the supports of the solution to improve the recovery performance of sparse signals with an unknown clustering pattern. This parameter does not exist in the other existing algorithms and is learned via our hierarchical SBL algorithm. While the proposed algorithm is constructed for the MMVs, it can also be applied to the single measurement vector (SMV) problems. Simulation results show the effectiveness of our algorithm compared to other algorithms for both SMV and MMVs.

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