Compressive Sensing Recovery Research Articles

Improving Rare Events Detection in WSN through Cluster-Based Power Control Mechanism

Rare events detection is one of the main applications in Wireless Sensor Networks (WSN) and is currently a central concern of a vast literature. Compressed Sensing (CS) theory has been proved to be quite adapted to this objective. Although this is not the first work on applying CS to sparse events detection in WSN, it is the first to highly justify the validity of the targets detection and counting problem formulation. In order to enhance the CS recovery capacity in WSN, this work considers an approach based on a coherence reduction of the sensing matrix premised on the transmitted power control (PC). Simulation results prove that, under the constraint of equal power consumption, the detection and counting performance is improved when the proposed power control scheme is employed compared to the case without PC.

Channel Estimation in OFDM System over Fading Channels: A Compressive Sensing based Approach

As Least Square (LS) and Minimum Mean Square Error (MMSE) do not give the satisfactory result to justify the features of the wireless channel, Compressed Sensing (CS) based on Discrete Sine Transform (DST) for channel impulse response has been studied which gained much more importance in digital signal processing. We have used Compressed Sensing to estimate the channel coefficients of the fading channel; then we have performed the CS recovery algorithm to estimate the channel and to nullify the fading effect, the thus much better result are obtained in the simulation which satisfies the better performance of the system as compared to the traditional method. Simulation results show a considerable improvement in Bit Error Rate (BER) performance on employing the Compressed Sensing approach in comparison to LS and MMSE. The improvement of the order of 2-9 dB of SNR is for a particular value of BER.

Compressed sensing magnetic resonance imaging based on dictionary updating and block‐matching and three‐dimensional filtering regularisation

Compressed sensing (CS) enables that magnetic resonance (MR) images can be exactly reconstructed from undersampled k-space data by exploiting the sparsity of MR images in some analytical sparsifying transform or some dictionary. Recent methods are exploiting adaptive patch-based dictionaries for image recovery by alternating between dictionary learning step and image reconstruction step. In this study, the authors propose a novel MR image reconstruction algorithm utilising dictionary updating, which consists of three steps: sparse coding, dictionary updating and image reconstruction. In the dictionary updating step, they perform a first-order series expansion for dictionary–coefficient matrix product via recursive method, and propose an efficient method to solve the new dictionary updating problem. To improve the reconstruction quality, the proposed block-matching and three-dimensional (3D) filtering regularisation is incorporated into the authors’ image CS recovery, which can combine the self-similarities within the image, the 3D transform sparsity and the local sparsity into image recovery process. Experimental simulations demonstrate their proposed algorithms can obtain better reconstruction quality than the previous CS algorithms.

Subband-dependent compressed sensing in local CT reconstruction

To achieve high-quality low-dose computed tomography (CT) images, compressed sensing (CS)-based CT reconstructions recover the images using fewer projections; and wavelet inverse Radon algorithms recover wavelet subbands of CT images from locally scanned projections. Moreover, it has been shown that subband CS algorithms accelerate the convergence of the CS recovery methods. Here, we propose an innovative combination of a newly developed accelerated wavelet inverse Radon transform and non-convex CS formulation to recover the wavelet subbands of CT images from a reduced number of locally scanned X-ray projections. Fast pseudo-polar Fourier transform is used to decrease the computational complexity of CS recovery. Therefore, the proposed method, denoted by AWiR-SISTA, reduces the radiation dose by simultaneously decreasing the X-ray exposure area and the number of projections, decreases the CS computational complexity, and accelerates the CS recovery convergence rate. Phantom-based simulations show that high-quality ultra-low-dose local CT images can be reconstructed using the proposed method in few seconds, without numerical optimization. Clinical chest CT images are used to demonstrate the practical potential of the method.

