Sparse Reconstruction Method Research Articles

Multi-Scale Semi-Coupled Convolutional Sparse Coding for the Super-Resolution Reconstruction of Remote Sensing Image

The traditional convolutional sparse coding super-resolution method only introduces the linear projection relationship in the feature space conversion and fails to consider the local detail in the feature map learning, which causes the reconstruction results to be unsatisfactory in terms of edges and details. The convolutional sparse coding theory is introduced into the super-resolution reconstruction framework of remote sensing images and a multi-scale semi-coupled convolutional sparse coding super-resolution reconstruction method is proposed. Firstly, the input image is decomposed by multi-scale to extract smooth components and multi-scale texture components, and the final smoothing components are reconstructed by bicubic interpolation. Then, the texture components of each scale are reconstructed by semi-coupled convolution sparse coding. The nonlinear convolution operator is used as the projection function between the high-resolution feature map and the low-resolution feature map of texture component at each scale and the non-local self-similarity structure in the feature map learning for constrained optimization is introduced to better reconstruct the texture image at each scale. Finally, the reconstructed smooth component and the texture component at each scale are superimposed to obtain the final reconstructed image. Remote sensing images from 4 different sensors are used as experimental images and the state-of-the-art super-resolution reconstruction methods are compared. Experimental results show that the reconstructed images obtained by the proposed method are better than other methods in quantitative analysis index PSNR and FSIM and show clearer boundary and detailed information and have a certain anti-noise performance.

Derivative-free MLSCD conjugate gradient method for sparse signal and image reconstruction in compressive sensing

Finding the sparse solution to under-determined or ill-condition equations is a fundamental problem encountered in most applications arising from a linear inverse problem, compressive sensing, machine learning and statistical inference. In this paper, inspired by the reformulation of the ?1-norm regularized minimization problem into a convex quadratic program problem by Xiao et al. (Nonlinear Anal Theory Methods Appl, 74(11), 3570-3577), we propose, analyze, and test a derivative-free conjugate gradient method to solve the ?1-norm problem arising from the reconstruction of sparse signal and image in compressive sensing. The method combines the MLSCD conjugate gradient method proposed for solving unconstrained minimization problem by Stanimirovic et al. (J Optim Theory Appl, 178(3), 860-884) and a line search method. Under some mild assumptions, the global convergence of the proposed method is established using the backtracking line search. Computational experiments are carried out to reconstruct sparse signal and image in compressive sensing. The numerical results indicate that the proposed method is stable, accurate and robust.

High-Resolution Radar Imaging of Off-Grid Maneuvering Targets Based on Parametric Sparse Bayesian Learning

In high-resolution radar imaging, the time-varying Doppler induced by maneuvering targets generally invalidates traditional methods. Although sparse signal reconstruction methods can be applied to achieve better performance, the off-grid problem embedded in these methods still prohibits well-focused imaging. In this article, we propose to perform high-resolution radar imaging of maneuvering targets with off-grid scattering centers in a Bayesian framework. First, the statistical model with a parametric dictionary is established, in which the Doppler frequencies of scattering centers are treated as unknown model parameters instead of being discretized into the grid. To be consistent with the physical characteristics, the posterior of the Doppler is approximated by the von Mises distribution. Then, the model parameters and rotation parameters are estimated iteratively by variational inference (VI) and the Newton method. Experiments have demonstrated that the proposed method provides an effective way for high-resolution and well-focused radar imaging of maneuvering targets with off-grid scattering centers in complex scenarios, such as incomplete data and low signal-to-noise ratio.

Sparse sampling and reconstruction for freeform surface based on low-rank matrix completion

The coordinate measuring machine (CMM) becomes an extensive and effective method for high precision inspection of free-form surfaces due to its ability to measure complex and irregular surfaces. Sampling strategy and surface restoration method have an important influence on the efficiency and precision of CMM. In this paper, a sparse sampling strategy and surface reconstruction method for free-form surfaces based on low-rank matrix completion (LRMC) is proposed. In this method, the free-form surface is sampled randomly with uniform distribution in the cartesian coordinate system to obtain sparse sampling points, and then optimizes the scanning path to obtain the shortest path through all measurement points, and finally, the LRMC algorithm based on alternating root mean square prop was used to reconstruct the surface with high precision. The simulation and experimental results show that under the premise of ensuring accuracy, the number of sampling points is greatly reduced and the measurement efficiency is greatly improved.

