Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

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.

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Identification of Sonar Detection Signal Based on Fractional Fourier Transform

Polish Maritime Research ◽

10.2478/pomr-2018-0083 ◽

2018 ◽

Vol 25 (s2) ◽

pp. 125-131

Author(s):

Wang Biao ◽

Tang Jiansheng ◽

Yu Fujian ◽

Zhu Zhiyu

Keyword(s):

Fourier Transform ◽

Fractional Fourier Transform ◽

Adaptive Threshold ◽

Good Time ◽

Transform Domain ◽

Time Frequency ◽

Watermark Embedding ◽

Before And After ◽

Different Characteristics ◽

Fourier Transform Domain

Abstract Aiming at the source of underwater acoustic emission, in order to identify the enemy emission sonar source accurately. Using the digital watermarking technology and combining with the good time-frequency characteristics of fractional Fourier transform (FRFT), this paper proposes a sonar watermarking method based on fractional Fourier transform. The digital watermark embedding in the fractional Fourier transform domain and combined with the coefficient properties of the sonar signal in the fractional Fourier transform to select the appropriate watermark position. Using the different characteristics of the signals before and after embedding, an adaptive threshold was set for the watermark detection to realize the discrimination of sonar signals. The simulation results show the feasibility and has better resolution and large watermark capacity of this method, while the robustness of the watermark is better, and the detection precision is further improved.

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Compressive Sensing Approach in the Hermite Transform Domain

Mathematical Problems in Engineering ◽

10.1155/2015/286590 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 10

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.

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