Compressed Sensing Reconstruction Algorithm Research Articles

Boosting Compressed Sensing Using Local Measurements and Sliding Window Reconstruction

In the framework of compressed sensing, image data is measured using less measurements than the total number of pixels. Each measurement consists of a (random) linear combination of all pixels. Since image data is approximately sparse in an appropriate transform domain, a reasonable reconstruction is possible for many measurement matrices, especially for i.i.d. Gaussian measurement matrices. In a seemingly different field, non-regular sampling techniques such as three-quarter sampling have shown promising results to enhance the resolution of an imaging sensor by effectively sub-sampling a higher resolution image. Here, the measurements can be described as linear combinations of only three pixels, which can also be seen as a (spectral) compressed sensing measurement. Since each measurement is spatially localized, the reconstruction can be performed in overlapping sliding windows. In this work, we show that compressed sensing reconstruction algorithms can greatly benefit from such an overlapping sliding window reconstruction. Compared to conventional block-wise compressed sensing with i.i.d. Gaussian measurement matrices, the reconstruction quality in terms of the PSNR increases up to +5dB using small, local i.d.d. Gaussian measurement blocks. Additionally, we propose a local joint sparse deconvolution and extrapolation (L-JSDE) to reconstruct images from arbitrary local measurements. For several applications with local measurements we show that L-JSDE increases the PSNR by +2.2dB relative to conventional block-wise i.i.d. Gaussian measurements reconstructed with the state-of-the-art reconstruction algorithm D-AMP using the same overall sampling density.

Hybrid-Weighted Total Variation and Nonlocal Low-Rank-Based Image Compressed Sensing Reconstruction

To reconstruct natural images from compressed sensing (CS) measurements accurately and effectively, a CS image reconstruction algorithm based on hybrid-weighted total variation (HWTV) and nonlocal low-rank (NLR) is proposed. It considers the local smoothness and nonlocal self-similarity (NSS) in image, improves traditional hybrid total variation (TV) model, and constructs a new edge detection operator with mean curvature to adaptively select the TV. The HWTV combines the advantages of first-order TV and second-order TV to preserve the edges of the image and avoid the staircase effect in the smooth areas. And NLR can effectively reduce the redundant information and retain the structural information of the image. In addition, the proposed algorithm constructs prior regularization terms with improved HWTV model and NLR model, and utilizes soft threshold function and smooth but non-convex function to solve the TV and low-rank optimization problems, respectively. Finally, the alternative direction multiplier method (ADMM) iterative strategy is used to separate the target model into several sub-problems, and the most efficient methods are adopted to solve each sub-problem. Experimental results show that, compared with the state-of-the-art CS reconstruction algorithms, the proposed algorithm can achieve higher reconstruction quality, especially in the case of low sampling rates.

Adaptive Block Compressive Sensing: Toward a Real-Time and Low-Complexity Implementation

Adaptive block-based compressive sensing (ABCS) algorithms are studied in the context of the practical realization of compressive sensing on resource-constrained image and video sensing platforms that use single-pixel cameras, multi-pixel cameras or focal plane processing sensors. In this paper, we introduce two novel ABCS algorithms that are suitable for compressively sensing images or intra-coded video frames. Both use deterministic 2D-DCT dictionaries when sensing the images instead of random dictionaries. The first uses a low number of compressive measurements to compute the block boundary variation (BBV) around each image block, from which it estimates the number of 2D-DCT transform coefficients to measure from each block. The second uses a low number of DCT domain (DD) measurements to estimate the total number of transform coefficients to capture from each block. The two algorithms permit reconstruction in real time, averaging 8 ms and 26 ms for 256x256 and 512x512 greyscale images, respectively, using a simple inverse 2D-DCT operation without requiring GPU acceleration. Furthermore, we show that an iterative compressive sensing reconstruction algorithm (IDA), inspired by the denoising-based approximate message passing algorithm, can be used as a post-processing, quality enhancement technique. IDA trades off real-time operation to yield performance improvement over state-of-the-art GPU-assisted algorithms of 1.31 dB and 0.0152 in terms of PSNR and SSIM, respectively. It also exceeds the PSNR performance of a state-of-the-art deep neural network by 0.4 dB and SSIM by 0.0126.