A General Reconstruction Method for Multidimensional Sparse Sampling Nuclear Magnetic Resonance Spectroscopy.

Multidimensional NMR spectroscopy provides a powerful tool for structure elucidation and dynamic analysis of complex samples, particularly for biological macromolecules. Multidimensional sparse sampling effectively accelerates NMR experiments while an efficient reconstruction method is generally required for unraveling spectra. Various reconstruction methods were proposed for pure Fourier NMR (only involving chemical shifts and J couplings detection). However, reconstruction concerned with Laplace-related NMR (i.e., involving relaxation or diffusion detection) is more challenging due to its ill-posed property. The existing Laplace-related NMR sparse sampling reconstruction methods suffer from poor resolution and possible artifacts in the resulting spectra owing to the pitfalls of the optimization algorithms. Herein, we propose a general approach for fast high-resolution reconstruction of multidimensional sparse sampling NMR, including pure Fourier, mixed Fourier-Laplace, and pure Laplace NMR, benefiting from the comprehensive sparse constraint and effective optimization algorithm and thus showing the promising prospects of multidimensional NMR.

Ultrafast and Ultrahigh-Resolution Diffuse Optical Tomography for Brain Imaging with Sensitivity Equation based Noniterative Sparse Optical Reconstruction (SENSOR)

We introduce a novel image reconstruction method for time-resolved diffuse optical tomography (DOT) that yields submillimeter resolution in less than a second. This opens the door to high-resolution real-time DOT in imaging of the brain activity. We call this approach the sensitivity equation based noniterative sparse optical reconstruction (SENSOR) method. The high spatial resolution is achieved by implementing an asymptotic l0-norm operator that guarantees to obtain sparsest representation of reconstructed targets. The high computational speed is achieved by employing the nontruncated sensitivity equation based noniterative inverse formulation combined with reduced sensing matrix and parallel computing. We tested the new method with numerical and experimental data. The results demonstrate that the SENSOR algorithm can achieve 1 mm3 spatial-resolution optical tomographic imaging at depth of ∼60 mean free paths (MFPs) in 20∼30 milliseconds on an Intel Core i9 processor.

Dense Robust 3D Reconstruction and Measurement for 3D Printing Process Based on Vision

The 3D printing process lacks real-time inspection, which is still an open-loop manufacturing process, and the molding accuracy is low. Based on the 3D reconstruction theory of machine vision, in order to meet the applicability requirements of 3D printing process detection, a matching fusion method is proposed. The fast nearest neighbor (FNN) method is used to search matching point pairs. The matching point information of FFT-SIFT algorithm based on fast Fourier transform is superimposed with the matching point information of AKAZE algorithm, and then fused to obtain more dense feature point matching information and rich edge feature information. Combining incremental SFM algorithm with global SFM algorithm, an integrated SFM sparse point cloud reconstruction method is developed. The dense point cloud is reconstructed by PMVs algorithm, the point cloud model is meshed by Delaunay triangulation, and then the accurate 3D reconstruction model is obtained by texture mapping. The experimental results show that compared with the classical SIFT algorithm, the speed of feature extraction is increased by 25.0%, the number of feature matching is increased by 72%, and the relative error of 3D reconstruction results is about 0.014%, which is close to the theoretical error.

