Proposed Compressed Sensing Method Research Articles

A signal-adaptive measurement matrix construction algorithm for compressed sensing of sEMG data

Abstract Surface electromyography (sEMG), serving as a pivotal wearable technology, is a promising tool to assess and monitor muscle function. Yet, the efficacy of a sEMG system faces inevitable constraints, primarily stemming from the challenges of transmission and energy consumption induced by big data. Compressed sensing (CS) is a promising data acquisition solution that takes advantage of the signal sparseness in a particular basis to significantly reduce the number of samples. Current CS methods usually employ random or deterministic measurement matrix to compress sEMG signal. However, these measurement matrices do not integrate the signal feature, which limits the performance of these CS methods. To address this problem, this paper proposes an improved CS method for sEMG data compression. This proposed method introduces a measurement matrix construction algorithm to produce a deterministic matrix tailored for processing sEMG signals. The deterministic measurement matrix integrates the characteristics of the magnitudes of sEMG signals. The sEMG signals acquired from the upper limb muscles of the stroke survivors were applied to evaluate the proposed CS method, with results showing that it achieves better reconstruction accuracy and robustness than the CS methods with other measurement matrices. The proposed method employing basis pursuit (BP) in the signal reconstruction presents better performance than that employing orthogonal matching pursuit (OMP). Hence, we can conclude that the proposed CS algorithm is of key importance for the popularization of sEMG in the wearable health monitoring devices.

Compressive Sensing Strategy on Sparse Array to Accelerate Ultrasonic TFM Imaging

Phased array ultrasonic testing (PAUT) based on full matrix capture (FMC) has recently been gaining popularity in the scientific and nondestructive testing communities. FMC is a versatile acquisition method that collects all the transmitter-receiver combinations from a given array. Furthermore, when postprocessing FMC data using the total focusing method (TFM), high-resolution images are achieved for defect characterization. Today, the combination of FMC and TFM is becoming more widely available in commercial ultrasonic phased array controllers. However, executing the FMC-TFM method is data-intensive, as the amount of data collected and processed is proportional to the square of the number of elements of the probe. This shortcoming may be overcome using a sparsely populated array in transmission followed by an efficient compression using compressive sensing (CS) approaches. The method can therefore lead to a massive reduction of data and hardware requirements and ultimately accelerate TFM imaging. In the present work, a CS methodology was applied to experimental data measured from samples containing artificial flaws. The results demonstrated that the proposed CS method allowed a reduction of up to 80% in the volume of data while achieving adequate FMC data recovery. Such results indicate the possibility of recovering experimental FMC signals using sampling rates under the Nyquist theorem limit. The TFM images obtained from the FMC, CS-FMC, and sparse CS approaches were compared in terms of contrast-to-noise ratio (CNR). It was seen that the CS-FMC combination produced images comparable to those acquitted using the FMC. Implementation of sparse arrays improved CS reconstruction times by up to 11 folds and reduced the firing events by approximately 90%. Moreover, image formation was accelerated by 6.6 times at the cost of only minor image quality degradation relative to the FMC.

Convex optimization for additive noise reduction in quantitative complex object wave retrieval using compressive off-axis digital holographic imaging

Abstract Image denoising is one of the important problems in the research field of computer vision, artificial intelligence, 3D vision, and image processing, where the fundamental aim is to recover the original image features from a noisy contaminated image. The camera sensor additive noise present in the holographic recording process reduces the quality of the retrieved image. Even though various techniques have been developed to minimize the noise in digital holography, the noise reduction still remains a challenging task. This article presents a compressive sensing (CS) technique to minimize the additive noise in the digital holographic reconstruction process. We demonstrate the reduction of additive noise using complex wave retrieval method as a sensing matrix in the CS model. The proposed CS method to suppress the noise during the reconstruction process is illustrated using numerical simulations. Only 50% of the pixel measurements are considered in the noisy hologram, which is far less than the original complex object pixels. The impact of additive gaussian noise in the recording plane on the reconstruction accuracy of both intensity and phase distribution is analysed. The CS method denoises and estimates the complex object information accurately. The numerical simulation results have shown that the proposed CS method has effectively minimized the noise in the reconstructed image and has greatly improved the quality of both intensity and phase information.

Complex object wave retrieval using single-pixel compressive imaging of an off-axis Fresnel hologram

A complex wavefield imaging using single-pixel compressive sensing of an off-axis digital Fresnel hologram is proposed. A digital micromirror device (DMD) sampling prior to the single-pixel detection does the sparse representation of the hologram. The digital hologram is computationally recovered using a compressive sensing (CS) algorithm, and then the complex object wavefield is reconstructed using a complex wave retrieval method. The impact of the use of two measurement operators namely random and Walsh–Hadamard measurement matrices on the reconstruction quality of the hologram and complex object wavefield is compared. The cases of CS algorithm using different sparsification criteria i.e. Haar wavelet, Fresnelet sparsification and without sparsification of the digital hologram are analysed. The computer simulation results of the proposed CS method reveals that the Walsh–Hadamard sampling with Fresnelet sparsification achieves good quality reconstructions of both intensity and phase of the object wavefield.

