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Compressed Sensing of ECG signal for Wireless system with New fast iterative method
... The new suggested method is an improvement of our old method that was explained in Ref. [20]. We used the same steps for a coding operation which was summarized in Ref. [20] (section 5); the only difference will appear in decoding operation. ...
... The new suggested method is an improvement of our old method that was explained in Ref. [20]. We used the same steps for a coding operation which was summarized in Ref. [20] (section 5); the only difference will appear in decoding operation. In decoding operation, we change the engine of recovering the sparse signal from using LS-OMP (Least Support-Orthogonal Matching Pursuit) to MSMP for each segment Si. ...
... The second stage is reconstructed signal using MSMP; the method is summarized in Fig. 1. Detailed explanation of Fig. 1 can be found in Ref. [20]. ...
Compressed sensing (CS) is a new field used for signal acquisition and design of sensor that made a large drooping in the cost of acquiring sparse signals. In this paper, new algorithms are developed to improve the performance of the greedy algorithms.
In this paper, a new greedy pursuit algorithm, SS-MSMP (Split Signal for Multiple Support of Matching Pursuit), is introduced and theoretical analyses are given. The SS-MSMP is suggested for sparse data acquisition, in order to reconstruct analog and efficient signals via a small set of general measurements. This paper proposes a new fast method which depends on a study of the behavior of the support indices through picking the best estimation of the corrosion between residual and measurement matrix.
The term multiple supports originates from an algorithm; in each iteration, the best support indices are picked based on maximum quality created by discovering correlation for a particular length of support.
We depend on this new algorithm upon our previous derivative of halting condition that we produce for Least Support Orthogonal Matching Pursuit (LS-OMP) for clear and noisy signal.
For better reconstructed results, SS-MSMP algorithm provides the recovery of support set for long signals such as signals used in WBAN.
Numerical experiments demonstrate that the new suggested algorithm performs well compared to existing algorithms in terms of many factors used for reconstruction performance.
... In many applications, the perfect knowledge of the projection matrix is infeasible and only a perturbed version of it is available for the reconstruction of the original sparse vector. Examples of such applications are gridbased approaches to time-delay/Doppler-shift/direction-of-arrival/position estimation in communications/radar systems or spectrum sensing in cognitive radio networks [4]- [10], mobile electrocardiogram (ECG) monitoring [11], X-ray imaging [12], plant biomass characterization [13], hyperspectral unmixing [14], information security [15], [16], and high-dimensional linear regression [17]. ...
... Some of the greedy PCS reconstruction algorithms combine the TLS estimation with a greedy support-detection method; others modify the classical greedy compressive-sensing reconstruction algorithms, such as the orthogonal matching pursuit algorithm, so that they can account for the perturbation in the projection matrix as well as the perturbation in the vector of projections. The algorithms proposed in [6], [11], [33]- [35] are a few examples. These algorithms along with those based on the ℓ 1 -regularized TLS estimation are among the most computationally efficient reconstruction algorithms for PCS. ...
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to reconstruction in fully-perturbed compressive-sensing setups where both the projected measurements of an unknown sparse vector and the knowledge of the associated projection matrix are perturbed due to noise, error, mismatch, etc. We propose a new iterative algorithm for tackling this problem. The proposed algorithm utilizes the proximal-gradient method to find a sparse total least-squares solution by minimizing an l1-regularized Rayleigh-quotient cost function. We determine the step-size of the algorithm at each iteration using an adaptive rule accompanied by backtracking line search to improve the algorithm's convergence speed and preserve its stability. The proposed algorithm is considerably faster than a popular previously-proposed algorithm, which employs the alternating-direction method and coordinate-descent iterations, as it requires significantly fewer computations to deliver the same accuracy. We demonstrate the effectiveness of the proposed algorithm via simulation results.
... This method was originally employed to select features for binary-class classification and has been used for feature selection and signal recovery. For example, Tawfic and Kayhan [11] proposed least support denoising-orthogonal matching pursuit (LSD-OMP) to reconstruct an original signal with the presence of noise. Then, Ji and Zhang [12] improved the reconstruction accuracy of the LSD-OPM through setting the threshold, eliminating some wrong atoms and combining some support sets to locate the optimal support set. ...
... As one of the main greedy pursuit algorithms, OMP is a forward search algorithm that was first proposed for continuous outcomes in the context of signal reconstruction [20]. Tawfic and Kayhan [11] proposed that least support denoising-orthogonal matching pursuit (LSD-OMP) enhanced OMP by choosing an optimum support set out of many in each iteration. Through setting the threshold, eliminating some wrong atoms and combining some support sets to locate the optimal support set, Ji and Zhang [12] proposed a regularized orthogonal matching pursuit-based multiple support (MS-ROMP) to improve the reconstruction accuracy of the LSD-OMP. ...