A novel sparse reconstruction method based on multi-objective Artificial Bee Colony algorithm

Compressed sensing is a signal processing method that performs the compressing and sensing processes at the same time. Sparse signal reconstruction is one of the most important issues of compressed sensing. The developments in sparse signal reconstruction methods directly affect the performance of the compressed sensing process. Many sparse signal reconstruction methods have been proposed in the literature. In general, these algorithms are classified as convex optimization, non-convex optimization, and greedy algorithms. In addition, multi-objective optimization algorithms have started to be used in sparse signal reconstruction lately. A sparse signal reconstruction method based on a Multi-objective Artificial Bee Colony algorithm is proposed in this study. The proposed algorithm optimizes the sparsity and measurement error at the same time. Furthermore, it uses the iterative half thresholding algorithm to improve the convergence acceleration of the method. The proposed method was evaluated by using various test signals. Additionally, it was compared with other sparse signal reconstruction algorithms. According to the obtained results, the proposed method has some superiority over the compared algorithms.

Minimum variance Lamb wave imaging based on weighted sparse decomposition coefficients in quasi-isotropic composite laminates

Lamb wave is a promising means for active structural health monitoring and nondestructive evaluation of laminated composite plates. The inevitable reflections from structural geometric boundaries and other interferences limits the imaging performance of many existing imaging methods. The image generated through the well-known delay-and-sum method holds a wide mainlobe width and high level of sidelobes. Although the sparse reconstruction method is free from those deficiencies, it is sensitive to the regularization parameter. To overcome those limitations, a Lamb wave imaging method to locate anomalies or damage in laminated composite plates is proposed. The scattering signals are sparsely decomposed one by one with a prior weights penalized on the undetermined sparse coefficients, and the minimum variance distortionless response algorithm is adopted to process those sparse coefficients so as to generate the image. Experimental results on a quasi-isotropic laminated composite plate demonstrate the effectiveness of the proposed method.

Smooth non-negative sparse representation for face and handwritten recognition

In sparse representation problem, there is always interest to reduce the solution space by introducing additional constraints. This can lead to efficient application-specific algorithms. Despite known advantages of sparsity and non-negativity for image data representation, limited studies have addressed these characteristics simultaneously, due to the challenges involved. In this paper, we propose a novel inexpensive sparse non-negative reconstruction method. We utilise a non-negativity penalty term within a convex function while imposing sparsity at the same time. Our method, termed as SnSA (smooth non-negative sparse approximation) applies a novel thresholding strategy on the sparse coefficients during the minimisation of the proposed convex function. The main advantage of SnSA algorithm is that hard zeroing the negative samples which leads to unstable and non-optimal sparse solution is avoided. Instead, a differentiable smoothing function is proposed that allows gradual suppression of negative samples leading to a sparse non-negative solution. This way, the algorithm is driven towards a solution with a balance in maximising the sparsity and minimising the reconstruction error. Our numerical and experimental results on both synthetic signals and well-established face and handwritten image databases, indicate higher classification performance of the proposed method compared to the state-of-the-art techniques.

Deep learning in magnetic resonance image reconstruction.

Magnetic resonance (MR) imaging visualises soft tissue contrast in exquisite detail without harmful ionising radiation. In this work, we provide a state-of-the-art review on the use of deep learning in MR image reconstruction from different image acquisition types involving compressed sensing techniques, parallel image acquisition and multi-contrast imaging. Publications with deep learning-based image reconstruction for MR imaging were identified from the literature (PubMed and Google Scholar), and a comprehensive description of each of the works was provided. A detailed comparison that highlights the differences, the data used and the performance of each of these works were also made. A discussion of the potential use cases for each of these methods is provided. The sparse image reconstruction methods were found to be most popular in using deep learning for improved performance, accelerating acquisitions by around 4-8 times. Multi-contrast image reconstruction methods rely on at least one pre-acquired image, but can achieve 16-fold, and even up to 32- to 50-fold acceleration depending on the set-up. Parallel imaging provides frameworks to be integrated in many of these methods for additional speed-up potential. The successful use of compressed sensing techniques and multi-contrast imaging with deep learning and parallel acquisition methods could yield significant MR acquisition speed-ups within clinical routines in the near future.

ECG Localization Method Based on Volume Conductor Model and Kalman Filtering.