Spatial Interpolation of Gauge Measured Rainfall Using Compressed Sensing

In this work, we suggest new spatial precipitation interpolation schemes using compressed sensing (CS), which is a new framework for signal acquisition and smart sensor design. Using CS, the precipitation maps are recovered in high resolution by obtaining sparse coefficients of radial basis functions(RBFs). Two types of methods are designed according to the construction methods of CS matrix. In the first type, the CS matrix is derived as the product of an m × n (n ≫ m) weights matrix of inverse distance weighting (IDW) and an n × n radial basis function (RBF) matrix. The second type of CS matrix consists of an m × n RBF matrix that depends on a few observation vectors and a number of n unknown vectors. The advantage of the proposed CS methods is that it can be represented at a high resolution because it is interpolated based on a large number of bases (or degrees of freedom). This prevents the variance value from being much smaller than the actual value due to interpolation using a few observation scales. To test our CS interpolation schemes, interpolation results were compared with IDW, Ordinary Kriging (OK) and RBF interpolation methods for analytic test function and some actual rainfall data. In the case of an analytic test function, when the proposed method is compared at high resolution, the error from the true value is the smallest. In real rainfall data, comparison with real values is not possible at high resolutions, but the error with the observed data is the smallest in terms of ‘spatial variogram’. In addition, the proposed CS method generates hight resolution data from rainfall cases, showing promising results when identifying peaks.

Group sparse structure and elastic-net regularization for compressive sensing of pulse-type physiological signals

ObjectiveGroup Gini (Gr. Gini) and average-group Gini (AvgGr. Gini) indexes are introduced for the evaluation of group-sparsity of rhythmic pulse-type physiological signals, and a new method for the reconstruction of physiological pulse-type rhythmic signals for compressive sensing (CS) applications is proposed. MethodsGr. Gini and AvgGr. Gini indexes are developed by generalizing the conventional Gini index, for the evaluation of sparsity of signals with grouped nonzero components. The signal reconstruction CS method is based on applying generalized Elastic-Net regularized least-squares. The elastic-net function is generalized by including nonconvex lp-pseudonorm, so that its minimization results in enhanced group-sparse structure on the first-order difference (FoD) and second-order difference (SoD) of the signal. It operates by taking advantage of the pre-existing group-sparse structure on the FoD and SoD components of the original signal. This method is effective for reconstructing signals with pulse-type structures by encouraging the grouping of significant signal components. ResultsSimulation results demonstrate that the Gr. Gini and AvgGr. Gini indexes can effectively evaluate group sparse-structure. The proposed CS method can offer improvement in signal-to-noise ratio (SNR), structural similarity index measure, Gr. Gini index, and AvgGr. Gini index. It is found to offer improvement of Gr.Gini index, AvgGr.Gini index, and SNR by 0.4%, 0.4%, and 5.29 dB respectively, for electrocardiogram (ECG) signals and by 5.89%, 5.89%, 16 dB, respectively, for foot-gait signals. ConclusionThe proposed CS method is effective for enhancing reconstruction performance of pulse-type physiological signals. SignificanceIt can be useful for the development of healthcare system for remote and long-term telemonitoring of pulse-type physiological signals.

GB-SAR Interferometry Based on Dimension-Reduced Compressive Sensing and Multiple Measurement Vectors Model

To reduce the data acquisition time and the high-level sidelobes produced by conventional focusing methods for ground-based synthetic aperture radar interferometry, we present a new method to provide accurate displacement maps based on the dimension-reduced compressive sensing (CS) method combined with the multiple measurement vectors (MMVs) model. The proposed CS method consists in selecting the supported area of targets, estimated by the fast conventional method with undersampled data. The following sparse reconstruction is applied only to the selected areas. The MMV-based approach allows increasing the coherence and the precision of displacement estimates. Two experiments are carried out to assess the performance of the proposed method.

Three-dimensional self-gated cardiac MR imaging for the evaluation of myocardial infarction in mouse model on a 3T clinical MR system.

PurposeTo develop and assess a three-dimensional (3D) self-gated technique for the evaluation of myocardial infarction (MI) in mouse model without the use of external electrocardiogram (ECG) trigger and respiratory motion sensor on a 3T clinical MR system.MethodsA 3D T1-weighted GRE sequence with stack-of-stars sampling trajectories was developed and performed on six mice with MIs that were injected with a gadolinium-based contrast agent at a 3T clinical MR system. Respiratory and cardiac self-gating signals were derived from the Cartesian mapping of the k-space center along the partition encoding direction by bandpass filtering in image domain. The data were then realigned according to the predetermined self-gating signals for the following image reconstruction. In order to accelerate the data acquisition, image reconstruction was based on compressed sensing (CS) theory by exploiting temporal sparsity of the reconstructed images. In addition, images were also reconstructed from the same realigned data by conventional regridding method for demonstrating the advantageous of the proposed reconstruction method. Furthermore, the accuracy of detecting MI by the proposed method was assessed using histological analysis as the standard reference. Linear regression and Bland-Altman analysis were used to assess the agreement between the proposed method and the histological analysis.ResultsCompared to the conventional regridding method, the proposed CS method reconstructed images with much less streaking artifact, as well as a better contrast-to-noise ratio (CNR) between the blood and myocardium (4.1 ± 2.1 vs. 2.9 ± 1.1, p = 0.031). Linear regression and Bland-Altman analysis demonstrated that excellent correlation was obtained between infarct sizes derived from the proposed method and histology analysis.ConclusionA 3D T1-weighted self-gating technique for mouse cardiac imaging was developed, which has potential for accurately evaluating MIs in mice at 3T clinical MR system without the use of external ECG trigger and respiratory motion sensor.