Biomarker selection for predictive analytics encounters the problem of identifying a minimal-size subset of genes that is maximally predictive of an outcome of interest. For lung cancer gene expression datasets, it is a great challenge to handle the characteristics of small sample size, high dimensionality, high noise as well as the low reproducibility of important biomarkers in different studies. In this paper, our proposed meta-analysis-based regularized orthogonal matching pursuit (MA-ROMP) algorithm not only gains strength by using multiple datasets to identify important genomic biomarkers efficiently, but also keeps the selection flexible among datasets to take into account data heterogeneity through a hierarchical decomposition on regression coefficients. For a case study of lung cancer, we downloaded GSE10072, GSE19188 and GSE19804 from the GEO database with inconsistent experimental conditions, sample preparation methods, different study groups, etc. Compared with state-of-the-art methods, our method shows the highest accuracy, of up to 95.63%, with the best discriminative ability (AUC 0.9756) as well as a more than 15-fold decrease in its training time. The experimental results on both simulated data and several lung cancer gene expression datasets demonstrate that MA-ROMP is a more effective tool for biomarker selection and learning cancer prediction.
... In the signal processing method, the CS is considered as a rising which set up the sparse signals acquisition in a diminutive set of linear projections [3]. The measurement vector size is lesser than the original signal nevertheless it still comprises the needed information for precise recovery of signal. ...
... In 2015, IsraaTawfic and SemaKayhan [3], presented two techniques using noise presence as well as absence, these techniques were LSD-OMP and LS-OMP. The techniques attain accurate support recovery without needing sparsity knowledge. ...
... It has also hardware implementation. FPGA (Field Programmable Gate Array) device has been intensively used and shows higher performance in [17] [18] [19] ECG, EEG, and other one-dimensional signal processing [20]. It also includes the transformation of a high dimensional signal to a lower one by means of matrix multiplication in parallel with original measurements from input [21]. ...
... Correlation analysis involves the evaluation of several randomly selected pairs of adjacent pixels aligned horizontally, vertically, and diagonally. For a particular figure print image with each pixel coordinates (x.y) and for randomly selected numbers of pairs , the correlation is given by eq. 17. (17) We effectively utilized eq.17 for 3000-pixel pairs of plain and compressed cipher images and plot distribution as shown in fig. 19. ...
This paper proposes a novel design approach for a secured compressed sensing system for fingerprint imaging and its transmission. In the proposed design, the first stage is acquiring the signal followed by sparsely modeling it using Orthogonal Matching Pursuit (OMP) algorithm. In addition to compressing, to guaranty its security, we multiply the sparse modeled data by a novel deterministic partially orthogonal Discrete Cosine Transform (DCT) sensing matrix. Furthermore, the construction of the sensing matrix uses a modified Multiplicative Linear Congruential Generator (MLCG) to select the row index appropriately from chaotically re-arranged rows of DCT pseudo-randomly. On the other hand, the simultaneous recovering and decryption of the compressed image accomplished with the help of a convex optimization method. The proposed system tested by employing different image and security assessment techniques. The results show that we have archived better Peak Signal to Noise Ratio (PSNR) than the recommended value for wireless transmission using samples below 25%.
... In many applications, the perfect knowledge of the projection matrix is infeasible and only a perturbed version of it is available for the reconstruction of the original sparse vector. Examples of such applications are gridbased approaches to time-delay/Doppler-shift/direction-of-arrival/position estimation in communications/radar systems or spectrum sensing in cognitive radio networks [4]- [10], mobile electrocardiogram (ECG) monitoring [11], X-ray imaging [12], plant biomass characterization [13], hyperspectral unmixing [14], information security [15], [16], and high-dimensional linear regression [17]. ...
... Some of the greedy PCS reconstruction algorithms combine the TLS estimation with a greedy support-detection method; others modify the classical greedy compressive-sensing reconstruction algorithms, such as the orthogonal matching pursuit algorithm, so that they can account for the perturbation in the projection matrix as well as the perturbation in the vector of projections. The algorithms proposed in [6], [11], [33]- [35] are a few examples. These algorithms along with those based on the ℓ 1 -regularized TLS estimation are among the most computationally efficient reconstruction algorithms for PCS. ...
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to reconstruction in fully-perturbed compressive-sensing setups where both the projected measurements of an unknown sparse vector and the knowledge of the associated projection matrix are perturbed due to noise, error, mismatch, etc. We propose a new iterative algorithm for tackling this problem. The proposed algorithm utilizes the proximal-gradient method to find a sparse total least-squares solution by minimizing an -regularized Rayleigh-quotient cost function. We determine the step-size of the algorithm at each iteration using an adaptive rule accompanied by backtracking line search to improve the algorithm’s convergence speed and preserve its stability. The proposed algorithm is considerably faster than a popular previously-proposed algorithm, which employs the alternating-direction method and coordinate-descent iterations, as it requires significantly fewer computations to deliver the same accuracy. We demonstrate the effectiveness of the proposed algorithm via simulation results.