The 12-lead electrocardiogram was invented more than 100 years ago and is still used as an essential tool in the early detection of heart disease. By estimating the time-varying source of the electrical activity from the potential changes, several types of heart disease can be noninvasively identified. However, most previous studies are based on signal processing, and thus an approach that includes physics modeling would be helpful for source localization problems. This study proposes a localization method for cardiac sources by combining an electrical analysis with a volume conductor model of the human body as a forward problem and a sparse reconstruction method as an inverse problem. Our formulation estimates not only the current source location but also the current direction. For a 12-lead electrocardiogram system, a sensitivity analysis of the localization to cardiac volume, tilted angle, and model inhomogeneity was evaluated. Finally, the estimated source location is corrected by Kalman filter, considering the estimated electrocardiogram source as time-sequence data. For a high signal-to-noise ratio (greater than 20 dB), the dominant error sources were the model inhomogeneity, which is mainly attributable to the high conductivity of the blood in the heart. The average localization error of the electric dipole sources in the heart was 12.6 mm, which is comparable to that in previous studies, where a less detailed anatomical structure was considered. A time-series source localization with Kalman filtering indicated that source mislocalization could be compensated, suggesting the effectiveness of the source estimation using the current direction and location simultaneously. For the electrocardiogram R-wave, the mean distance error was reduced to less than 7.3 mm using the proposed method. Considering the physical properties of the human body with Kalman filtering enables highly accurate estimation of the cardiac electric signal source location and direction. This proposal is also applicable to electrode configuration, such as ECG sensing systems.

Fast sparse image reconstruction method in through-the-wall radars using limited memory Broyden–Fletcher–Goldfarb–Shanno algorithm

AbstractCompressed sensing allows recovery of image signals using a portion of data – a technique that has drastically revolutionized the field of through-the-wall radar imaging (TWRI). This technique can be accomplished through nonlinear methods, including convex programming and greedy iterative algorithms. However, such (nonlinear) methods increase the computational cost at the sensing and reconstruction stages, thus limiting the application of TWRI in delicate practical tasks (e.g. military operations and rescue missions) that demand fast response times. Motivated by this limitation, the current work introduces the use of a numerical optimization algorithm, called Limited Memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS), to the TWRI framework to lower image reconstruction time. LBFGS, a well-known Quasi-Newton algorithm, has traditionally been applied to solve large scale optimization problems. Despite its potential applications, this algorithm has not been extensively applied in TWRI. Therefore, guided by LBFGS and using the Euclidean norm, we employed the regularized least square method to solve the cost function of the TWRI problem. Simulation results show that our method reduces the computational time by 87% relative to the classical method, even under situations of increased number of targets or large data volume. Moreover, the results show that the proposed method remains robust when applied to noisy environment.

Training Data Selection and Optimal Sensor Placement for Deep-Learning-Based Sparse Inertial Sensor Human Posture Reconstruction.

Although commercial motion-capture systems have been widely used in various applications, the complex setup limits their application scenarios for ordinary consumers. To overcome the drawbacks of wearability, human posture reconstruction based on a few wearable sensors have been actively studied in recent years. In this paper, we propose a deep-learning-based sparse inertial sensor human posture reconstruction method. This method uses bidirectional recurrent neural network (Bi-RNN) to build an a priori model from a large motion dataset to build human motion, thereby the low-dimensional motion measurements are mapped to whole-body posture. To improve the motion reconstruction performance for specific application scenarios, two fundamental problems in the model construction are investigated: training data selection and sparse sensor placement. The problem of deep-learning training data selection is to select independent and identically distributed (IID) data for a certain scenario from the accumulated imbalanced motion dataset with sufficient information. We formulate the data selection into an optimization problem to obtain continuous and IID data segments, which comply with a small reference dataset collected from the target scenario. A two-step heuristic algorithm is proposed to solve the data selection problem. On the other hand, the optimal sensor placement problem is studied to exploit most information from partial observation of human movement. A method for evaluating the motion information amount of any group of wearable inertial sensors based on mutual information is proposed, and a greedy searching method is adopted to obtain the approximate optimal sensor placement of a given sensor number, so that the maximum motion information and minimum redundancy is achieved. Finally, the human posture reconstruction performance is evaluated with different training data and sensor placement selection methods, and experimental results show that the proposed method takes advantages in both posture reconstruction accuracy and model training time. In the 6 sensors configuration, the posture reconstruction errors of our model for walking, running, and playing basketball are 7.25°, 8.84°, and 14.13°, respectively.

