Variation Constraint Research Articles

A signal detection model for quantifying overregularization in nonlinear image reconstruction.

Many useful image quality metrics for evaluating linear image reconstruction techniques do not apply to or are difficult to interpret for nonlinear image reconstruction. The vast majority of metrics employed for evaluating nonlinear image reconstruction are based on some form of global image fidelity, such as image root mean square error (RMSE). Use of such metrics can lead to overregularization in the sense that they can favor removal of subtle details in the image. To address this shortcoming, we develop an image quality metric based on signal detection that serves as a surrogate to the qualitative loss of fine image details. The metric is demonstrated in the context of a breast CT simulation, where different equal-dose configurations are considered. The configurations differ in the number of projections acquired. Image reconstruction is performed with a nonlinear algorithm based on total variation constrained least-squares (TV-LSQ). The resulting images are studied as a function of three parameters: number of views acquired, total variation constraint value, and number of iterations. The images are evaluated visually, with image RMSE, and with the proposed signal-detection-based metric. The latter uses a small signal, and computes detectability in the sinogram and in the reconstructed image. Loss of signal detectability through the image reconstruction process is taken as a quantitative measure of loss of fine details in the image. Loss of signal detectability is seen to correlate well with the blocky or patchy appearance due to overregularization with TV-LSQ, and this trend runs counter to the image RMSE metric, which tends to favor the over-regularized images. The proposed signal detection-based metric provides an image quality assessment that is complimentary to that of image RMSE. Using the two metrics in concert may yield a useful prescription for determining CT algorithm and configuration parameters when nonlinear image reconstruction is used.

Accelerated model-based quantitative diffusion MRI: A feasibility study for musculoskeletal application

PurposeTo develop a model-based reconstruction technique for diffusion quantification based on accelerated two-dimensional echo planar data, obtained with multiple b-weightings. In combination with a dedicated undersampling pattern, acceleration factors above three were proven feasible in a clinical setting. MethodsThe proposed model-based method minimizes a cost function considering the l2-norm of the difference between the Fourier transformation of a synthetic diffusion-model-generated k-space and the measured k-space data. Further regularization is performed by introduction of a total variation (TV) constraint to the cost function. Acceleration is achieved by a non-random undersampling pattern using acceleration factors that correspond to the total number of b-values. A rectangular region of variable size, centered in k-space, remains fully sampled for correction of phase variations, introduced by the different diffusion-encoding strengths. ResultsQualitative analysis of the resulting images (S0 and ADC) demonstrates the potential of the suggested undersampling pattern in combination with a model-based iterative reconstruction. An edge analysis highlights the preservation of high-frequency information for all investigated undersampling factors. In comparison to a conventional SENSE-accelerated reconstruction, the quantitative analysis of the ADC maps revealed a significantly (P<0.05) superior performance of the suggested technique, enabling acceleration factors of R=3.65 without compromising diffusion data fidelity. ConclusionThe presented work shows the potential of model-based ADC quantification, which, in combination with a suited undersampling pattern for multiple b-values, enables more than three-fold acceleration using two-dimensional EPI without sacrificing ADC fidelity.

Polarization prior to single-photon counting image denoising.

Single-photon counting (SPC) imaging technique, which can detect targets in extremely low light levels, has attracted considerable research interest in recent years. To reduce the influence of noise under the low light condition, traditional approaches typically seek various priors from images themselves to construct denoising models, leading to inferior performance as the signal and noise cannot be efficiently distinguished. To address this challenging problem, in this study we propose a novel polarization prior to SPC image denoising based on the observation that a special polarization SPC (PSPC) image has a higher SNR than the SPC image. It enables us to construct a polarization prior to the PSPC image that can transfer efficient targets' spatial details to the denoised SPC image, and hence improves the denoising performance. Specifically, we group similar patches of the PSPC image to form 'anti-noise' dictionaries with high SNR. Then we construct a non-local prior-oriented sparse representation constraint based on the fact that each noisy patch of the SPC image can be sparsely represented by the corresponding 'anti-noise' dictionary. According to this sparse representation constraint, we further formulate an SPC image denoising model by incorporating two terms, i.e., a negative Poisson log-likelihood function for preserving the data fidelity and a total variation constraint to reduce the influence of noise, which is solved by an efficient variable splitting method. In the experiment, we have verified the effectiveness of the proposed method from simulated and real data in terms of visual comparison and quantitative analysis, respectively.

Phenotypic stability in scalar calcium of freshwater fish across a wide range of aqueous calcium availability in nature.

