scholarly journals Compressive Sensing Approach in the Hermite Transform Domain

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Srdjan Stanković ◽  
Ljubiša Stanković ◽  
Irena Orović
Keyword(s):  
Compressive Sensing ◽  
Signal Reconstruction ◽  
Transform Domain ◽  
Numerical Examples ◽  
Hermite Transform ◽  
Sensing Applications ◽  
Random Samples ◽  
Significant Interest ◽  
Small Set ◽  
Short Time

Compressive sensing has attracted significant interest of researchers providing an alternative way to sample and reconstruct the signals. This approach allows us to recover the entire signal from just a small set of random samples, whenever the signal is sparse in certain transform domain. Therefore, exploring the possibilities of using different transform basis is an important task, needed to extend the field of compressive sensing applications. In this paper, a compressive sensing approach based on the Hermite transform is proposed. The Hermite transform by itself provides compressed signal representation based on a smaller number of Hermite coefficients compared to the signal length. Here, it is shown that, for a wide class of signals characterized by sparsity in the Hermite domain, accurate signal reconstruction can be achieved even if incomplete set of measurements is used. Advantages of the proposed method are demonstrated on numerical examples. The presented concept is generalized for the short-time Hermite transform and combined transform.

scholarly journals Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Irena Orović ◽  
Vladan Papić ◽  
Cornel Ioana ◽  
Xiumei Li ◽  
Srdjan Stanković
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Compressive Sensing ◽  
Signal Reconstruction ◽  
Signal Acquisition ◽  
Transform Domain ◽  
Hermite Transform ◽  
Time Frequency ◽  
Reconstruction Methods ◽  
Fourier Transform Domain

Compressive sensing has emerged as an area that opens new perspectives in signal acquisition and processing. It appears as an alternative to the traditional sampling theory, endeavoring to reduce the required number of samples for successful signal reconstruction. In practice, compressive sensing aims to provide saving in sensing resources, transmission, and storage capacities and to facilitate signal processing in the circumstances when certain data are unavailable. To that end, compressive sensing relies on the mathematical algorithms solving the problem of data reconstruction from a greatly reduced number of measurements by exploring the properties of sparsity and incoherence. Therefore, this concept includes the optimization procedures aiming to provide the sparsest solution in a suitable representation domain. This work, therefore, offers a survey of the compressive sensing idea and prerequisites, together with the commonly used reconstruction methods. Moreover, the compressive sensing problem formulation is considered in signal processing applications assuming some of the commonly used transformation domains, namely, the Fourier transform domain, the polynomial Fourier transform domain, Hermite transform domain, and combined time-frequency domain.

scholarly journals On some common compressive sensing recovery algorithms and applications

2017 ◽  
Vol 30 (4) ◽  
pp. 477-510 ◽  
Author(s):  
Andjela Draganic ◽  
Irena Orovic ◽  
Srdjan Stankovic
Keyword(s):  
Signal Processing ◽  
Compressive Sensing ◽  
Signal Reconstruction ◽  
Practical Applications ◽  
Sensing Applications ◽  
Different Types ◽  
Acquisition Strategy ◽  
Basic Ideas ◽  
Significant Attention ◽  
Intensive Growth

Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy with significantly reduced number of samples needed for accurate signal reconstruction. The basic ideas and motivation behind this approach are provided in the theoretical part of the paper. The commonly used algorithms for missing data reconstruction are presented. The Compressive Sensing applications have gained significant attention leading to an intensive growth of signal processing possibilities. Hence, some of the existing practical applications assuming different types of signals in real-world scenarios are described and analyzed as well.

Compressive sensing of signals sparse in 2D Hermite transform domain

2016 ◽  
Author(s):  
Milos Brajovic ◽  
Irena Orovic ◽  
Milos Dakovic ◽  
Srdan Stankovic
Keyword(s):  
Compressive Sensing ◽  
Transform Domain ◽  
Hermite Transform

Gradient‐based signal reconstruction algorithm in Hermite transform domain

2016 ◽  
Vol 52 (1) ◽  
pp. 41-43 ◽  
Author(s):  
M. Brajović ◽  
I. Orović ◽  
M. Daković ◽  
S. Stanković
Keyword(s):  
Signal Reconstruction ◽  
Reconstruction Algorithm ◽  
Transform Domain ◽  
Hermite Transform ◽  
Gradient Based

FHSS signal sparsification in the Hermite transform domain

2016 ◽  
Author(s):  
Milos Brajovic ◽  
Andjela Draganic ◽  
Irena Orovic ◽  
Srdjan Stankovic
Keyword(s):  
Transform Domain ◽  
Hermite Transform

scholarly journals Compressive sensing-based vibration signal reconstruction using sparsity adaptive subspace pursuit

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879087 ◽  
Author(s):  
Lin Zhou ◽  
Qianxiang Yu ◽  
Daozhi Liu ◽  
Ming Li ◽  
Shukai Chi ◽  
...  
Keyword(s):  
Compressive Sensing ◽  
Data Storage ◽  
Wireless Sensors ◽  
Signal Reconstruction ◽  
Estimation Method ◽  
Vibration Signal ◽  
Estimation Accuracy ◽  
Offshore Structure ◽  
Vibration Signals ◽  
Reconstructed Signal

Wireless sensors produce large amounts of data in long-term online monitoring following the Shannon–Nyquist theorem, leading to a heavy burden on wireless communications and data storage. To address this problem, compressive sensing which allows wireless sensors to sample at a much lower rate than the Nyquist frequency has been considered. However, the lower rate sacrifices the integrity of the signal. Therefore, reconstruction from low-dimension measurement samples is necessary. Generally, the reconstruction needs the information of signal sparsity in advance, whereas it is usually unknown in practical applications. To address this issue, a sparsity adaptive subspace pursuit compressive sensing algorithm is deployed in this article. In order to balance the computational speed and estimation accuracy, a half-fold sparsity estimation method is proposed. To verify the effectiveness of this algorithm, several simulation tests were performed. First, the feasibility of subspace pursuit algorithm is verified using random sparse signals with five different sparsities. Second, the synthesized vibration signals for four different compression rates are reconstructed. The corresponding reconstruction correlation coefficient and root mean square error are demonstrated. The high correlation and low error result mean that the proposed algorithm can be applied in the vibration signal process. Third, implementation of the proposed approach for a practical vibration signal from an offshore structure is carried out. To reduce the effect of signal noise, the wavelet de-noising technique is used. Considering the randomness of the sampling, many reconstruction tests were carried out. Finally, to validate the reliability of the reconstructed signal, the structure modal parameters are calculated by the Eigensystem realization algorithm, and the result is only slightly different between original and reconstructed signal, which means that the proposed method can successfully save the modal information of vibration signals.

Sign in / Sign up

Export Citation Format

Share Document