Direction-of-arrival estimation for co-located multiple-input multiple-output radar using structural sparsity Bayesian learning**Project supported by the National Natural Science Foundation of China (Grant Nos. 61071163, 61271327, and 61471191), the Funding for Outstanding Doctoral Dissertation in Nanjing University of Aeronautics and Astronautics, China (Grant No. BCXJ14-08), the Funding of Innovation Program for Graduate Education of Jiangsu Province, China (Grant No. KYLX 0277),

This paper addresses the direction of arrival (DOA) estimation problem for the co-located multiple-input multiple-output (MIMO) radar with random arrays. The spatially distributed sparsity of the targets in the background makes compressive sensing (CS) desirable for DOA estimation. A spatial CS framework is presented, which links the DOA estimation problem to support recovery from a known over-complete dictionary. A modified statistical model is developed to accurately represent the intra-block correlation of the received signal. A structural sparsity Bayesian learning algorithm is proposed for the sparse recovery problem. The proposed algorithm, which exploits intra-signal correlation, is capable being applied to limited data support and low signal-to-noise ratio (SNR) scene. Furthermore, the proposed algorithm has less computation load compared to the classical Bayesian algorithm. Simulation results show that the proposed algorithm has a more accurate DOA estimation than the traditional multiple signal classification (MUSIC) algorithm and other CS recovery algorithms.

Hierarchical frame based spatial–temporal recovery for video compressive sensing coding

In this paper, the divide-and-conquer based hierarchical video compressive sensing (CS) coding framework is proposed, in which the whole video is independently divided into non-overlapped blocks of the hierarchical frames. The proposed framework outperforms the traditional framework through the better exploitation of frames correlation with reference frames, the unequal sample subrates setting among frames in different layers and the reduction of the error propagation. At the encoder, compared with the video/frame based CS, the proposed hierarchical block based CS matrix can be easily implemented and stored in hardware. Each measurement of the block in a different hierarchical frame is obtained with the different sample subrate. At the decoder, by considering the spatial and temporal correlations of the video sequence, a spatial–temporal sparse representation based recovery is proposed, in which the similar blocks in the current frame and these recovered reference frames are organized as a spatial–temporal group unit to be represented sparsely. Finally, the recovery problem of video compressive sensing coding can be solved by adopting the split Bregman iteration. Experimental results show that the proposed method achieves better performance against many state-of-the-art still-image CS and video CS recovery algorithms.

A CS Recovery Algorithm for Model and Time Delay Identification of MISO-FIR Systems

This paper considers identifying the multiple input single output finite impulse response (MISO-FIR) systems with unknown time delays and orders. Generally, parameters, orders and time delays of an MISO system are separately identified from different algorithms. In this paper, we aim to perform the model identification and time delay estimation simultaneously from a limited number of observations. For an MISO-FIR system with many inputs and unknown input time delays, the corresponding identification model contains a large number of parameters, requiring a great number of observations for identification and leading to a heavy computational burden. Inspired by the compressed sensing (CS) recovery theory, a threshold orthogonal matching pursuit algorithm (TH-OMP) is presented to simultaneously identify the parameters, the orders and the time delays of the MISO-FIR systems. The proposed algorithm requires only a small number of sampled data compared to the conventional identification methods, such as the least squares method. The effectiveness of the proposed algorithm is verified by simulation results.

Palatal Patterns Based RGB Technique for Personal Identification

The main contribution of this paper is using compressive sensing (CS) theory for crypto steganography system to increase both the security and the capacity and preserve the cover image imperceptibility. For CS implementation, the discrete Cosine transform (DCT) as sparse domain and random sensing matrix as measurement domain are used. We consider 7 MRI images as the secret and 7 gray scale test images as cover. In addition, three sampling rates for CS are used. The performance of seven CS recovery algorithms in terms of image imperceptibility, achieved peak signal to noise ratio (PSNR), and the computation time are compared with other references. We showed that the proposed crypto steganography system based on CS works properly even though the secret image size is greater than the cover image.