Compressive Sensing in Wireless Powered Network: Regarding Transmission as Measurement

With large numbers of nodes applied in wireless powered network (WPN), it becomes a great challenge for the orthogonal multi-access (OMA) schemes to collect data. In this letter, a novel WPN based on compressive sensing (CS) is proposed, which utilizes the sparsity of data and regards transmission as measurement. It collects the coherent measurements of sensing data from the concurrent transmission of all nodes and then recovers the sensing data by CS reconstruction algorithm, which indeed accelerates data collection. Compared with the WPN based on OMA, the proposed WPN is always superior on delay and owns higher collecting rate with the conditions of linear and sub-linear sparsity case satisfied. Further, when the allocation strategy is adjustable, a joint optimization of time and power is proposed based on maximizing the collecting rate. Simulation results illustrate the superiority of the proposed WPN.

Statistical Sparse Channel Modeling for Measured and Simulated Wireless Temporal Channels

Time-domain wireless channels are generally modeled by Tapped Delay Line (TDL) model and its variants. These models are not effective for channel representation and estimation when the number of multipath taps is large. Compressive sensing (CS) provides a powerful tool for sparse channel modeling and estimation. Most of the research has been focusing on sparse channel estimation, while sparse channel modeling (SCM) is rarely considered for centimetre-wave channels. In this paper, we investigate statistical sparse channel modeling, using both measured and simulated channels over a frequency range of 6 to 8.5 GHz. We first introduce the triple equilibrium principle to explore the trade-off between sparsity, modeling accuracy, and algorithm complexity in SCM, and provide a methodology for characterizing the sparsity of time-domain channels using single-measurement-vector compressive sensing algorithms. Using mainly the selected wavelet dictionary and various CS reconstruction (aka recovery) algorithms, we then present comprehensive statistical sparse channel models, including channel sparsity, magnitude decaying profile, sparse coefficient distribution and atomic index distribution. Connections between the parameters of conventional TDL and sparse channel models are mathematically established. We also propose three methods for generating simulated channels from the developed sparse channel models, which validates their effectiveness.

A novel method to remove impulse noise from atomic force microscopy images based on Bayesian compressed sensing.

A novel method based on Bayesian compressed sensing is proposed to remove impulse noise from atomic force microscopy (AFM) images. The image denoising problem is transformed into a compressed sensing imaging problem of the AFM. First, two different ways, including interval approach and self-comparison approach, are applied to identify the noisy pixels. An undersampled AFM image is generated by removing the noisy pixels from the image. Second, a series of measurement matrices, all of which are identity matrices with some rows removed, are constructed by recording the position of the noise-free pixels. Third, the Bayesian compressed sensing reconstruction algorithm is applied to recover the image. Different from traditional compressed sensing reconstruction methods in AFM, each row of the AFM image is reconstructed separately in the proposed method, which will not reduce the quality of the reconstructed image. The denoising experiments are conducted to demonstrate that the proposed method can remove the impulse noise from AFM images while preserving the details of the image. Compared with other methods, the proposed method is robust and its performance is not influenced by the noise density in a certain range.

DeepBinaryMask: Learning a binary mask for video compressive sensing

In this paper, we propose an encoder-decoder neural network model referred to as DeepBinaryMask for video compressive sensing. In video compressive sensing one frame is acquired using a set of coded masks (sensing matrix) from which a number of video frames, equal to the number of coded masks, is reconstructed. The proposed framework is an end-to-end model where the sensing matrix is trained along with the video reconstruction. The encoder maps a video block to compressive measurements by learning the binary elements of the sensing matrix. The decoder is trained to map the measurements from a video patch back to a video block via several hidden layers of a Multi-Layer Perceptron network. The predicted video blocks are stacked together to recover the unknown video sequence. The reconstruction performance is found to improve when using the trained sensing mask from the network as compared to other mask designs such as random, across a wide variety of compressive sensing reconstruction algorithms. Finally, our analysis and discussion offers insights into understanding the characteristics of the trained mask designs that lead to the improved reconstruction quality.