Real-time dynamic vocal tract imaging using an accelerated spiral GRE sequence and low rank plus sparse reconstruction

PurposeTo develop a real-time dynamic vocal tract imaging method using an accelerated spiral GRE sequence and low rank plus sparse reconstruction. MethodsSpiral k-space sampling has high data acquisition efficiency and thus is suited for real-time dynamic imaging; further acceleration can be achieved by undersampling k-space and using a model-based reconstruction. Low rank plus sparse reconstruction is a promising method with fast computation and increased robustness to global signal changes and bulk motion, as the images are decomposed into low rank and sparse terms representing different dynamic components. However, the combination with spiral scanning has not been well studied. In this study an accelerated spiral GRE sequence was developed with an optimized low rank plus sparse reconstruction and compared with L1-SPIRiT and XD-GRASP methods. The off-resonance was also corrected using a Chebyshev approximation method to reduce blurring on a frame-by-frame basis. ResultsThe low rank plus sparse reconstruction method is sensitive to the weights of the low rank and sparse terms. The optimized reconstruction showed advantages over other methods with reduced aliasing and improved SNR. With the proposed method, spatial resolution of 1.3*1.3 mm2 with 150 mm field-of-view (FOV) and temporal resolution of 30 frames-per-second (fps) was achieved with good image quality. Blurring was reduced using the Chebyshev approximation method. ConclusionThis work studies low rank plus sparse reconstruction using the spiral trajectory and demonstrates a new method for dynamic vocal tract imaging which can benefit studies of speech disorders.

Two-dimensional multiradar ISAR fusion imaging based on fast linearized Bregman iteration algorithm

The two-dimensional (2D) resolution is poor due to the narrow transmitting bandwidth and the limited observation angle in monostatic ISAR imaging. A multiradar fusion imaging method based on fast linearized Bregman iteration (FLBI) algorithm is proposed to improve the 2D resolution of the ISAR imaging. First, the sparsity of the ISAR imaging echo data is exploited to establish the multiradar fusion ISAR imaging model based on sparse representation, which can be converted into a one-dimensional sparse vector reconstruction problem. Then, a sparse reconstruction method based on FLBI is proposed to solve the sparse representation problem with large scales and achieve the ISAR fusion imaging. Combined with the weighted back-adding residual and condition number optimization of the sensing matrix, the FLBI algorithm can further accelerate the iterative convergence speed. The proposed algorithm only involves matrix–vector multiplications and componentwise shrinkages, which greatly improves the imaging efficiency. Finally, the simulation results show that the proposed method can effectively improve the iterative convergence speed and achieve the better 2D ISAR fusion imaging.

Sparse SAR Imaging and Quantitative Evaluation Based on Nonconvex and TV Regularization

Sparse signal processing has been used in synthetic aperture radar (SAR) imaging due to the maturity of compressed sensing theory. As a typical sparse reconstruction method, L1 regularization generally causes bias effects as well as ignoring region-based features. Our team has proposed to linearly combine the nonconvex penalty and the total variation (TV)-norm penalty as a compound regularizer in the imaging model, called nonconvex and TV regularization, which can not only reduce the bias caused by L1 regularization but also enhance point-based and region-based features. In this paper, we use the variable splitting scheme and modify the alternating direction method of multipliers (ADMM), generating a novel algorithm to solve the above optimization problem. Moreover, we analyze the radiometric properties of sparse-signal-processing-based SAR imaging results and introduce three indexes suitable for sparse SAR imaging for quantitative evaluation. In experiments, we process the Gaofen-3 (GF-3) data utilizing the proposed method, and quantitatively evaluate the reconstructed SAR image quality. Experimental results and image quality analysis verify the effectiveness of the proposed method in improving the reconstruction accuracy and the radiometric resolution without sacrificing the spatial resolution.