... The authors of [184] Israa Tawfic et al. explored CS for wireless ECG system with iterative method using WBAN and DWT sparsification. They presented two greedy pursuit techniques named Least Support Orthogonal Matching Pursuit (LS-OMP) and Least Support Denoising-Orthogonal Matching Pursuit (LSD-OMP). ...
Nowadays, healthcare is becoming very modern, and the support of Internet of Things (IoT) is inevitable in a personal healthcare system. A typical personal healthcare system acquires vital parameters from human users and stores them in a cloud platform for further analysis. Acquiring fundamental biomedical signal, such as with the Electrocardiograph (ECG), is also considered for specific disease analysis in personal healthcare systems. When such systems are scaled up, there is a heavy demand for internet channel capacity to accommodate real time seamless flow of discrete samples of biomedical signals. So, there is a keen need for real time data compression of biomedical signals. Compressive Sensing (CS) has recently attracted more interest due to its compactness and its feature of the faithful reconstruction of signals from fewer linear measurements, which facilitates less than Shannon’s sampling rate by exploiting the signal sparsity. The most common biomedical signal that is to be analyzed is the ECG signal, as the prediction of heart failure at an early stage can save a human life. This review is for a vast use-case of IoT framework in which CS measurements of ECG are acquired, communicated through Internet to a server, and the arrhythmia are analyzed using Machine learning (ML). Assuming this use-case specific for ECG, in this review many technical aspects are considered regarding various research components. The key aspect is on the investigation of the best sensing method, and to address this, various sensing matrices are reviewed, analyzed and recommended. The next aspect is the selection of the optimal sparsifying method, and the review recommends unexplored ECG compression algorithms as sparsifying methods. The other aspects are optimum reconstruction algorithms, best hardware implementations, suitable ML methods and effective modality of IoT. In this review all these components are considered, and a detailed review is presented which enables us to orchestrate the use-case specified above. This review focuses on the current trends in CS algorithms for ECG signal compression and its hardware implementation. The key to successful reconstruction of the CS method is the right selection of sensing and sparsifying matrix, and there are many unexplored sparsifying methods for the ECG signal. In this review, we shed some light on new possible sparsifying techniques. A detailed comparison table of various CS algorithms, sensing matrix, sparsifying techniques with different ECG dataset is tabulated to quantify the capability of CS in terms of appropriate performance metrics. As per the use-case specified above, the CS reconstructed ECG signals are to be subjected to ML analysis, and in this review the compressive domain inference approach is discussed. The various datasets, methodologies and ML models for ECG applications are studied and their model accuracies are tabulated. Mostly, the previous research on CS had studied the performance of CS using numerical simulation, whereas there are some good attempts for hardware implementations for ECG applications, and we studied the uniqueness of each method and supported the study with a comparison table. As a consolidation, we recommend new possibilities of the research components in terms of new transforms, new sparsifying methods, suggestions for ML approaches and hardware implementation.
... While Ref. [22,39,50,64,66] uses a predictable random or pseudo-random matrix, unlike the previous two systems, they are generated from hardware like FPGA (Field Programmable Gate Array) and microcontroller. Since they are deterministic, they can generate multiple sensing matrices. ...
A secured compressed sensing (CS) systems design approach uses a novel deterministic sensing matrix to sense and transmit fingerprint images. The performance of the CS system was studied in detail by varying CS and security parameters. The sampling and sparse coefficient are the parameters considered from compressed sensing, whereas the encryption key is from the security scheme. The simultaneous compression and encryption has been achieved by multiplying the sparse modeled data with the proposed deterministic partial bounded orthogonal sensing matrix. A chaotic model-based permutation is applied to scramble the DCT matrix rows to build the sensing matrix. Recovering and decryption of the compressed image are accomplished with the help of the L1 optimization method. The experimental test shows that a sparse vector of 121 widths has been recovered by taking about 25 samples. This indicates that up to 1 : 5 compression ratio is supported without damaging the fingerprint minutiae. If only compression is required without encryption, up to a 1 : 16 ratio can be achieved. The peak signal-to-noise ratio (PSNR) is 27.65 dB for both compression ratios under fulfilments of all necessary security requirements. The 7.20 value of the entropy, histogram analysis, and the correlation analysis show the proposed scheme possesses adequate randomness. Furthermore, the ability of the system resistance against attacks is proved by 100% NPCR (Net Pixel Change Rate) and 0.92% UACI (Unified Average Changing Intensity) values.