Adaptive block forward and backward stagewise orthogonal matching pursuit algorithm applied to rolling bearing fault signal reconstruction.

In the process of block compressed sensing (CS) applied to the rolling bearing fault signal, the reconstruction accuracy of the signal is low due to the large difference in sparsity between blocks and the unreasonable components of reconstruction support set, which affects the overall reconstruction effect of the signal. To improve the signal reconstruction results, forward and backward stagewise orthogonal matching pursuit (FBStOMP) based on the adaptive block method is proposed. First, to equalize the sparsity of each block signal, the fault signal is divided into blocks according to the adaptive block length, which is obtained by the short-time autocorrelation algorithm. Then, the K-singular value decomposition algorithm is used to train the sparse dictionary to obtain a better sparse effect. Finally, the FBStOMP algorithm is proposed. The atom backtracking and screening process is added in the reconstruction process to improve the possibility that all the effective atoms can be selected into the support set. The experimental analysis of the simulation signal and bearing fault signal show that, compared with the traditional CS reconstruction algorithm, the adaptive block-FBStOMP algorithm proposed in the paper can effectively improve the reconstruction accuracy of the bearing fault signal.

Inverse synthetic aperture radar imaging using complex‐value deep neural network

As compared with traditional ISAR imaging methods, the compressive sensing (CS)-based imaging methods can obtain high-quality images using much less under-sampled data. However, the availability or appropriateness of the sparse representation of the target scene and the relatively low computational efficiency of image reconstruction algorithms limit the performance and application of the CS-based ISAR imaging methods. In recent years, the deep learning technology has been applied in many fields and achieved outstanding performance in image classification, image reconstruction etc. DL implements the tasks using the deep neural network (DNN), which composes multiple hidden layers and non-linear activation layer. In this study, a novel ISAR imaging method that uses a complex-value deep neural network (CV-DNN) to perform the image formation using under-sampled data is proposed. The CV-DNN architecture can extract and exploit the sparse feature of the target image extremely well by multilayer non-linear processing. The experimental results show that the proposed CV-DNN-based ISAR imaging method can provide better shape reconstruction of target with less data than state-of-the-art CS reconstruction algorithms and improve the imaging efficiency obviously.

Modified meta-heuristic-oriented compressed sensing reconstruction algorithm for bio-signals

In signal processing, several applications necessitate the efficient reprocessing and representation of data. Compression is the standard approach that is used for effectively representing the signal. In modern era, many new techniques are developed for compression at the sensing level. Compressed sensing (CS) is a rising domain that is on the basis of disclosure, which is a little gathering of a sparse signal’s linear projections including adequate information for reconstruction. The sampling of the signal is permitted by the CS at a rate underneath the Nyquist sampling rate while relying on the sparsity of the signals. Additionally, the reconstruction of the original signal from some compressive measurements can be authentically exploited using the varied reconstruction algorithms of CS. This paper intends to exploit a new compressive sensing algorithm for reconstructing the signal in bio-medical data. For this purpose, the signal can be compressed by undergoing three stages: designing of stable measurement matrix, signal compression and signal reconstruction. In this, the compression stage includes a new working model that precedes three operations. They are signal transformation, evaluation of [Formula: see text] and normalization. In order to evaluate the theta ([Formula: see text]) value, this paper uses the Haar wavelet matrix function. Further, this paper ensures the betterment of the proposed work by influencing the optimization concept with the evaluation procedure. The vector coefficient of Haar wavelet function is optimally selected using a new optimization algorithm called Average Fitness-based Glowworm Swarm Optimization (AF-GSO) algorithm. Finally, the performance of the proposed model is compared over the traditional methods like Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Firefly (FF), Crow Search (CS) and Glowworm Swarm Optimization (GSO) algorithms.