Treelet-Based Clustered Compressive Data Aggregation for Wireless Sensor Networks

Compressive sensing (CS)-based data aggregation has become an increasingly important research topic for large-scale wireless sensor networks since conventional data aggregations are shown to be inefficient and unstable in handling huge data traffic. However, for CS-based techniques, the discrete cosine transform, which is the most widely adopted sparsification basis, cannot sufficiently sparsify real-world signals, which are unordered due to random sensor distribution, thus weakening advantages of CS. In this paper, an energy-efficient CS-based scheme, which is called “treelet-based clustered compressive data aggregation” (T-CCDA), is proposed. Specifically, as a first step, treelet transform is adopted as a sparsification tool to mine sparsity from signals for CS recovery. This approach not only enhances the performance of CS recovery but reveals localized correlation structures among sensor nodes as well. Then, a novel clustered routing algorithm is proposed to further facilitate energy saving by taking advantage of the correlation structures, thus giving our T-CCDA scheme. Simulation results show that the proposed scheme outperforms other reference approaches in terms of communication overhead per reconstruction error for adopted data sets.

Efficient Compressed Sensing SENSE pMRI Reconstruction With Joint Sparsity Promotion.

The theory and techniques of compressed sensing (CS) have shown their potential as a breakthrough in accelerating k-space data acquisition for parallel magnetic resonance imaging (pMRI). However, the performance of CS reconstruction models in pMRI has not been fully maximized, and CS recovery guarantees for pMRI are largely absent. To improve reconstruction accuracy from parsimonious amounts of k-space data while maintaining flexibility, a new CS SENSitivity Encoding (SENSE) pMRI reconstruction framework promoting joint sparsity (JS) across channels (JS CS SENSE) is proposed in this paper. The recovery guarantee derived for the proposed JS CS SENSE model is demonstrated to be better than that of the conventional CS SENSE model and similar to that of the coil-by-coil CS model. The flexibility of the new model is better than the coil-by-coil CS model and the same as that of CS SENSE. For fast image reconstruction and fair comparisons, all the introduced CS-based constrained optimization problems are solved with split Bregman, variable splitting, and combined-variable splitting techniques. For the JS CS SENSE model in particular, these techniques lead to an efficient algorithm. Numerical experiments show that the reconstruction accuracy is significantly improved by JS CS SENSE compared with the conventional CS SENSE. In addition, an accurate residual-JS regularized sensitivity estimation model is also proposed and extended to calibration-less (CaL) JS CS SENSE. Numerical results show that CaL JS CS SENSE outperforms other state-of-the-art CS-based calibration-less methods in particular for reconstructing non-piecewise constant images.

A Douglas-Rachford Splitting Approach to Compressed Sensing Image Recovery Using Low-Rank Regularization.

In this paper, we study the compressed sensing (CS) image recovery problem. The traditional method divides the image into blocks and treats each block as an independent sub-CS recovery task. This often results in losing global structure of an image. In order to improve the CS recovery result, we propose a nonlocal (NL) estimation step after the initial CS recovery for denoising purpose. The NL estimation is based on the well-known NL means filtering that takes an advantage of self-similarity in images. We formulate the NL estimation as the low-rank matrix approximation problem, where the low-rank matrix is formed by the NL similarity patches. An efficient algorithm, nonlocal Douglas-Rachford (NLDR), based on Douglas-Rachford splitting is developed to solve this low-rank optimization problem constrained by the CS measurements. Experimental results demonstrate that the proposed NLDR algorithm achieves significant performance improvements over the state-of-the-art in CS image recovery.

Dictionary learning for data recovery in positron emission tomography

Compressed sensing (CS) aims to recover images from fewer measurements than that governed by the Nyquist sampling theorem. Most CS methods use analytical predefined sparsifying domains such as total variation, wavelets, curvelets, and finite transforms to perform this task. In this study, we evaluated the use of dictionary learning (DL) as a sparsifying domain to reconstruct PET images from partially sampled data, and compared the results to the partially and fully sampled image (baseline).A CS model based on learning an adaptive dictionary over image patches was developed to recover missing observations in PET data acquisition. The recovery was done iteratively in two steps: a dictionary learning step and an image reconstruction step. Two experiments were performed to evaluate the proposed CS recovery algorithm: an IEC phantom study and five patient studies. In each case, 11% of the detectors of a GE PET/CT system were removed and the acquired sinogram data were recovered using the proposed DL algorithm. The recovered images (DL) as well as the partially sampled images (with detector gaps) for both experiments were then compared to the baseline. Comparisons were done by calculating RMSE, contrast recovery and SNR in ROIs drawn in the background, and spheres of the phantom as well as patient lesions.For the phantom experiment, the RMSE for the DL recovered images were 5.8% when compared with the baseline images while it was 17.5% for the partially sampled images. In the patients’ studies, RMSE for the DL recovered images were 3.8%, while it was 11.3% for the partially sampled images. Our proposed CS with DL is a good approach to recover partially sampled PET data. This approach has implications toward reducing scanner cost while maintaining accurate PET image quantification.