... The OMP algorithm needs at most K iterations to reconstruct a sparse signal, with K being the sparsity of the signal. The LSD-OMP algorithm [13,14], on the other hand, can select more than one atom at each iteration without knowledge of the sparsity value and it can reconstruct the sparse signal in less than K iterations. This significantly reduces the number of iterations and the latency of the reconstruction and provides faster execution time for real-time applications. ...
... Furthermore, the scope of compressed sensing is not limited by analytical computations, and there is also hardware implementation. A field-programmable gate array or FPGA device is used and shows higher performance in ECG, EEG [16] [17] [18] and other one-dimensional signal processing [19]. ...
A novel deterministic sensing matrix design approach applied to enable secured compressed sensing and transmission of fingerprint images. The performance of the sensing matrix was analyzed in detail by varying compressed sensing and security parameters. The number of sampling and sparse coefficient are the parameters taken under consideration from compressed sensing, whereas the encryption key is from the security scheme. The first stage in the performance study is acquiring the signal, and followed by sparsely modelling it using Orthogonal Matching Pursuit (OMP) algorithm. The sparse modelled data is multiplied by the proposed deterministic partial orthogonal Discrete Cosine Transform (DCT) sensing matrix to reduce its dimension and encrypt it. To introduce confusion on the DCT matrix rows, the pseudo-random permutation is applied to the DCT matrix rows before sensing matrix derivation. Additionally, recovering and decryption of the compressed image accomplished with the help of a convex optimization method. The results obtained from the simulation of the proposed system confirmed that a better Peak Signal to Noise Ratio (PSNR) than the recommended value for wireless transmission is archived using a sample below 25% without losing a significant number of fingerprint minutiae.
... It also has hardware implementation. FPGA (Field Programmable Gate Array) device has been intensively used and shows higher performance in ECG, EEG [17] [18] [19], and other one-dimensional signal processing [20]. It also demonstrates the transformation of a high dimensional signal to a lower one employing matrix multiplication in parallel with measurements from input [21]. ...
This paper proposes a novel design approach for a secured compressed sensing system for fingerprint sensing and transmission. In the proposed design, the first stage is acquiring the signal followed by sparsely modeling it using Orthogonal Matching Pursuit (OMP) algorithm then compressing. In addition to compressing, we multiply the sparse modeled data by a novel, deterministic, and partially orthogonal Discrete Cosine Transform (DCT) sensing matrix to guarantee its security. Furthermore, the construction of the sensing matrix uses a modified Multiplicative Linear Congruential Generator (MLCG) to select the row index appropriately from chaotically re-arranged rows of DCT pseudo-randomly. On the other hand, the compressed image's simultaneous recovery and decryption accomplished using a convex optimization method—the proposed system tested by employing different image and security assessment techniques. The results show that we have archived a better Peak Signal to Noise Ratio (PSNR) than the recommended value for wireless transmission using samples below 25%.
... The signal quality is maintained at 80% CR. The comparison table showing the comparison with other researchers 11,12,14,32,33 is shown in Table 5. The input and output waveforms are shown ...
An electrocardiogram (ECG) signal is an important diagnostic tool for cardiologists to detect the abnormality. In continuous monitoring, an ambulatory huge amount of ECG data is involved. This leads to high storage requirements and transmission costs. Hence, to reduce the storage and transmission cost, there is a requirement for an efficient compression or coding technique. One of the most promising compression techniques is Compressive Sensing (CS) which makes efficient compression of signals. By this methodology, a signal can easily be reconstructed if it has a sparse representation. This paper presents the Block Sparse Bayesian Learning (BSBL)-based multiscale compressed sensing (MCS) method for the compression of ECG signals. The main focus of the proposed technique is to achieve a reconstructed signal with less error and more energy efficiency. The ECG signal is sparsely represented by wavelet transform. MIT-BIH Arrhythmia database is used for testing purposes. The Huffman technique is used for encoding and decoding. The signal recovery is appropriate up to 75% of compression. The quality of the signal is ascertained using the standard performance measures such as signal-to-noise ratio (SNR) and Percent root mean square difference (PRD). The quality of the reconstructed ECG signal is also validated through the visual method. This method is most suitable for telemedicine applications.
... Provides information compression ratio on the degree to which blank data compression methods are removed [21]. The higher the compression rate, the less number of bits needed to store or transfer data [7,22,23]. í µí µ = í µí µí µí µí µí µí µí µí µí µí µí µí µ í µí µí µí µ í µí µí µí µí µí µí µí µí µí µí µ í µí µí µí µ ...