A Distributed Compressive Data Gathering Framework For Mobile Crowdsensing

Existing work on data gathering in mobile crowdsensing (MCS) usually assumes that the motion of the participants is either known or predictable via a mobility model. As such, the organizers can tell them when/where to sense, ensuring the data can be gathered from the target area with a minimized number of participants. Knowing exactly where the participants go, however, is not trivial, since the movements of the participants are in fact autonomous and random. In this paper, we investigate a common compressive data gathering framework for MCS, without trying to predict how a specific participant moves. We notice a key observation: while the participants move autonomously in the target sensing area, each trajectory itself provides a random, and thus valuable coverage for a sensing task. With compressive sensing (CS), these random trajectories can be utilized to exploit the spatio-temporal data correlation. Given this, we first introduce a novel idea of virtual sensor network to define the target sensing area, and then propose a distributed CS-based encoding algorithm to compress the data in the target area such that the number of the participants involved in data gathering can be reduced. We further propose a round-based CS reconstruction algorithm to exploit the inter-round data correlation and improve the accuracy of the data reconstruction. Experimental results using real sensor readings show that the proposed scheme achieves better performance than existing ones with dedicated sensor networks.

A Portable Ultrasound Imaging System Utilizing Deep Generative Learning-Based Compressive Sensing On Pre-Beamformed RF Signals.

Recent advances in the unsupervised and generative models of deep learning have shown promise for application in biomedical signal processing. In this work, we present a portable resource-constrained ultrasound (US) system trained using Variational Autoencoder (VAE) network which performs compressive-sensing on pre-beamformed RF signals. The encoder network compresses the RF data, which is further transmitted to the cloud. At the cloud, the decoder reconstructs back the ultrasound image, which can be used for inferencing. The compression is done with an undersampling ratio of 1/2, 1/3, 1/5 and 1/10 without significant loss of the resolution. We also compared the model by state-of-the-art compressive-sensing reconstruction algorithm and it shows significant improvement in terms of PSNR and MSE. The innovation in this approach resides in training with binary weights at the encoder, shows its feasibility for the hardware implementation at the edge. In the future, we plan to include our field-programmable gate array (FPGA) based design directly interfaced with sensors for real-time analysis of Ultrasound images during medical procedures.

WSNs Compressed Sensing Signal Reconstruction Based on Improved Kernel Fuzzy Clustering and Discrete Differential Evolution Algorithm

To reconstruct compressed sensing (CS) signal fast and accurately, this paper proposes an improved discrete differential evolution (IDDE) algorithm based on fuzzy clustering for CS reconstruction. Aiming to overcome the shortcomings of traditional CS reconstruction algorithm, such as heavy dependence on sparsity and low precision of reconstruction, a discrete differential evolution (DDE) algorithm based on improved kernel fuzzy clustering is designed. In this algorithm, fuzzy clustering algorithm is used to analyze the evolutionary population, which improves the pertinence and scientificity of population learning evolution while realizing effective clustering. The differential evolutionary particle coding method and evolutionary mechanism are redefined. And the improved fuzzy clustering discrete differential evolution algorithm is applied to CS reconstruction algorithm, in which signal with unknown sparsity is considered as particle coding. Then the wireless sensor networks (WSNs) sparse signal is accurately reconstructed through the iterative evolution of population. Finally, simulations are carried out in the WSNs data acquisition environment. Results show that compared with traditional reconstruction algorithms such as StOMP, the reconstruction accuracy of the algorithm proposed in this paper is improved by 36.4-51.9%, and the reconstruction time is reduced by 15.1-31.3%.