Spatial environmental gradients can promote adaptive differences among conspecific populations as a result of local adaptation or phenotypic plasticity. Such divergence can be opposed by various constraints, including gene flow, limited genetic variation, temporal fluctuations, or developmental constraints. We focus on the constraint that can be imposed when some populations are found in locations characterized by low levels of an essential nutrient. We use scales of wild fish to investigate phenotypic effects of spatial variation in a potentially limiting nutrient—calcium. If scale calcium (we use “scalar” calcium for consistency with the physiology literature) simply reflects environmental calcium availability, we expect higher levels of scalar calcium in fish from calcium‐rich water, compared to fish from calcium‐poor water. To consider this “passive response” scenario, we analyzed scalar calcium concentrations from three native fish species (Lepomis gibbosus, Percina caprodes, and Perca flavescens) collected at multiple sites across a dissolved calcium gradient in the Upper St. Lawrence River. Contradicting the “passive response" scenario, we did not detect strong or consistent relationships between scalar calcium and water calcium. Instead, for a given proportional increase in water calcium across the wide environmental gradient, the corresponding proportional change in scalar calcium was much smaller. We thus favor the alternative “active homeostasis” scenario, wherein fish from calcium‐poor water are better able to uptake, mobilize, and deposit calcium than are fish from calcium‐rich water. We further highlight the importance of studying functional traits, such as scales, in their natural setting as opposed to only laboratory studies.

Joint Inversion of Multiphysical Parameters Based on a Combination of Cosine Dot-Gradient and Joint Total Variation Constraints

The joint inversion of structural constraints is a new and rapidly developing detection technology in comprehensive geophysical interpretation. In this article, a new structural constraint 2-D multiphysical parameter joint inversion algorithm for magnetotelluric (MT), gravity, and magnetic data is developed. The structural constraint term is a combination of cosine dot-gradient (CDG) and joint total variation (JTV) constraints, which not only has characteristics of traditional dot product and cross-gradient structure constraints but also avoids the uncertainty of dot product constraints predicting the gradient direction of the model parameters, overcomes the need for high-order differential approximation of the cross-gradient constraint, ignores the influence of the gradient amplitude of different model parameters on the weight of the structural constraint of different regions, and enhances the reconstruction accuracy of the underground discontinuous interface. To more easily combine multiple optimization algorithms to improve the resolution and computational efficiency of joint inversion, an adaptive inexact structural resemblance (IESR) algorithm is developed to minimize numerical solutions to the objective function. Experimental results have demonstrated that the CDG constraint has a wider use range than the traditional structural constraint, the addition of the JTV constraint can recover the underground discontinuous interface, and an inversion result of higher resolution can be obtained using the adaptive IESR algorithm.

Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration

This paper presents a novel medical image registration algorithm named total variation constrained graph-regularization for non-negative matrix factorization (TV-GNMF). The method utilizes non-negative matrix factorization by total variation constraint and graph regularization. The main contributions of our work are the following. First, total variation is incorporated into NMF to control the diffusion speed. The purpose is to denoise in smooth regions and preserve features or details of the data in edge regions by using a diffusion coefficient based on gradient information. Second, we add graph regularization into NMF to reveal intrinsic geometry and structure information of features to enhance the discrimination power. Third, the multiplicative update rules and proof of convergence of the TV-GNMF algorithm are given. Experiments conducted on datasets show that the proposed TV-GNMF method outperforms other state-of-the-art algorithms.

Variational principles of liquid–porous material interactions with applications to approximate solutions and finite-element modelling

For liquid–porous material interactions (LPMI), three variational principles are developed in Biot's theory of porous materials in association with Darcy's Law. First one takes solid acceleration, and fluid velocity, acceleration, pressure with time derivative as five variables, while second and third, respectively, have three and two variables when Darcy's Law used as variational constraint reducing variables. These principles provide a means to derive approximate solutions and finite-element (FE) models for LPMI. Each LPMI element includes fluid and solid together with it being no longer necessary to distinguish fluid domain from solid. Examples illustrate applications to establish FE model for numerical solutions of LPMI. Solution of a one-dimensional problem reveals that LPMI behaves a coupled-frequency separation measured by a defined-coupling factor. Dynamic response explores coupled-dynamic absorber mechanism in LPMI system, from which it is found that the external force at fluid does not contribute to fluid response but fully absorbed by solid local resonance if the force frequency equals the solid natural frequency; while in the reverse case when the force frequency equals the fluid one, the force at solid does not produce the solid response but fully absorbed by fluid local resonance. New findings with defined LPMI coupling factor provide guidelines for designing LPMI system with expected dynamic behaviour meeting engineering requirements.

