Total Variation Constraint Research Articles

Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

Intrinsic Image Sequence Decomposition Using Low-Rank Sparse Model

Intrinsic image decomposition from a single image or image sequences is always a challenging task in computer vision and image processing due to the ill-posed characteristics. In order to attain a reasonable estimation of intrinsic images, in this paper, we present a low-rank sparse model (LRSM) to derive intrinsic images from an image sequence of the same scene under various lightings. Due to the dependance of varying lightings and the excellent edge-preserving ability of the total variation constraint, both are joined together to formulate the LRSM as a spatiotemporal prior. When considering the relationships among images of a scene as well as those between color channels of a color image, the proposed model involves a complex objective function and makes the solving much more difficult than that on a single gray-scale image. Therefore, we design an iterative numerical scheme based on the alternating direction method of multipliers framework to solve the objective function efficiently. We further specify the application of the proposed method to object recoloring. The experimental results demonstrate that the proposed LSRM and the iterative scheme are effective and efficient.

Full model wavenumber inversion: Identifying sources of information for the elusive middle model wavenumbers

We recognized over the years that our conventional surface seismic recording can effectively identify two main features of the earth: its seismic propagation attributes and those attributes resulting in echoes or reflections. Thus, the resulting expression of the earth is dominated by the generally smooth (long-wavelength) features that control wave propagation, which we use to invert for the short-wavelength features causing reflections in a process we refer to as migration velocity analysis and imaging, respectively. The features of the earth that fall in between these two model scales — the middle wavenumbers — have been elusive, which is a dilemma for full-waveform inversion because we need to build the full velocity model (a broad band of model wavenumbers). We analyze the middle model wavenumber gap, but we focus more here on potential sources of information for such middle model wavenumbers. Such sources include regularization, objective function enhancements, and multiscattered energy. Regularization, provided by a total variation (TV) constraint admits middle and high model wavenumber components into the model to enforce the model’s compliance with such a constraint. As opposed to minimizing the TV, such a constraint merely reduces the model space, and thus, these injected middle model wavenumbers are as good as the projected data information to the reduced model space. Such data information includes large offsets, but also multiscattered energy, in which the energy through wavepath and scattering updates can admit more of the elusive middle-wavenumber information that comes from the data. The combination of the right level of allowable model variations with the added data information from large offsets and multiscattering can help in filling the elusive middle model wavenumber gap and admit plausible models.

A Novel 3D Anisotropic Total Variation Regularized Low Rank Method for Hyperspectral Image Mixed Denoising

Known to be structured in several patterns at the same time, the prior image of interest is always modeled with the idea of enforcing multiple constraints on unknown signals. For instance, when dealing with a hyperspectral restoration problem, the combination of constraints with piece-wise smoothness and low rank has yielded promising reconstruction results. In this paper, we propose a novel mixed-noise removal method by employing 3D anisotropic total variation and low rank constraints simultaneously for the problem of hyperspectral image (HSI) restoration. The main idea of the proposed method is based on the assumption that the spectra in an HSI lies in the same low rank subspace and both spatial and spectral domains exhibit the property of piecewise smoothness. The low rankness of an HSI is approximately exploited by the nuclear norm, while the spectral-spatial smoothness is explored using 3D anisotropic total variation (3DATV), which is defined as a combination of 2D spatial TV and 1D spectral TV of the HSI cube. Finally, the proposed restoration model is effectively solved by the alternating direction method of multipliers (ADMM). Experimental results of both simulated and real HSI datasets validate the superior performance of the proposed method in terms of quantitative assessment and visual quality.

A Three-Dimensional Enhanced Imaging Method on Human Body for Ultra-Wideband Multiple-Input Multiple-Output Radar

High-resolution three-dimensional (3D) images can be acquired by the planar Multiple-Input Multiple-Output (MIMO) array radar making future work like detection and tracking easier. However, regarding portability and to save the costs of radar system, MIMO radar array adopts sparse type with limited number of antennas, so the imaging performance of a MIMO radar system is limited. In this paper, the 3D back projection imaging algorithm is verified by the experimental results of planar MIMO array for human body and an enhanced radar imaging method is proposed. The Lucy-Richardson (LR) algorithm based on deconvolution that is normally used for optical images is applied in radar images. Since the LR algorithm can amplify the noise level in a noise-contaminated system, a regularization method based on the Total Variation constraint is further incorporated in the LR algorithm to suppress the ill-posed characteristics. The proposed method shows a higher image Signal-to-Noise Ratio, a faster rate of convergence, a higher structure similarity and a smaller relative error compared to some similar methods. In the meantime, it also reduces the loss of image information after image enhancement and improves the radar image quality (get less grating lobe and clearer human limbs). The proposed method overcomes the disadvantages mentioned above and is verified by simulation experiment and real data measurement.