Reconstruction for block-based compressive sensing of image with reweighted double sparse constraint

Block compressive sensing reduces the computational complexity by dividing the image into multiple patches for processing, but the performance of the reconstruction algorithm is decreased. Generally, the reconstruction algorithm improves the quality of reconstructed image by adding various constraints and regularization terms, namely prior information. In this paper, a reweighted double sparse constraint reconstruction model which combines the residual sparsity and ℓ1 regularization term is proposed. The residual sparsity aims to exploit the nonlocal similarity of image patches, and the ℓ1 regularization term is used to utilize the local sparsity of image patches. The resulting model is solved under the frame of split Bregman iteration (SBI). A large number of experiments show that the algorithm in this paper can reconstruct the original image efficiently and is comparable to the current representative compressive sensing reconstruction algorithm.

Comparison of compressed sensing reconstruction algorithms for 31P magnetic resonance spectroscopic imaging

Phosphorus MR spectroscopy and spectroscopic imaging (31P-MRS/MRSI) provide information about energy metabolism, membrane degradation and pH in vivo. In spite of their proven utility, 31P-MRS/MRSI are not often used primarily because of the challenges imposed by the low sensitivity and low concentration of metabolites leading to low signal to noise ratio (SNR), coarse spatial resolution and prolonged acquisition time. More recently there has been considerable interest in compressed sensing as an acceleration method for MR signal acquisition. This approach takes advantage of the intrinsic sparsity of the spectral data. In this work, we present a 31P-MRSI sequence that combines a flyback EPSI trajectory and compressed sensing, and we compared two different reconstruction methods, L1 norm minimization and low rank Hankel matrix completion. Our phantom results showed good preservation of spectral quality for both ×2.0 and ×3.0 acceleration factors, using both CS reconstruction methods. However, in vivo 31P-MRS brain data showed the low rank reconstruction approach was most suitable. Overall, this study shows the feasibility of combining a flyback EPSI trajectory and compressed sensing in the acquisition of 31P-MRSI as well as the better suitability of a low rank reconstruction approach.

An Efficient FPGA Implementation of Orthogonal Matching Pursuit With Square-Root-Free QR Decomposition

Compressive sensing (CS) is a novel signal processing technology to reconstruct the sparse signal at sub-Nyquist rate. Orthogonal matching pursuit (OMP) is one of the most widely used signal reconstruction algorithms. However, the least square problem (LSP) in OMP algorithm limits its performance. This paper presents a fast CS reconstruction algorithm implemented on field-programmable gate array (FPGA) using OMP. The proposed algorithm adopts an incremental QR decomposition (QRD) method to efficiently solve the LSP. The incremental QRD is further optimized to eliminate the square root operation to facilitate hardware implementation. The proposed architecture avoiding the complex square root unit mainly consists of some more basic computing units, where the computing process is broken down into several simple operations to map to the corresponding hardware for pipelining. The proposed implementation based on Xilinx Kintex-7 FPGA exploits the parallelism by a well-planned workload schedule and reaches an optimal tradeoff between the latency and frequency. The experimental results demonstrate that the proposed architecture can run at a frequency of 210 MHz with a reconstruction time of 238 $\mu \text{s}$ for 36-sparse 1024-length signal, which improves the signal reconstruction speed by $1.43\times $ compared to the state-of-the-art implementations.