Compressive Sensing With Prior Support Quality Information and Application to Massive MIMO Channel Estimation With Temporal Correlation

In this paper, we consider the problem of compressive sensing (CS) recovery with a prior support and the prior support quality information available. Different from classical works which exploit prior support blindly, we shall propose novel CS recovery algorithms to exploit the prior support adaptively based on the quality information. We analyze the distortion bound of the recovered signal from the proposed algorithm and we show that a better quality prior support can lead to better CS recovery performance. We also show that the proposed algorithm would converge in $\mathcal{O}\left(\log\mbox{SNR}\right)$ steps. To tolerate possible model mismatch, we further propose some robustness designs to combat incorrect prior support quality information. Finally, we apply the proposed framework to sparse channel estimation in massive MIMO systems with temporal correlation to further reduce the required pilot training overhead.

Compressively Sampled MR Image Reconstruction Using Hyperbolic Tangent-Based Soft-Thresholding

The application of compressed sensing (CS) to magnetic resonance (MR) images utilizes the transformed domain sparsity to enable the reconstruction from an under-sampled k-space (Fourier) data using a non-linear recovery algorithm. In order to estimate the missing k-space data from the partial Fourier samples, the reconstruction algorithms minimize an objective function based on mixed l1 − l2 norms. Iterative-shrinkage algorithms, such as parallel coordinate descent (PCD) and separable surrogate functional, provide an efficient numerical technique to minimize the l1-regularized least square optimization problem. These algorithms require a thresholding step to induce sparsity in the solution, which is an essential requirement of the CS recovery. This paper introduces a novel soft-thresholding method based on the hyperbolic tangent function. It has been shown that by using the proposed thresholding function in the sparsifying domain and a data consistency step in the k-space, the iterative-shrinkage algorithms can be used effectively to recover the under-sampled MR images. For the purpose of demonstration, we use the proposed soft-thresholding and data consistency with the PCD algorithm and compare its performance with the conventional PCD, projection onto convex sets and low-resolution reconstruction methods. The metrics used to compare the various algorithms are the artifact power, the peak signal-to-noise ratio, the correlation and the structural similarity index. The experimental results are validated using Shepp–Logan phantom image as well as real human head MR images taken from the MRI scanner at St. Mary’s Hospital, London.

Sequential Compressed Sensing With Progressive Signal Reconstruction in Wireless Sensor Networks

This paper considers sequential compressed acquisition and progressive reconstruction of spatially and temporally correlated sensor data streams in wireless sensor networks (WSNs) via compressed sensing (CS). We develop a sequential framework based on sliding window processing, in which the sink can efficiently reconstruct the current sensors' readings from a sequence of periodically delivered CS measurements by exploiting the joint compressibility via Kronecker sparsifying bases. Specifically, we derive a recursive CS recovery method which utilizes the estimates from the preceding decoding instants via a regularization and reweighted ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -minimization to improve the reconstruction accuracy of sensor data streams while reducing the necessary communications. As beneficial features, the method produces estimates for the current sensors' readings without additional decoding delay, and, via adjusting the window size, it can dynamically trade-off between the CS recovery performance and decoding complexity. Numerical results show that our proposed method achieves higher reconstruction accuracy with a smaller number of required transmissions, and with lower decoding delay and complexity as compared to those of the state of the art CS methods.

