Reconstruction Of Sparse Signals Using Likelihood Maximization from Compressive Measurements with Gaussian And Saturation Noise

AbstractCirculant measurement matrices constructed by partial cyclically shifts of one generating sequence, are easier to be implemented in hardware than widely used random measurement matrices; however, the diminishment of randomness makes it more sensitive to signal noise. Selecting a deterministic sequence with optimal periodic autocorrelation property (PACP) as generating sequence, would enhance the noise robustness of circulant measurement matrix, but this kind of deterministic circulant matrices only exists in the fixed periodic length. Actually, the selection of generating sequence doesn't affect the compressive performance of circulant measurement matrix but the subspace energy in spectrally sparse signals. Sparse circulant matrices, whose generating sequence is a sparse sequence, could keep the energy balance of subspaces and have similar noise robustness to deterministic circulant matrices. In addition, sparse circulant matrices have no restriction on length and are more suitable for the compressed sampling of spectrally sparse signals at arbitrary dimensionality.

Download Full-text

Recovery of Sparse Signals Using Multiple Orthogonal Least Squares

IEEE Transactions on Signal Processing ◽

10.1109/tsp.2016.2639467 ◽

2017 ◽

Vol 65 (8) ◽

pp. 2049-2062 ◽

Cited By ~ 26

Author(s):

Jian Wang ◽

Ping Li

Keyword(s):

Least Squares ◽

Sparse Signals ◽

Orthogonal Least Squares

Download Full-text

On the detection probability of sparse signals with sensor networks based on distributed subspace pursuit

2015 IEEE China Summit and International Conference on Signal and Information Processing (ChinaSIP) ◽

10.1109/chinasip.2015.7230417 ◽

2015 ◽

Cited By ~ 2

Author(s):

Wenqiang Zhao ◽

Gang Li

Keyword(s):

Sensor Networks ◽

Detection Probability ◽

Sparse Signals

Download Full-text

A Novel Detection Scheme with Multiple Observations for Sparse Signal Based on Likelihood Ratio Test with Sparse Estimation

Mathematical Problems in Engineering ◽

10.1155/2016/8535486 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14

Author(s):

Hongbo Zhao ◽

Lei Chen ◽

Wenquan Feng ◽

Chuan Lei

Keyword(s):

Likelihood Ratio ◽

Likelihood Ratio Test ◽

Prior Information ◽

Finite Size ◽

Sparse Signals ◽

Ratio Test ◽

Sparse Estimation ◽

Detection Scheme ◽

Error Exponent ◽

Multiple Observations

Recently, the problem of detecting unknown and arbitrary sparse signals has attracted much attention from researchers in various fields. However, there remains a peck of difficulties and challenges as the key information is only contained in a small fraction of the signal and due to the absence of prior information. In this paper, we consider a more general and practical scenario of multiple observations with no prior information except for the sparsity of the signal. A new detection scheme referred to as the likelihood ratio test with sparse estimation (LRT-SE) is presented. Under the Neyman-Pearson testing framework, LRT-SE estimates the unknown signal by employing thel1-minimization technique from compressive sensing theory. The detection performance of LRT-SE is preliminarily analyzed in terms of error probabilities in finite size and Chernoff consistency in high dimensional condition. The error exponent is introduced to describe the decay rate of the error probability as observations number grows. Finally, these properties of LRT-SE are demonstrated based on the experimental results of synthetic sparse signals and sparse signals from real satellite telemetry data. It could be concluded that the proposed detection scheme performs very close to the optimal detector.

Download Full-text