Neural network model assisted Fourier ptychography with Zernike aberration recovery and total variation constraint.

.Significance: Fourier ptychography (FP) is a computational imaging approach that achieves high-resolution reconstruction. Inspired by neural networks, many deep-learning-based methods are proposed to solve FP problems. However, the performance of FP still suffers from optical aberration, which needs to be considered.Aim: We present a neural network model for FP reconstructions that can make proper estimation toward aberration and achieve artifact-free reconstruction.Approach: Inspired by the iterative reconstruction of FP, we design a neural network model that mimics the forward imaging process of FP via TensorFlow. The sample and aberration are considered as learnable weights and optimized through back-propagation. Especially, we employ the Zernike terms instead of aberration to decrease the optimization freedom of pupil recovery and perform a high-accuracy estimation. Owing to the auto-differentiation capabilities of the neural network, we additionally utilize total variation regularization to improve the visual quality.Results: We validate the performance of the reported method via both simulation and experiment. Our method exhibits higher robustness against sophisticated optical aberrations and achieves better image quality by reducing artifacts.Conclusions: The forward neural network model can jointly recover the high-resolution sample and optical aberration in iterative FP reconstruction. We hope our method that can provide a neural-network perspective to solve iterative-based coherent or incoherent imaging problems.

Question tags across New Englishes

This paper presents a cross-variety analysis of (variant and invariant) question tags in Philippine and Trinidadian English, using six dialogic text types from the corresponding components of the International Corpus of English (ICE). The cross-variety comparison considers the similarities and differences across the two New Englishes in terms of question tag forms and functions and the constraints of variation, particularly the effect of text type. This analysis demonstrates that there are mainly differences in terms of forms, however, several similarities predominate: Filipino and Trinidadian speakers have the same communicative needs in specific situations and use question tags in similar ways, often selecting the same forms for the same functions. In-depth analyses of question tags – and discourse markers in general – offer new possibilities for corpus-based research on world Englishes, as established tools like ICE can be used in innovative ways.

Bayesian adversarial multi-node bandit for optimal smart grid protection against cyber attacks

The cyber security of smart grids has become one of key problems in developing reliable modern power and energy systems. This paper introduces a non-stationary adversarial cost with a variation constraint for smart grids and enables us to investigate the problem of optimal smart grid protection against cyber attacks in a relatively practical scenario. In particular, a Bayesian multi-node bandit (MNB) model with adversarial costs is constructed and a new regret function is defined for this model. An algorithm called Thompson–Hedge algorithm is presented to solve the problem and the superior performance of the proposed algorithm is proven in terms of the convergence rate of the regret function. The applicability of the algorithm to real smart grid scenarios is verified and the performance of the algorithm is also demonstrated by numerical examples.

Toward Moving Target Detection in Through-the-Wall Radar Imaging

With the advances in radar technology, through-the-wall radar imaging (TWRI) has become a viable sensing modality that can allow fire-and-rescue personnel, police, and military forces to detect, localize, and identify targets behind opaque obstacles. Many of the existing TWRI approaches detect either stationary or moving targets but not both of them simultaneously. In this article, a method is proposed to detect both stationary and moving targets from a sequence of radar signals. The proposed method decomposes the 3-D radar data, i.e., frequency, space, and time data into a low-rank tensor and two sets of sparse images. One set of images comprises the stationary targets, and the other set of images contains the moving targets. Wall clutter removal and target detection are formulated into an optimization problem regularized by tensor low-rank, joint sparsity, and total variation constraints. Then, an alternating direction technique is developed to reconstruct the sets of stationary and moving target images. Experiments using simulated and real radar signals are conducted. The experimental results illustrate the effectiveness of the proposed method to detect and separate the stationary and moving targets into a pair of sparse images.

Modeling human observer detection in undersampled magnetic resonance imaging (MRI).