... At present, there are few researches on compressive sensing for HS signals at home and abroad, but they are at the beginning stage. Such as I. W. Selesnick described a method for one-dimensional signal denoising that simultaneously utilizes both sparse optimization principles and conventional linear time-invariant (LTI) filtering, this method is used in ECG accurately preserves the spikes in the ECG waveform [6]; Block Sparse Bayesian Learning Framework proposed by Haibin Wang et al. to implement block-based processing of HS signals Compressive sensing reconstruction [7]; Israa Tawfic and Sema Kayhan presented two methods for ECG with absence and presence of noise, these methods are Least Support Orthogonal Matching Pursuit (LS-OMP) and Least Support Denoising-Orthogonal Matching Pursuit (LSD-OMP) [8]; Balouchestanol achieved undersampling of ECG signals in wireless body area networks using compressive sensing and sparse Bayesian learning structures [9]. These studies have shown that compressive sensing is of great value in the study of physiological signals in humans. ...
The rapid development of wearable biosensors based on Internet of Things (IoT) provides a new solution for heart disease analysis and prediction of sudden death from heart failure. However, how to deal with the large amount of data generated by heart sound signals is an urgent problem to be solved. Based on the characteristics of heart sound signals, we propose a parallel compressive sensing model for the multi-channel synchronous acquisition of heart sound signals. Furthermore, we provide a series of experiments to assess the performance of the model. The experimental results demonstrate that the reconstruction speed of the proposed model is 9 to 10 times faster than block sparse Bayesian learning algorithm and orthogonal matching pursuit algorithm, and the reconstruction effect is better. Meanwhile, the proposed model can effectively reconstruct the normal heart sound signal and abnormal heart sound signal of four-channel of synchronous acquisition. Therefore, the proposed model is the feasibility.
... Besides, some researchers confirmed that 4 or less-channel EEG system can be used in sleeping assessment, epilepsy diagnosis, person identification and BCI applications [31][32][33][34] It is certain that high-precision EEG systems are not necessary for some applications. Furthermore, the similar trends are found in other bio-signals sensing schemes like ECG and blood pressure [35,36]. Thus, effective wearable solutions should be vital future proof [37]. ...
Daily-life emotion recognition is a new procedure developed from basic emotion recognition. It records and analyzes emotion-related bio-signals to evaluate emotional states of subjects when they are participating in daily tasks instead of receiving specific stimulations. This paper develops a wearable biosensor network to take a step further towards daily-life emotion recognition. Multimodal bio-signals (electroencephalography, pulse, skin temperature and blood pressure) are recorded by the sensor nodes and transmitted to the remote web data center through a body station to realize the web-enabled recognition scheme. In total, a 103-day emotion diary is kept from Jun 2015 to Feb 2016, discontinuously. The remarkably different appearing possibilities of 4 emotional states (horror, happiness, boredom and relaxation) and the noisy sensing environment create an imbalanced and noisy dataset. Thus, a reputation-driven imbalanced fuzzy support vector machine (RI-FSVM) classification method is proposed to reduce the adverse effects caused by both within-class noisy samples and between-class imbalance. The fuzzy membership function is determined by the reputation values (indicating the reliability of samples) and the class-imbalanced ratios. The experiment convinces that the wearable biosensor network works well and successfully extracts efficient features from multimodal bio-signals. These features are convinced to have better performance than the related work in both centrality and distinguishability. The proposed method improves the sensitivity, specificity and Gm of emotion classification compared with the typical classification methods. Eventually, our research achieves a competitive accuracy with a low-cost consumer-grade sensing system. The main contributions of this paper are the quantitative analysis on emotion diary and the imbalanced classification algorithm for daily-life emotion recognition.
This paper presents a novel under-sampling method for ECG signals, aimed at reducing the sampling rate and power consumption in IoT-based ECG wearable devices. The key contribution addresses the common issue of model mismatch in existing methods, which negatively impacts signal reconstruction accuracy. Initially, the ECG signal is modeled as a linear combination of several Gaussian second-order derivative functions, which can be efficiently represented with only a few parameters, thus mitigating the problem of large model matching errors. To further enhance reconstruction accuracy, an improved two-channel FRI sampling framework is introduced, effectively addressing the non-ideal effects caused by the low-pass filter during sampling. Additionally, a modified annihilating filter reconstruction algorithm is proposed, allowing high-precision signal reconstruction using a small number of sampling points to estimate parameters. The validity of the proposed method is confirmed through simulations with real ECG signals from the MIT-BIH arrhythmia database, and a hardware platform is developed to verify its feasibility in a practical system. Experimental results demonstrate that, compared to the existing methods, the proposed approach significantly reduces reconstruction error (achieving a PRD as low as 2.29% and an SRR of 11.77 dB), and exhibits better robustness in noisy environments.