Morphology-adaptive total variation for the reconstruction of quantitative susceptibility map from the magnetic resonance imaging phase.

Quantitative susceptibility mapping (QSM) is a magnetic resonance imaging technique that quantifies the magnetic susceptibility distribution within biological tissues. QSM calculates the underlying magnetic susceptibility by deconvolving the tissue magnetic field map with a unit dipole kernel. However, this deconvolution problem is ill-posed. The morphology enabled dipole inversion (MEDI) introduces total variation (TV) to regularize the susceptibility reconstruction. However, MEDI results still contain artifacts near tissue boundaries because MEDI only imposes TV constraint on voxels inside smooth regions. We introduce a Morphology-Adaptive TV (MATV) for improving TV-regularized QSM. The MATV method first classifies imaging target into smooth and nonsmooth regions by thresholding magnitude gradients. In the dipole inversion for QSM, the TV regularization weights are a monotonically decreasing function of magnitude gradients. Thus, voxels inside smooth regions are assigned with larger weights than those in nonsmooth regions. Using phantom and in vivo datasets, we compared the performance of MATV with that of MEDI. MATV results had better visual quality than MEDI results, especially near tissue boundaries. Preliminary brain imaging results illustrated that MATV has potential to improve the reconstruction of regions near tissue boundaries.

Constrained nonlinear amplitude variation with offset inversion using Zoeppritz equations

The inversion of prestack seismic data using amplitude variation with offset (AVO) has received increased attention in the past few decades because of its key role in estimating reservoir properties. AVO is mainly governed by the Zoeppritz equations, but traditional inversion techniques are based on various linear or quasilinear approximations to these nonlinear equations. We have developed an efficient algorithm for nonlinear AVO inversion of precritical reflections using the exact Zoeppritz equations in multichannel and multi-interface form for simultaneous estimation of the P-wave velocity, S-wave velocity, and density. The total variation constraint is used to overcome the ill-posedness while solving the forward nonlinear model and to preserve the sharpness of the interfaces in the parameter space. The optimization is based on a combination of Levenberg’s algorithm and the split Bregman iterative scheme, in which we have to refine the data and model parameters at each iteration. We refine the data via the original nonlinear equations, but we use the traditional cost-effective linearized AVO inversion to construct the Jacobian matrix and update the model. Numerical experiments show that this new iterative procedure is convergent and converges to a solution of the nonlinear problem. We determine the performance and optimality of our nonlinear inversion algorithm with various simulated and field seismic data sets.

Longitudinally Guided Super-Resolution of Neonatal Brain Magnetic Resonance Images.

Neonatal magnetic resonance (MR) images typically have low spatial resolution and insufficient tissue contrast. Interpolation methods are commonly used to upsample the images for the subsequent analysis. However, the resulting images are often blurry and susceptible to partial volume effects. In this paper, we propose a novel longitudinally guided super-resolution (SR) algorithm for neonatal images. This is motivated by the fact that anatomical structures evolve slowly and smoothly as the brain develops after birth. We propose a strategy involving longitudinal regularization, similar to bilateral filtering, in combination with low-rank and total variation constraints to solve the ill-posed inverse problem associated with image SR. Experimental results on neonatal MR images demonstrate that the proposed algorithm recovers clear structural details and outperforms state-of-the-art methods both qualitatively and quantitatively.

Total Variation Regularization Strategies in Full-Waveform Inversion

We propose an extended full-waveform inversion formulation that includes general convex constraints on the model. Though the full problem is highly nonconvex, the overarching optimization scheme arrives at geologically plausible results by solving a sequence of relaxed and warm-started constrained convex subproblems. The combination of box, total variation, and successively relaxed asymmetric total variation constraints allows us to steer free from parasitic local minima while keeping the estimated physical parameters laterally continuous and in a physically realistic range. For accurate starting models, numerical experiments carried out on the challenging 2004 BP velocity benchmark demonstrate that bound and total variation constraints improve the inversion result significantly by removing inversion artifacts, related to source encoding, and by clearly improved delineation of top, bottom, and flanks of a high-velocity high-contrast salt inclusion. The experiments also show that for poor starting models these two constraints by themselves are insufficient to detect the bottom of high-velocity inclusions such as salt. Inclusion of the one-sided asymmetric total variation constraint overcomes this issue by discouraging velocity lows to buildup during the early stages of the inversion. To the best of the authors' knowledge the presented algorithm is the first to successfully remove the imprint of local minima caused by poor starting models and band-width limited finite aperture data.