A robust compressed sensing based method for X-ray Pulsar Profile construction

X-ray pulse profile is an important physical quantity for X-ray pulsar based navigation (XPNAV). In order to improve the Signal-to-Noise-Ratio (SNR) of pulse profile and reduce computation complexity, this paper proposed an efficient pulse profile construction method based on Compressed Sensing (CS). This method first builds models for standard and integrated pulse profiles. Then, a sensing matrix based on Hadamard matrix is proposed for enhancing the percentage of successful construction. Finally, based on the sparse coefficient vector calculated by the proposed CS method, a pulse profile with high SNR will be obtained. The proposed method is validated using the real data of Crab pulsar observed by Rossi X-ray Timing Explorer (RXTE). Compared with the random 0–1 matrix and random Gaussian matrix, the pulse profile can be completely constructed by using the proposed matrix when the sampling ratio is 0.6, and compared with Epoch Folding method, the proposed CS method can improve the SNR of the pulse profile at least 15.859dB when the observation time is 1s and at least 20.33dB when the observation time is 700s. The results demonstrate the high performance of the proposed method in constructing pulse profile of high SNR with short-time observation data, which can significantly facilitate the real-time and high precision time-of-arrival (TOA) estimation and the position and velocity measurement in XPNAV.

Energy-efficient image transmission in wireless multimedia sensor networks using block-based Compressive Sensing

Wireless multimedia sensor networks (WMSNs) are capable of retrieving audio, image and video data in addition to scalar sensor data. The lifetime of these networks is mainly dependent on the communication and computational energy consumption of the node. In this paper, compressed sensing (CS)-based image transmission is proposed to reduce the energy consumption considerably with acceptable image quality. A unique encoding algorithm is formulated for the CS measurements attained with the Bernoulli measurement matrix. The proposed CS method produces better results at a lower sparsity range. Experimental analysis is performed using the Atmega 128 processor of Mica2 to compute the execution time and energy consumption in the hardware platform. The proposed CS method has a considerable reduction in energy consumption and better image quality than the conventional CS method. The simulation results show the efficiency of the proposed method.

Compressed sensing for SAR‐based wideband three‐dimensional microwave imaging system using non‐uniform fast Fourier transform

A new compressed sensing (CS) image reconstruction method is proposed for high-resolution wideband threedimensional synthetic aperture radar (SAR) imaging systems. In contrast to existing CS SAR methods that employ only a forward SAR transform in pre- or post-processing, the proposed method employs both forward SAR and reverse SAR (R-SAR) transforms in each CS iteration to improve the quality of reconstructed images. This study proposes a simple and elegant truncation repair method to combat the truncation error and utilises non-uniform fast Fourier transform to reduce the SAR and R-SAR transform errors, thereby ensuring the convergence of the CS algorithm and improving the quality of the reconstructed images. The proposed CS SAR method is applied to microwave and millimeter wave imaging systems for non-destructive evaluation of materials embedded in stratified media. Three different specimens under test are measured by conventional uniform sampling and by random under-sampling with 20% or 30% spatial points of the uniform sampling. The reconstructed images show that, albeit having much less measurement points, the proposed CS method achieves better image quality and lower background artefacts than the images reconstructed from the fullysampled uniform measurements.

A COMPRESSED SENSING BASED APPROACH FOR SUBTYPING OF LEUKEMIA FROM GENE EXPRESSION DATA

With the development of genomic techniques, the demand for new methods that can handle high-throughput genome-wide data effectively is becoming stronger than ever before. Compressed sensing (CS) is an emerging approach in statistics and signal processing. With the CS theory, a signal can be uniquely reconstructed or approximated from its sparse representations, which can therefore better distinguish different types of signals. However, the application of CS approach to genome-wide data analysis has been rarely investigated. We propose a novel CS-based approach for genomic data classification and test its performance in the subtyping of leukemia through gene expression analysis. The detection of subtypes of cancers such as leukemia according to different genetic markups is significant, which holds promise for the individualization of therapies and improvement of treatments. In our work, four statistical features were employed to select significant genes for the classification. With our selected genes out of 7,129 ones, the proposed CS method achieved a classification accuracy of 97.4% when evaluated with the cross validation and 94.3% when evaluated with another independent data set. The robustness of the method to noise was also tested, giving good performance. Therefore, this work demonstrates that the CS method can effectively detect subtypes of leukemia, implying improved accuracy of diagnosis of leukemia.