Compressed Sensing (CS) has been considered a very effective means of reducing energy consumption at the energy-constrained wireless body sensor networks for monitoring the multi-channel Electrocardiogram (MECG) signals. In this paper, we have used the Kronecker sparsifying bases to exploit the spatio-temporal correlations of the MECG signals for improving the compression of the signals transmitted by the sensors. Furthermore, a compressed sensing-based method with low-rank constraint is proposed for effective data acquisition and signal reconstruction in the energy-constrained wireless body sensor networks. More specifically, in the proposed algorithm, an optimization formula consisting of two constraints is defined. The sparsity constraint is presented through the minimization of the l1 norm and the low-rank constraint is specified through the minimization of the nuclear norm. Afterward, a robust and efficient alternating direction method of multipliers (ADMM) based method is developed for the reconstruction of the MECG signals that solves the resulting optimization problem more effectively. Numerical experiments verify that the proposed algorithm achieves greater reconstruction accuracy with the smaller number of required transmissions, lower computational complexity, and smaller reconstruction errors, as compared to the latest CS-based recovery methods.
The purpose of this study is to solve the issues in reconstruction computation complexity of the current method in wireless body area network (WBAN) through developing compressed sensing (CS) for multichannel electroencephalogram, performing model optimization, designing a system for compressing and collecting electroencephalogram (EEG) signals, and implementing real time compression and collection of multichannel signals. Firstly, based on the distributed compressed sensing theory, we analyze the sparsity of EEG signal, screen digital sensing matrix models, design multichannel joint reconstruction algorithm, and perform optimization analysis as well as simulation verification at each step. Secondly, based on field programmable gate array (FPGA), we realize real time collection, storage, compression, and transmission of multichannel EEG by setting up a compression and collection system. Lastly, each system function module is inspected, and the performance of the compressed multichannel EEG system is evaluated from the perspective of computation complexity, reconstruction accuracy, instantaneity, etc. Evaluation results show that the improvement of real-time performance is contributed by the application of binary permutation block diagonal matrix (BPBD), which converts CS multiplications into additions with a simple circuit and reduces the computational time drastically. The average signal to noise distortion ratio for signal reconstruction reaches 21.74 dB under the compression ratio of 2, which also meets the requirement of WBAN. The proposed method has faster computation, better accuracy, and simpler coding, can be utilized in a variety of applications related to multichannel EEG, especially in situations where the system power consumption and real-time performance are critical.
ECG is one of the most popular fields in biosignals research. There are many studies conducted to develop an ECG instrument, both in hardware development and software development. One of the most recent trends is the development of remote monitoring of ECG signal using wireless technology. In this paper, we presented design, development, and implementation of our preliminary research about wireless ECG monitoring using android phone as a hub to connect it to the cloud server. The system that has been built meets the initial requirement of our design. The system has successfully recorded the ECG signal from the user, transfer it to the smartphone as a hub, store it locally, upload it to the server, and finally display it in the front-end web app.
Recent results in telecardiology show that compressed sensing (CS) is a promising tool to lower energy consumption in wireless body area networks for electrocardiogram (ECG) monitoring. However, the performance of current CS-based algorithms, in terms of compression rate and reconstruction quality of the ECG, still falls short of the performance attained by state-of-the-art wavelet based algorithms. In this paper, we propose to exploit the structure of the wavelet representation of the ECG signal to boost the performance of CS-based methods for compression and reconstruction of ECG signals. More precisely, we incorporate prior information about the wavelet dependencies across scales into the reconstruction algorithms and exploit the high fraction of common support of the wavelet coefficients of consecutive ECG segments. Experimental results utilizing the MIT-BIH Arrhythmia Database show that significant performance gains, in terms of compression rate and reconstruction quality, can be obtained by the proposed algorithms compared to current CS-based methods.
Recent results in telecardiology show that compressed sensing (CS) is a
promising tool to lower energy consumption in wireless body area networks for
electrocardiogram (ECG) monitoring. However, the performance of current
CS-based algorithms, in terms of compression rate and reconstruction quality of
the ECG, still falls short of the performance attained by state-of-the-art
wavelet based algorithms. In this paper, we propose to exploit the structure of
the wavelet representation of the ECG signal to boost the performance of
CS-based methods for compression and reconstruction of ECG signals. More
precisely, we incorporate prior information about the wavelet dependencies
across scales into the reconstruction algorithms and exploit the high fraction
of common support of the wavelet coefficients of consecutive ECG segments.
Experimental results utilizing the MIT-BIH Arrhythmia Database show that
significant performance gains, in terms of compression rate and reconstruction
quality, can be obtained by the proposed algorithms compared to current
CS-based methods.