GPU-Accelerated Dynamic Wavelet Thresholding Algorithm for X-Ray CT Metal Artifact Reduction

The computed tomography (CT) imaging technique has been used to diagnose widespread disease for many years; however, severe streaking artifacts have been observed to appear in the reconstructed images of examinate contains metal objects. In this paper, we propose a dynamic wavelet thresholding metal artifact reduction (MAR) algorithm based on a statistic iterative reconstruction (SIR) model for 2-D fan beam CT. Cubic spline interpolation is utilized to remove blocky black artifacts caused by incomplete projections, and it also makes the solution closer to the optimum. The dynamic wavelet thresholding method contains the benefits of both wavelet soft and hard thresholding methods and promotes the sparsity of the image, which is used to erase residual streaking artifacts and accelerate the convergence of the SIR. The algorithm is accelerated by graphics processing unit programming and costs 14.44s with 40 iterations, meeting the demand of clinical practice. The performance of the proposed algorithm is compared with two classical MAR algorithms: the total variation (TV) constraint SIR algorithm and the reweighted TV constraint SIR algorithm. The experimental datasets include nine artificial datasets. Both qualitative and quantitative evaluation results show the outstanding performance of the proposed algorithm in suppressing the metal artifacts and preserving the image details.

Anomaly Detection for Hyperspectral Images Based on Anisotropic Spatial-Spectral Total Variation and Sparse Constraint

A novel anomaly detection method for hyperspectral images (HSIs) is proposed based on anisotropic spatial-spectral total variation and sparse constraint. HSIs are assumed to be not only smooth in spectral dimension but also piecewise smooth in spatial dimension. The proposed method adopts the anisotropic spatial-spectral total variation model which combines 2D spatial total variation and 1D spectral variation to explore the spatial-spectral smooth property of HSIs. Meanwhile, the sparse property of anomalies is exploited for its low probability in the image. To utilize both the spatial and spectral information of HSIs, we preserve the original cubic form of HSIs and divide the HSIs into three 3D arrays, each representing the background, the anomaly, and the noise respectively. By using anisotropic spatial-spectral total variation regularization on the background component and sparse constraint on the anomaly component, this anomaly detection problem has therefore been formulated as a constraint optimization problem whose solution has been derived by alternately using Split Bregman Method and Go Decomposition (GoDec) Method. Experimental results on hyperspectral datasets illustrate that our proposed method has a better detection performance than state-of-the-art hyperspectral anomaly detection methods.

Image Reconstruction for Electrical Impedance Tomography Using Enhanced Adaptive Group Sparsity With Total Variation

A novel image reconstruction algorithm for electrical impedance tomography using enhanced adaptive group sparsity with total variation constraint is proposed in this paper. The new algorithm simultaneously utilizes the prior knowledge of regional structure feature and global characteristic of the conductivity distribution. The regional structure feature is encoded by using an enhanced adaptive group sparsity constraint. Meanwhile, the global characteristic of inclusion boundary is considered by imposing total variation constraint on the whole image. An enhanced adaptive pixel grouping algorithm is proposed based on Otsu's thresholding method, which demonstrates good noise immunity. An accelerated alternating direction method of multipliers is utilized to solve the proposed problem for a faster convergence rate. The performance of the proposed algorithm is thoroughly evaluated by numerical simulation and experiments. Comparing with the state-of-the-art algorithms, such as the L1 regularization, total variation regularization, and our former work on adaptive group sparsity, the proposed method has demonstrated superior spatial resolution and better noise reduction performance. Combined with the total variation constraint, distinct boundary of inclusions has also been obtained.