Recovery From Linear Measurements With Complexity-Matching Universal Signal Estimation

We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal during recovery, the signal structure that can be leveraged is often not known a priori. In this paper, we consider universal CS recovery, where the statistics of a stationary ergodic signal source are estimated simultaneously with the signal itself. Inspired by Kolmogorov complexity and minimum description length, we focus on a maximum a posteriori (MAP) estimation framework that leverages universal priors to match the complexity of the source. Our framework can also be applied to general linear inverse problems where more measurements than in CS might be needed. We provide theoretical results that support the algorithmic feasibility of universal MAP estimation using a Markov chain Monte Carlo implementation, which is computationally challenging. We incorporate some techniques to accelerate the algorithm while providing comparable and in many cases better reconstruction quality than existing algorithms. Experimental results show the promise of universality in CS, particularly for low-complexity sources that do not exhibit standard sparsity or compressibility.

Accurate OFDM Sparse Channel Estimation by Optimal Deterministic Pilot Pattern

ABSTRACTIn orthogonal frequency division multiplexing (OFDM) systems the wireless channel impulse response can be modelled as a sparse vector. Recently emerged compressed sensing (CS) theory can be used for reconstruction and estimation of unknown non-zero channel taps. In CS-based channel estimation, the number of pilot sub-carriers can be decreased, so the spectral efficiency of the system can be increased. The efficiency and performance of sparse channel estimation (SCE) highly depend on the measurement matrix, which in turn depends on the pilot pattern. In this paper, based on minimization of the correlation between all columns of measurement matrix, a new criterion is proposed. In addition, a deterministic pilot pattern optimization algorithm for OFDM SCE is introduced. Greedy CS recovery methods, such as orthogonal matching pursuit (OMP) and regularized OMP are used for estimation of the channel taps. The simulation results confirm the efficiency and accuracy of proposed criterion and optimization algorithm in terms of mean square error.

Fractal compressed sensing imaging with sparse difference based on fractal and entropy recognition

Compressed sensing (CS) is a topic of great interest in many research fields, especially image processing. However, in the traditional CS framework, one disadvantage is that the computational cost of sparse representation (SR) is too high to meet basic application requirements. Another is that l1-norm minimisation, as the object function of CS recovery, is unsuitable for the approximation of image details. Therefore, this paper presents a novel fractal CS (FCS) framework for digital imaging. The FCS framework is basically as follows: first, the sparse difference (SD) is used to solve the hard problem of sparse representation; then, acquisition of SD is based on the results of classification under a combined fractal and entropy feature space; finally, fractal minimisation is used instead of l1-norm minimisation as the object function to realise high-quality CS recovery of image details. Several experiments show the feasibility and dependability of the FCS imaging framework.

Compressed Sensing Methods for DNA Microarrays, RNA Interference, and Metagenomics

Compressed sensing (CS) is a sparse signal sampling methodology for efficiently acquiring and reconstructing a signal from relatively few measurements. Recent work shows that CS is well-suited to be applied to problems in genomics, including probe design in microarrays, RNA interference (RNAi), and taxonomic assignment in metagenomics. The principle of using different CS recovery methods in these applications has thus been established, but a comprehensive study of using a wide range of CS methods has not been done. For each of these applications, we apply three hitherto unused CS methods, namely, l1-magic, CoSaMP, and l1-homotopy, in conjunction with CS measurement matrices such as randomly generated CS m matrix, Hamming matrix, and projective geometry-based matrix. We find that, in RNAi, the l1-magic (the standard package for l1 minimization) and l1-homotopy methods show significant reduction in reconstruction error compared to the baseline. In metagenomics, we find that l1-homotopy as well as CoSaMP estimate concentration with significantly reduced time when compared to the GPSR and WGSQuikr methods.

Row-sparse blind compressed sensing for reconstructing multi-channel EEG signals

This communication concentrates on application of blind compressed sensing (BCS) framework for reconstruction of multichannel electroencephalograph (EEG) signal for wireless body area networks (WBANs). Compressed sensing (CS) based techniques employ a known sparsifying basis (wavelet/DCT/Gabor). BCS learns the sparsifying dictionary while recovering the signal. The BCS framework was proposed for recovering sparse signals. A recent work showed that, EEG signals can be better recovered by exploiting inter-channel correlation. This led to a row-sparse recovery problem. In this work, we modify the basic BCS framework for recovering row-sparse signal ensembles – this leads to better EEG reconstruction accuracy compared to prior CS recovery methods. The success of this technique enables reducing the energy expenditure of the sensor nodes of the WBAN.