AFISTA: Accelerated FISTA for sparse signal recovery and compressive sensing

This paper presents a new fast iterative shrinkage-thresholding algorithm, termed AFISTA. The essential idea is to improve the convergence rate of FISTA using a new continuation strategy leading to a less number of iterations compared to FISTA. The convergence theorem of the AFISTA is proposed. In order to further accelerate the AFISTA method, it is equipped with the Barzilai-Borwein (BB) method. Also, for applications with orthogonal sensing matrix A, we proposed a specialized version of the AFISTA method. AFISTA is tailored for solving the basis pursuit problem which can be applied successfully on a variety of problems arising in signal and image processing issues such as sparse signal recovery, signal and image denoising, image restoration, and compressive sensing. To show the efficiency of the method, we compare our results with generalizations of linearized Bregman and fixed - point continuation (FPC) methods in sparse signal recovery applications, with split Bregman method in compressive sensing for sparse MRI and with Gradient projection for sparse reconstruction (GPSR) method in image deconvolution. Numerical results demonstrate that AFISTA overcomes all of the compared methods in convergence rate and some of them in both convergence rate and quality of reconstructed results.

Sparse Bayesian Learning Based Direction-of-Arrival Estimation under Spatially Colored Noise Using Acoustic Hydrophone Arrays

Direction-of-arrival (DOA) estimation in a spatially isotropic white noise background has been widely researched for decades. However, in practice, such as underwater acoustic ambient noise in shallow water, the ambient noise can be spatially colored, which may severely degrade the performance of DOA estimation. To solve this problem, this paper proposes a DOA estimation method based on sparse Bayesian learning with the modified noise model using acoustic vector hydrophone arrays. Firstly, an applicable linear noise model is established by using the prolate spheroidal wave functions (PSWFs) to characterize spatially colored noise and exploiting the excellent performance of the PSWFs in extrapolating band-limited signals to the space domain. Then, using the proposed noise model, an iterative method for sparse spectrum reconstruction is developed under a sparse Bayesian learning (SBL) framework to fit the actual noise field received by the acoustic vector hydrophone array. Finally, a DOA estimation algorithm under the modified noise model is also presented, which has a superior performance under spatially colored noise. Numerical results validate the effectiveness of the proposed method.

Sparse image reconstruction of intracerebral hemorrhage with electrical impedance tomography.

Purpose: Intracerebral hemorrhage (ICH) is a common disease that is known for its high morbidity, high mortality, and high disability. The fast and accurate detection of ICH is essential for the acute care of patients. Electrical impedance tomography (EIT) offers an alternative with which pathological tissues can be detected by reconstructing conductivity variation. Nevertheless, the sensitive field of EIT is greatly affected by medium distribution, which is referred to as soft-field effect. In addition, the image reconstruction is a severely ill-posed inverse problem. Furthermore, due to the low conductivity of skull, the sensitivity in the sensing area is extremely low. Therefore, the reconstruction of ICH with EIT is great challenge. Approach: A sparse image reconstruction method is proposed for EIT to visualize the conductivity variation caused by ICH. To reduce the impact of soft-field effect, the normalization of sensitivity distribution is conducted for monolayer and three-layer head model. In addition, a constrained sparse -norm minimization model is developed for the image reconstruction. Augmented Lagrangian multiplier method and alternating minimization scheme are adopted to solve the proposed model. Results: The results show that the sensitivity in the sensing area is largely enhanced. Numerical simulation based on monolayer head model and three-layer head model is respectively carried out. Both the reconstructed images and the quantitative evaluations show that image reconstructed by the proposed method is much better than that reconstructed by traditional Tikhonov method. The reconstructions evaluated under the impact of noise also show that the proposed method has superior anti-noise performance. Conclusions: With the proposed method, the quality of the reconstructed image would be greatly improved. It is an effective approach for imaging ICH with EIT technique.