A sequential solution for anisotropic total variation image denoising with interval constraints

We show that two problems involving the anisotropic total variation (TV) and interval constraints on the unknown variables admit, under some conditions, a simple sequential solution. Problem 1 is a constrained TV penalized image denoising problem; problem 2 is a constrained fused lasso signal approximator. The sequential solution entails finding first the solution to the unconstrained problem, and then applying a thresholding to satisfy the constraints. If the interval constraints are uniform, this sequential solution solves problem 1. If the interval constraints furthermore contain zero, the sequential solution solves problem 2. Here uniform interval constraints refer to all unknowns being constrained to the same interval. A typical example of application is image denoising in x-ray CT, where the image intensities are non-negative as they physically represent linear attenuation coefficient in the patient body. Our results are simple yet seem unknown; we establish them using the Karush–Kuhn–Tucker conditions for constrained convex optimization.

Medical Image Fusion and Denoising with Alternating Sequential Filter and Adaptive Fractional Order Total Variation

Medical image fusion aims at integrating information from multimodality medical images to obtain a more complete and accurate description of the same object, which provides an easy access for image-guided medical diagnostic and treatment. Unfortunately, medical images are often corrupted by noise in acquisition or transmission, and the noise signal is easily mistaken for a useful characterization of the image, making the fusion effect drop significantly. Thus, the existence of noise presents a great challenge for most of traditional image fusion methods. To address this problem, an effective variation model for multimodality medical image fusion and denoising is proposed. First, a multiscale alternating sequential filter is exploited to extract the useful characterizations (e.g., details and edges) from noisy input medical images. Then, a recursive filtering-based weight map is constructed to guide the fusion of main features of input images. Additionally, total variation (TV) constraint is developed by constructing an adaptive fractional order $p$ based on the local contrast of fused image, further effectively suppressing noise while avoiding the staircase effect of the TV. The experimental results indicate that the proposed method performs well with both noisy and normal medical images, outperforming conventional methods in terms of fusion quality and noise reduction.

Variational framework for low-light image enhancement using optimal transmission map and combined [formula omitted] and [formula omitted]-minimization

This paper presents a novel variational framework for low-light image enhancement. The proposed enhancement algorithm simultaneously performs brightness enhancement and noise reduction using a variational optimization. An edge-preserved noise reduction is performed by minimizing the total variation constraint term in the energy function. In addition, the proposed method estimates the optimal transmission map to restore the low-light image by minimizing the ℓ2-norm smoothness and data-fidelity terms. To minimize the proposed energy functional, the proposed method splits the ℓ1-derivative term under the split Bregman iteration framework. The performance of the proposed method is evaluated using both simulated and natural low-light images. Experimental results show that the proposed enhancement method can significantly improve the quality of the low-light images without noise amplification.

Technical Note: Evaluation of pre-reconstruction interpolation methods for iterative reconstruction of radial k-space data.

To evaluate the use of three different pre-reconstruction interpolation methods to convert non-Cartesian k-space data to Cartesian samples such that iterative reconstructions can be performed more simply and more rapidly. Phantom as well as cardiac perfusion radial datasets were reconstructed by four different methods. Three of the methods used pre-reconstruction interpolation once followed by a fast Fourier transform (FFT) at each iteration. The methods were: bilinear interpolation of nearest-neighbor points (BINN), 3-point interpolation, and a multi-coil interpolator called GRAPPA Operator Gridding (GROG). The fourth method performed a full non-Uniform FFT (NUFFT) at each iteration. An iterative reconstruction with spatiotemporal total variation constraints was used with each method. Differences in the images were quantified and compared. The GROG multicoil interpolation, the 3-point interpolation, and the NUFFT-at-each-iteration approaches produced high quality images compared to BINN, with the GROG-derived images having the fewest streaks among the three preinterpolation approaches. However, all reconstruction methods produced approximately equal results when applied to perfusion quantitation tasks. Pre-reconstruction interpolation gave approximately an 83% reduction in reconstruction time. Image quality suffers little from using a pre-reconstruction interpolation approach compared to the more accurate NUFFT-based approach. GROG-based pre-reconstruction interpolation appears to offer the best compromise by using multicoil information to perform the interpolation to Cartesian sample points prior to image reconstruction. Speed gains depend on the implementation and relatively standard optimizations on a MATLAB platform result in preinterpolation speedups of ~ 6 compared to using NUFFT at every iteration, reducing the reconstruction time from around 42 min to 7 min.