Task-based assessment of image quality in undersampled magnetic resonance imaging (MRI) using constraints is important because of the need to quantify the effect of the artifacts on task performance. Fluid-attenuated inversion recovery (FLAIR) images are used in detection of small metastases in the brain. In this work we carry out two-alternative forced choice (2-AFC) studies with a small signal known exactly (SKE) but with varying background for reconstructed FLAIR images from undersampled multi-coil data. Using a 4x undersampling and a total variation (TV) constraint we found that the human observer detection performance remained fairly constant for a broad range of values in the regularization parameter before decreasing at large values. Using the TV constraint did not improve task performance. The non- prewhitening eye (NPWE) observer and sparse difference-of-Gaussians (S-DOG) observer with internal noise were used to model human observer detection. The parameters for the NPWE and the internal noise for the S-DOG were chosen to match the average percent correct (PC) in 2-AFC studies for three observers using no regularization. The NPWE model observer tracked the performance of the human observers as the regularization was increased but slightly over-estimated the PC for large amounts of regularization. The S-DOG model observer with internal noise tracked human performace for all levels of regularization studied. To our knowledge this is the first time that model observers have been used to track human observer detection for undersampled MRI.

Seismic Data Denoising Based on Tensor Decomposition With Total Variation

In order to remove random noise in seismic data, this letter proposes a seismic data denoising method based on tensor decomposition and total variation (TDTV). Based on the self-similarity of seismic data, this method first groups similar patches into a stack, then utilizes the low-rank tensor approximation strategy to restore the structural effective information of the seismic section. Considering that the approximate seismic section obtained after CANDECOMP/PARAFAC (CP) decomposition and patch aggregation is unsmooth, this letter introduces the total variation (TV) constraint to perform anisotropic diffusion, and protects edge information while smoothing. Finally, the gradient descent method is used to solve the whole model. The TDTV method proposed in this letter can not only effectively denoise synthetic and field seismic section but also restore structural and edge information. Experimental results show that the proposed method outperforms many state-of-the-art denoising methods.

Robust wideband adaptive beamforming based on covariance matrix reconstruction in the spatial‐frequency domain

Without the response variation constraint, the main-lobe responses of wideband beamforming usually vary with the frequencies of interest, and the beam pointing may deviate from the incident angle of the desired signal. If the interference-plus-noise covariance matrix (INCM) is directly replaced by the sample covariance matrix, the desired signal in the sample data may result in self-null problem, which can lead to the degradation of the performance of wideband beamformers. Through frequency division, a novel wideband adaptive beamforming is proposed by reconstructing the INCM and solving the convex optimisation problem. Using fast Fourier transform (FFT), the time-domain samples are transformed into the frequency field, and the covariance matrix of each subband can be obtained from the frequency-domain data. In the spatial-frequency domain, the INCM and signal-plus-noise covariance matrix can be respectively reconstructed by integrating the stacked steering vector and the Capon spatial spectrum over the corresponding angular region. Then, we establish the optimisation criteria, that is, minimising the output interference-plus-noise power, minimising the main-lobe spatial response variation, and constraining the response deviation of the desired signal. A novel convex optimisation model can be established, and then the weight coefficients for time-domain wideband beamforming can be obtained by solving the optimisation problem. The simulation and experimental results demonstrate that the proposed beamformer can provide better performance compared with other tested beamformers and maintain good robustness in various applications.

Magnetic resonance parameter mapping using model-guided self-supervised deep learning.

To develop a model-guided self-supervised deep learning MRI reconstruction framework called reference-free latent map extraction (RELAX) for rapid quantitative MR parameter mapping. Two physical models are incorporated for network training in RELAX, including the inherent MR imaging model and a quantitative model that is used to fit parameters in quantitative MRI. By enforcing these physical model constraints, RELAX eliminates the need for full sampled reference data sets that are required in standard supervised learning. Meanwhile, RELAX also enables direct reconstruction of corresponding MR parameter maps from undersampled k-space. Generic sparsity constraints used in conventional iterative reconstruction, such as the total variation constraint, can be additionally included in the RELAX framework to improve reconstruction quality. The performance of RELAX was tested for accelerated T1 and T2 mapping in both simulated and actually acquired MRI data sets and was compared with supervised learning and conventional constrained reconstruction for suppressing noise and/or undersampling-induced artifacts. In the simulated data sets, RELAX generated good T1 /T2 maps in the presence of noise and/or undersampling artifacts, comparable to artifact/noise-free ground truth. The inclusion of a spatial total variation constraint helps improve image quality. For the in vivo T1 /T2 mapping data sets, RELAX achieved superior reconstruction quality compared with conventional iterative reconstruction, and similar reconstruction performance to supervised deep learning reconstruction. This work has demonstrated the initial feasibility of rapid quantitative MR parameter mapping based on self-supervised deep learning. The RELAX framework may also be further extended to other quantitative MRI applications by incorporating corresponding quantitative imaging models.