Imaging through coda wave interferometryvia sparse reconstruction

The coda wave interferometry is widely used in the fields of geophysics and material science. As an extension of coda wave interferometry, imaging through coda wave interferometry is a technique to obtain the spatial distribution of small velocity perturbations within a scattering medium by using time lapse and sensitivity kernels in the diffusion approximation. However, imaging through coda wave interferometry is essentially an undetermined problem without definite solution, resulting in some difficulties in accurately locating small velocity perturbations within a scattering medium. Meanwhile, compressed sensing has been used in many physical imaging systems in recent years. In this paper, we present an imaging method through coda wave interferometry to solve aforementioned problems by using sparse reconstruction algorithm which is involved in compressed sensing theory. The sparsity of velocity perturbation in its space distribution is taken into account in the proposed method. Firstly, the undetermined equation for inversion imaging is established based on the time-lapse data obtained by coda wave interferometry and the sensitivity kernel matrix in the diffusion approximation. Secondly, the inversion equation is reconstructed by using the sparse transformation within the framework of compressed sensing theory. Finally, the minimization of <i>l</i><sub>1</sub> norm is solved by the compressed sensing reconstruction algorithm, and the imaginary part for the spatial distribution of velocity perturbations is subsequently obtained. This method can accurately capture the spatial locations and ranges of both single velocity perturbation and multiple velocity perturbations in scattering medium with high computational efficiency. The numerical simulations are compared with the results from the existing linear least squares method, demonstrating that the proposed method can avoid the complex parameter determination operation, thus greatly improving the accuracy of inversion images, and also significantly reducing the calculating time.

A Fast and Accurate Compressed Sensing Reconstruction Algorithm for ISAR Imaging

Compressed sensing (CS) has provided a novel way for inverse synthetic aperture radar (ISAR) imaging. In CS based ISAR imaging, the continuous range-Doppler plane is divided into grids, and the strong scattering points are assumed on the grids. However, the strong scattering points may not be on the grids, which will degrade the performance of CS greatly. This is the off-grid problem. To solve the problem, most of existing methods aim at estimating off-grid error and sparse solution jointly. But the computational cost is relatively high. To reduce the computational cost, a fast and accurate algorithm has been proposed in this paper. Interestingly, the joint optimization problem can be solved efficiently through two least squares problems based on first order Taylor approximation. When applied into simulated chirp signal and quasi real ISAR data, the proposed algorithm has got much better imaging results than existing algorithms. Therefore, it is a promising off-grid CS based ISAR imaging algorithm.

Three-Dimensional Reconstruction of Abdominal Aortic Aneurysm Based on Compressive Sensing With Iterative Optimization and Its Application in 3D Printing

Three-dimensional reconstruction of abdominal aortic aneurysm is the key technology to improve the success rate of surgical and reduce complications. However, the outer contour of abdominal aortic aneurysm(AAA)is fuzzy, which make it difficult for recent existing method to obtain its accurate segmentation performance and high reconstruction accuracy. In this paper, an improved compressive sensing reconstruction algorithm is proposed, which defines a differentiable and convex total variation (TV) function as an optimization goal function and further reduces the number of projections and improve the quality of reconstructed images. Our proposed algorithm improves the speed and stability of the reconstruction algorithm in three-dimensional reconstruction of abdominal aortic aneurysm. The experimental results show that the proposed model can be used for 3D modeling in 3-D printing to improve the accuracy of endovascular repair and the adaptability of the stent, which is suitable for the application of bioengineering medicine.

Maximum correntropy adaptation approach for robust compressive sensing reconstruction

Robust compressive sensing (CS) aims to recover the sparse signals from noisy measurements perturbed by non-Gaussian (i.e., heavy-tailed) noises, where traditional CS reconstruction algorithms may perform poorly owing to utilizing the l2 error norm in optimization. In this paper, we propose a novel maximum correntropy adaptation approach for robust CS reconstruction. The task is formulated as a l0 regularized maximum correntropy criterion (l0-MCC) optimization problem and is solved by adaptive filtering approach. The proposed l0-MCC algorithm has a simple algorithm structure and can adaptively estimate the sparsity. It can efficiently alleviate the negative impact of noise in the presence of large outliers. Moreover, a novel theoretical analysis on convergence of l0-MCC is also performed. Furthermore, a mini-batch-based l0-MCC (MB-l0-MCC) algorithm is developed to speed up the convergence. Comparison with existing robust CS reconstruction algorithms is conducted via simulations, showing that the proposed methods can achieve better performance than existing state-of-the-art algorithms.