Overview of Compressed Sensing: Sensing Model, Reconstruction Algorithm, and Its Applications

Li, Lixiang; Liu, Liwei; Peng, Haipeng; Kurths, Jürgen; Yang, Yixian

doi:10.3390/app10175909

Cited by 50 publications

(21 citation statements)

References 91 publications

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“…However, when we compared our method, DCSR, in terms of computational complexity, our approach is not the most advantageous; however, real-time processing is largely feasible. Hence, complexity reduction techniques such as block-compressed sensing [ 54 ] or deep learning technique [ 55 ] are feasible.…”

Section: Discussionmentioning

confidence: 99%

Image Denoising Using a Compressive Sensing Approach Based on Regularization Constraints

Mahdaoui

Ouahabi

Moulay

2022

Sensors

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In remote sensing applications and medical imaging, one of the key points is the acquisition, real-time preprocessing and storage of information. Due to the large amount of information present in the form of images or videos, compression of these data is necessary. Compressed sensing is an efficient technique to meet this challenge. It consists in acquiring a signal, assuming that it can have a sparse representation, by using a minimum number of nonadaptive linear measurements. After this compressed sensing process, a reconstruction of the original signal must be performed at the receiver. Reconstruction techniques are often unable to preserve the texture of the image and tend to smooth out its details. To overcome this problem, we propose, in this work, a compressed sensing reconstruction method that combines the total variation regularization and the non-local self-similarity constraint. The optimization of this method is performed by using an augmented Lagrangian that avoids the difficult problem of nonlinearity and nondifferentiability of the regularization terms. The proposed algorithm, called denoising-compressed sensing by regularization (DCSR) terms, will not only perform image reconstruction but also denoising. To evaluate the performance of the proposed algorithm, we compare its performance with state-of-the-art methods, such as Nesterov’s algorithm, group-based sparse representation and wavelet-based methods, in terms of denoising and preservation of edges, texture and image details, as well as from the point of view of computational complexity. Our approach permits a gain up to 25% in terms of denoising efficiency and visual quality using two metrics: peak signal-to-noise ratio (PSNR) and structural similarity (SSIM).

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Section: Discussionmentioning

confidence: 99%

Image Denoising Using a Compressive Sensing Approach Based on Regularization Constraints

Mahdaoui

Ouahabi

Moulay

2022

Sensors

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“…Compressed perception theory can efficiently capture information from sparse signals and perceive measurements through noncorrelation, a property that makes compressed perception widely used in real-life applications. Compressed perception theory has brought a revolutionary breakthrough by solving the current bottleneck in information acquisition and processing technology and has received widespread attention from scholars in various countries, ranging from medical imaging and signal coding to astronomy and geophysics [ 4 ]. The Boolean model [ 5 – 7 ] is an early text representation paradigm that uses a collection of “1” and “0” variables to represent the feature items of the related text.…”

Section: Introductionmentioning

confidence: 99%

Text Feature Extraction for Public English Vocabulary Based on Wavelet Transform

Shi

2022

Computational and Mathematical Methods in Medicine

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Text interpretation of public English vocabulary is a critical task in the subject of natural language processing, which uses technology to allow humans and computers to communicate effectively using natural language. Text feature extraction is one of the most fundamental and crucial elements in allowing computers to effectively grasp and read text. This paper proposes a text feature extraction method based on wavelet analysis that performs fast discrete wavelet transform and inverse discrete wavelet transform on the feature vectors under the traditional TF-IDF vector space model to address the problem of low feature differentiation of high-dimensional data in text feature extraction. In particular, due to the design of the Mallat algorithm, there is frequency aliasing in the signal decomposition process. This phenomenon is a problem that cannot be ignored when using wavelet analysis for feature extraction. Therefore, this paper proposes an improved inverse discrete wavelet transform method, in which the signal is decomposed by Mallat algorithm to obtain wavelet coefficients at each scale and then reconstructed to the required wavelet space coefficients according to the reconstruction method, and the reconstructed coefficients are used to analyze the signal at that scale instead of the wavelet coefficients obtained at the corresponding scale. Experiments on the public English vocabulary dataset reveal that the wavelet transform-based strategy suggested in this research outperforms existing feature extraction methods while maintaining greater classification accuracy while reducing the dimensionality of the TF-IDF vector space model.

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“…Peak signal-to-noise ratio (PSNR) is an engineering term for the ratio between the maximum possible signal's power and the power of noise. PSNR can be characterized as follows [31][32][33]:…”

Section: Peak Signal To Noise Ratiomentioning

confidence: 99%

Efficient Data Compression of ECG Signal Based on Modified Discrete Cosine Transform

Hassan¹,

Alzaidi²,

Ghoneim³

et al. 2022

Computers, Materials &Amp; Continua

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This paper introduced an efficient compression technique that uses the compressive sensing (CS) method to obtain and recover sparse electrocardiography (ECG) signals. The recovery of the signal can be achieved by using sampling rates lower than the Nyquist frequency. A novel analysis was proposed in this paper. To apply CS on ECG signal, the first step is to generate a sparse signal, which can be obtained using Modified Discrete Cosine Transform (MDCT) on the given ECG signal. This transformation is a promising key for other transformations used in this search domain and can be considered as the main contribution of this paper. A small number of wavelet components can describe the ECG signal as related work to obtain a sparse ECG signal. A sensing technique for ECG signal compression, which is a novel area of research, is proposed. ECG signals are introduced randomly between any successive beats of the heart. MIT-BIH database can be represented as the experimental database in this domain of research. The MIT-BIH database consists of various ECG signals involving a patient and standard ECG signals. MATLAB can be considered as the simulation tool used in this work. The proposed method's uniqueness was inspired by the compression ratio (CR) and achieved by MDCT. The performance measurement of the recovered signal was done by calculating the percentage root mean difference (PRD), mean square error (MSE), and peak signal to noise ratio (PSNR) besides the calculation of CR. Finally, the simulation results indicated that this work is one of the most important works in ECG signal compression.

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Overview of Compressed Sensing: Sensing Model, Reconstruction Algorithm, and Its Applications

Cited by 50 publications

References 91 publications

Image Denoising Using a Compressive Sensing Approach Based on Regularization Constraints

Image Denoising Using a Compressive Sensing Approach Based on Regularization Constraints

Text Feature Extraction for Public English Vocabulary Based on Wavelet Transform

Efficient Data Compression of ECG Signal Based on Modified Discrete Cosine Transform

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