Image compression-encryption method based on two-dimensional sparse recovery and chaotic system

In this paper, we propose an image compression-encryption method based on two-dimensional (2D) sparse representation and chaotic system. In the first step of this method, the input image is extended in a transform domain to obtain a sparse representation. To achieve better performance of image compression by 2D sparse recovery, the sparse representation is scrambled via a chaotic confusion. This step helps the satisfaction of the uniqueness conditions for sparse recovery, and the security level of encryption is increased. Then, two orthogonal measurement matrices are generated using the chaotic time series. The singular value decomposition is used to compress the sparse scrambled representation in two dimensions. Finally, to reduce the correlation between adjacent pixels in the compressed matrix, and obtain a uniform distribution in the encrypted image, a compressed scrambling matrix based on chaotic confusion is used. Then, XOR operation is applied for final encryption. In the decryption process, to improve the compression efficiency, the total variation constraint is added to the 2D sparse recovery problem based on the smoothed norm. The simulation results demonstrate the satisfying performance of the proposed method for different compression ratios. Security analysis describes the effectiveness of the proposed encryption approach.

Covert MIMO Communications Under Variational Distance Constraint

The problem of covert communication over Multiple-Input Multiple-Output (MIMO) Additive White Gaussian Noise (AWGN) channels is investigated, in which a transmitter attempts to reliably communicate with a legitimate receiver while avoiding detection by a passive adversary. The covert capacity of the MIMO AWGN is characterized under a variational distance covertness constraint when the MIMO channel matrices are static and known. The characterization of the covert capacity is also extended to a class of channels in which the legitimate channel matrix is known but the adversary's channel matrix is only known up to a rank and a spectral norm constraint.

Multi-Timeslots Data Collection With Low Rank and Modified Second-Order Horizontal Total Variation for Wireless Sensor Networks

Decreasing the number of data gathered is the most highly effective way to decrease the power consumption for wireless sensor networks. Compressed Data Gathering, as it known to all, is a data collection method in wireless sensor networks, but it cannot achieve sparse sensing as all data need to be sensed and then transmitted in most practical applications. At the same time, it has been shown the effectiveness of the total variation and low rank constraints in data restoration. In order to enhance the accuracy of data recovery and decrease energy cost in wireless sensor networks, we propose a Multi-Timeslots Data Collection scheme, which includes two aspects: Structure Random Sparse Sampling method and data restoration algorithm with Low Rank and Modified Second-Order Horizontal Total Variation Constraints. By adopting the proposed sampling method, the number of data sensing and transmission is greatly reduced, thereby prolong the network lifetime. We fully exploit temporal stability and low rank characteristics of wireless sensor networks data, and build a temporal-stability based nuclear norm regularization minimization model. Meanwhile, we apply the alternating direction method to solve the problem. The simulation results present that the proposed sampling method has a corresponding enhancement effect on the matrix-completion based data restoration algorithms. In terms of recovery precision, the proposed scheme outperforms the state-of-the-art methods for different types of data in the network. Moreover, with the compression ratio increasing, the proposed scheme can still exactly recover the lost data and the advantages become increasingly obvious.

A Method with Convergence Rates for Optimization Problems with Variational Inequality Constraints

We consider a class of optimization problems with Cartesian variational inequality (CVI) constraints, where the objective function is convex and the CVI is associated with a monotone mapping and a ...

MIMO Radar Accurate Imaging and Motion Estimation for 3-D Maneuvering Ship Target

Image deterioration problem occurs in radar imaging for ship target, which results from the complex time-varying motions of ship, the noise in channels, and the clutter on sea surface. It is hard to be solved effectively due to coherent accumulation sampling time and high-dimensional parametric model. Hence, an accurate imaging and motion estimation method based on multiple-input–multiple-out (MIMO) radar is presented. First, the multidimensional signal model is built to characterize target features accurately. To reduce the interference from sea clutters, a preprocessing strategy is exerted based on the space–time adaptive processing (STAP) theory, clutter signals can be suppressed effectually with constructing a Doppler spectrum model. Then, for accurate imaging and motion estimation, a combined trace norm minimization problem is deduced based on the relaxation of tensor rank, where the noise in sea environments is also considered. Meanwhile, generalized tensor total variation constraint is developed to ensure stable estimation and smooth imaging results when separating the noise term. Accordingly, an effective decomposition criterion is formulated based on alternating direction multiplier method (ADMM) strategy, and motion parameters can be precisely calculated based on the least square (LS) method. Finally, theoretical analysis and simulation results present the accurate performance of the proposed method.