Compressed sensing (CS) shows that a signal having a sparse or compressible
representation can be recovered from a small set of linear measurements. In
classical CS theory, the sampling matrix and dictionary are assumed be known
exactly in advance. However, uncertainties exist due to sampling distortion,
finite grids of the parameter space of dictionary, etc. In this paper, we take
a generalized sparse signal model, which simultaneously considers the sampling
and dictionary uncertainties. Based on the new signal model, a new optimization
model for robust sparse signal recovery is proposed. This optimization model
can be deduced with stochastic robust approximation analysis. Both convex
relaxation and greedy algorithm are used to solve the optimization problem. For
the convex relaxation method, a sufficient condition for recovery by convex
relaxation method and the uniqueness of solution are given too; For the greedy
sparse algorithm, it is realized by the introduction of a pre-processing of the
sensing matrix and the measurements. In numerical experiments, both simulated
data and real-life ECG data based results show that the proposed method has a
better performance than the current methods.
Compressed sensing (CS) can recover sparse signals from under-sampled measurements. In this work, we have developed an advanced CS framework for photoacoustic computed tomography (PACT). During the reconstruction, a small part of the nonzero signals’ locations in the transformed sparse domain is used as partially known support (PKS). PACT reconstructions have been performed with under-sampled in vivo image data of human hands and a rat. Compared to PACT with basic CS, PACT with CS-PKS can recover signals using fewer ultrasonic transducer elements and can improve convergence speed, which may ultimately enable high-speed, low-cost PACT for various biomedical applications.
Telemonitoring of electroencephalogram (EEG) through wireless body-area
networks is an evolving direction in personalized medicine. Among various
constraints in designing such a system, three important constraints are energy
consumption, data compression, and device cost. Conventional data compression
methodologies, although effective in data compression, consumes significant
energy and cannot reduce device cost. Compressed sensing (CS), as an emerging
data compression methodology, is promising in catering to these constraints.
However, EEG is non-sparse in the time domain and also non-sparse in
transformed domains (such as the wavelet domain). Therefore, it is extremely
difficult for current CS algorithms to recover EEG with the quality that
satisfies the requirements of clinical diagnosis and engineering applications.
Recently, Block Sparse Bayesian Learning (BSBL) was proposed as a new method to
the CS problem. This study introduces the technique to the telemonitoring of
EEG. Experimental results show that its recovery quality is better than
state-of-the-art CS algorithms, and sufficient for practical use. These results
suggest that BSBL is very promising for telemonitoring of EEG and other
non-sparse physiological signals.
Wireless body sensor networks (WBSN) hold the promise to be a key enabling information and communications technology for next-generation patient-centric telecardiology or mobile cardiology solutions. Through enabling continuous remote cardiac monitoring, they have the potential to achieve improved personalization and quality of care, increased ability of prevention and early diagnosis, and enhanced patient autonomy, mobility, and safety. However, state-of-the-art WBSN-enabled ECG monitors still fall short of the required functionality, miniaturization, and energy efficiency. Among others, energy efficiency can be improved through embedded ECG compression, in order to reduce airtime over energy-hungry wireless links. In this paper, we quantify the potential of the emerging compressed sensing (CS) signal acquisition/compression paradigm for low-complexity energy-efficient ECG compression on the state-of-the-art Shimmer WBSN mote. Interestingly, our results show that CS represents a competitive alternative to state-of-the-art digital wavelet transform (DWT)-based ECG compression solutions in the context of WBSN-based ECG monitoring systems. More specifically, while expectedly exhibiting inferior compression performance than its DWT-based counterpart for a given reconstructed signal quality, its substantially lower complexity and CPU execution time enables it to ultimately outperform DWT-based ECG compression in terms of overall energy efficiency. CS-based ECG compression is accordingly shown to achieve a 37.1% extension in node lifetime relative to its DWT-based counterpart for “good” reconstruction quality.
This paper introduces a new framework of fast and efficient sensing matrices
for practical compressive sensing, called Structurally Random Matrix (SRM). In
the proposed framework, we pre-randomize a sensing signal by scrambling its
samples or flipping its sample signs and then fast-transform the randomized
samples and finally, subsample the transform coefficients as the final sensing
measurements. SRM is highly relevant for large-scale, real-time compressive
sensing applications as it has fast computation and supports block-based
processing. In addition, we can show that SRM has theoretical sensing
performance comparable with that of completely random sensing matrices.
Numerical simulation results verify the validity of the theory as well as
illustrate the promising potentials of the proposed sensing framework.
