The adaptive normal-hypergeometric-inverted-beta priors for sparse signals

2020 ◽  
pp. 1-24
Author(s):  
Hanjun Yu ◽  
Xinyi Xu ◽  
Di Cao
Keyword(s):  
Sparse Signals

Basis selection for wavelet processing of sparse signals

2008 ◽  
Vol 88 (9) ◽  
pp. 2340-2345 ◽  
Author(s):  
Ian C. Atkinson ◽  
Farzad Kamalabadi
Keyword(s):  
Sparse Signals ◽  
Selection For

Compressed Sampling of Spectrally Sparse Signals Using Sparse Circulant Matrices

Frequenz ◽  
2014 ◽  
Vol 68 (11-12) ◽  
Author(s):  
Guangjie Xu ◽  
Huali Wang ◽  
Lei Sun ◽  
Weijun Zeng ◽  
Qingguo Wang
Keyword(s):  
Circulant Matrices ◽  
Noise Robustness ◽  
Sparse Signals ◽  
Measurement Matrix ◽  
Compressed Sampling ◽  
Random Measurement ◽  
Compressive Performance ◽  
Generating Sequence ◽  
Periodic Autocorrelation ◽  
Selection Of

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.

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

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.

SUPPOSe Deconvolution + AI Denoising: Super-resolving Sparse Signals Blurred and Buried in Noise

2021 ◽  
Author(s):  
Axel M. Lacapmesure ◽  
Micaela Toscani ◽  
Guillermo Brinatti Vazquez ◽  
Sandra R. Martínez ◽  
Oscar E. Martínez
Keyword(s):  
Sparse Signals

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.

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