Suppose x is an unknown vector in Ropfm (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible by transform coding with a known transform, and we reconstruct via the nonlinear procedure defined here, the number of measurements n can be dramatically smaller than the size m. Thus, certain natural classes of images with m pixels need only n=O(m1/4log5/2(m)) nonadaptive nonpixel samples for faithful recovery, as opposed to the usual m pixel samples. More specifically, suppose x has a sparse representation in some orthonormal basis (e.g., wavelet, Fourier) or tight frame (e.g., curvelet, Gabor)-so the coefficients belong to an lscrp ball for 0<ples1. The N most important coefficients in that expansion allow reconstruction with lscr2 error O(N1/2-1p/). It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients. Moreover, a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing. The nonadaptive measurements have the character of "random" linear combinations of basis/frame elements. Our results use the notions of optimal recovery, of n-widths, and information-based complexity. We estimate the Gel'fand n-widths of lscrp balls in high-dimensional Euclidean space in the case 0<ples1, and give a criterion identifying near- optimal subspaces for Gel'fand n-widths. We show that "most" subspaces are near-optimal, and show that convex optimization (Basis Pursuit) is a near-optimal way to extract information derived from these near-optimal subspaces
Low energy consumption is crucial for body area networks (BANs). In BAN-enabled ECG monitoring, the continuous monitoring entails the need of the sensor nodes to transmit a huge data to the sink node, which leads to excessive energy consumption. To reduce airtime over energy-hungry wireless links, this paper presents an energy-efficient compressed sensing (CS)-based approach for on-node ECG compression. At first, an algorithm called minimal mutual coherence pursuit is proposed to construct sparse binary measurement matrices, which can be used to encode the ECG signals with superior performance and extremely low complexity. Second, in order to minimize the data rate required for faithful reconstruction, a weighted l1 minimization model is derived by exploring the multisource prior knowledge in wavelet domain. Experimental results on MIT-BIH arrhythmia database reveals that the proposed approach can obtain higher compression ratio than the state-of-the-art CS-based methods. Together with its low encoding complexity, our approach can achieve significant energy saving in both encoding process and wireless transmission.
This article considers sparse signal recovery in the presence of noise. A mutual incoherence condition which was previously used for exact recovery in the noiseless case is shown to be sufficient for stable recovery in the noisy case. Furthermore, the condition is proved to be sharp. A specific counterexample is given. In addition, an oracle inequality is derived under the mutual incoherence condition in the case of Gaussian noise.
We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques, and reconstruc- tion accuracy of the same order as that of LP optimization methods. The presented analysis shows that in the noiseless setting, the proposed algorithm can exactly reconstruct arbitrary sparse signals provided that the sensing matrix satisfies the restricted isometry property with a constant parameter. In the noisy setting and in the case that the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by constant multiples of the measurement and signal perturbation energies.
This paper provides a simple proof of the mutual incoherence condition under which K-sparse signal can be accurately reconstructed
from a small number of linear measurements using the orthogonal matching
pursuit (OMP) algorithm. Our proof, based on mathematical induction, is built
on an observation that the general step of the OMP process is in essence same
as the initial step since the residual is considered as a new measurement
preserving the sparsity level of an input vector.
Compressive sampling offers a new paradigm for acquiring signals that are compressible
with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling
is to approximate a compressible signal from noisy samples. This paper describes a new iterative
recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based
approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage.
It is likely to be extremely efficient for practical problems because it requires only matrix-vector
multiplies with the sampling matrix. For compressible signals, the running time is just O(N log^2 N),
where N is the length of the signal.
This lecture note presents a new method to capture and represent compressible signals at a rate significantly below the Nyquist rate. This method, called compressive sensing, employs nonadaptive linear projections that preserve the structure of the signal; the signal is then reconstructed from these projections using an optimization process.
This paper considers a natural error correcting problem with real valued input/output. We wish to recover an input vector f∈Rn from corrupted measurements y=Af+e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to recover f exactly from the data y? We prove that under suitable conditions on the coding matrix A, the input f is the unique solution to the ℓ1-minimization problem (||x||ℓ1:=Σi|xi|) min(g∈Rn) ||y - Ag||ℓ1 provided that the support of the vector of errors is not too large, ||e||ℓ0:=|{i:ei ≠ 0}|≤ρ·m for some ρ>0. In short, f can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted. This work is related to the problem of finding sparse solutions to vastly underdetermined systems of linear equations. There are also significant connections with the problem of recovering signals from highly incomplete measurements. In fact, the results introduced in this paper improve on our earlier work. Finally, underlying the success of ℓ1 is a crucial property we call the uniform uncertainty principle that we shall describe in detail.
Sparse Signal Reconstruction from Noisy Compressive Measurements using Cross Validation, supported by ONR grants N00014-06-1-0768 and the Texas Instruments Leadership University Program
- P Boufounos
- M F Duarte
- R G Baraniuk
P. Boufounos, M.F. Duarte, R.G. Baraniuk, Sparse Signal
Reconstruction from Noisy Compressive Measurements
using Cross Validation, supported by ONR grants
N00014-06-1-0768 and the Texas Instruments Leadership
University Program, 2015.
COSAMP: iterative signal recovery from in complete and inaccurate samples
- J A Troop
D. needell, J.A. Troop, COSAMP: iterative signal recovery
from in complete and inaccurate samples, Elsevier Appl.
Comput. Harmon. Anal. 26 (3) (2009) 301-321.