Research and application of spectral inversion technique in frequency domain to improve resolution of converted PS-wave

Multi-wave exploration is an effective means for improving precision in the exploration and development of complex oil and gas reservoirs that are dense and have low permeability. However, converted wave data is characterized by a low signal-to-noise ratio and low resolution, because the conventional deconvolution technology is easily affected by the frequency range limits, and there is limited scope for improving its resolution. The spectral inversion techniques is used to identify λ/8 thin layers and its breakthrough regarding band range limits has greatly improved the seismic resolution. The difficulty associated with this technology is how to use the stable inversion algorithm to obtain a high-precision reflection coefficient, and then to use this reflection coefficient to reconstruct broadband data for processing. In this paper, we focus on how to improve the vertical resolution of the converted PS-wave for multi-wave data processing. Based on previous research, we propose a least squares inversion algorithm with a total variation constraint, in which we uses the total variance as a priori information to solve under-determined problems, thereby improving the accuracy and stability of the inversion. Here, we simulate the Gaussian fitting amplitude spectrum to obtain broadband wavelet data, which we then process to obtain a higher resolution converted wave. We successfully apply the proposed inversion technology in the processing of high-resolution data from the Penglai region to obtain higher resolution converted wave data, which we then verify in a theoretical test. Improving the resolution of converted PS-wave data will provide more accurate data for subsequent velocity inversion and the extraction of reservoir reflection information.

3D CMRO2 mapping in human brain with direct 17O MRI: Comparison of conventional and proton-constrained reconstructions

Oxygen metabolism is altered in brain tumor regions and is quantified by the cerebral metabolic rate of oxygen consumption (CMRO2). Direct dynamic 17O MRI with inhalation of isotopically enriched 17O2 gas can be used to quantify CMRO2; however, pixel-wise CMRO2 quantification in human brain is challenging due to low natural abundance of 17O isotope and, thus, the low signal-to-noise ratio (SNR) of 17O MR images. To test the feasibility CMRO2 mapping at a clinical 3 T MRI system, a new iterative reconstruction was proposed, which uses the edge information contained in a co-registered 1H gradient image to construct a non-homogeneous anisotropic diffusion (AD) filter. AD-constrained reconstruction of 17O MR images was compared to conventional Kaiser-Bessel gridding without and with Hanning filtering, and to iterative reconstruction with a total variation (TV) constraint. For numerical brain phantom and in two in vivo data sets of one healthy volunteer, AD-constrained reconstruction provided 17O images with improved resolution of fine brain structures and resulted in higher SNR. CMRO2 values of 0.78 – 1.55µmol/gtissue/min (white brain matter) and 1.03 – 2.01µmol/gtissue/min (gray brain matter) as well as the CMRO2 maps are in a good agreement with the results of 15O-PET and 17O MRI at 7 T and at 9.4 T. In conclusion, the proposed AD-constrained reconstruction enabled calculation of 3D CMRO2 maps at 3 T MRI system, which is an essential step towards clinical translation of 17O MRI for non-invasive CMRO2 quantification in tumor patients.

Integration of optical flow and Multi-Path-Viterbi algorithm for stereo vision

This paper proposes a novel stereo matching algorithm to solve environment sensing problems. It integrates a non-convex optical flow and Viterbi process. The non-convex optical flow employs a new adaptive weighted non-convex Total Generalized Variation (TGV) model, which can obtain sharp disparity maps. Structural similarity, total variation constraint, and a specific merging strategy are combined with the 4 bi-directional Viterbi process to improve the robustness. In the fusion of the optical flow and Viterbi process, a new occlusion processing method is incorporated in order to get more sharp disparity and more robust result. Extensive experiments are conducted to compare this algorithm with other state-of-the-art methods. Experimental results show the superiority of our algorithm.

Low Dose PET Image Reconstruction with Total Variation Using Alternating Direction Method.

In this paper, a total variation (TV) minimization strategy is proposed to overcome the problem of sparse spatial resolution and large amounts of noise in low dose positron emission tomography (PET) imaging reconstruction. Two types of objective function were established based on two statistical models of measured PET data, least-square (LS) TV for the Gaussian distribution and Poisson-TV for the Poisson distribution. To efficiently obtain high quality reconstructed images, the alternating direction method (ADM) is used to solve these objective functions. As compared with the iterative shrinkage/thresholding (IST) based algorithms, the proposed ADM can make full use of the TV constraint and its convergence rate is faster. The performance of the proposed approach is validated through comparisons with the expectation-maximization (EM) method using synthetic and experimental biological data. In the comparisons, the results of both LS-TV and Poisson-TV are taken into consideration to find which models are more suitable for PET imaging, in particular low-dose PET. To evaluate the results quantitatively, we computed bias, variance, and the contrast recovery coefficient (CRC) and drew profiles of the reconstructed images produced by the different methods. The results show that both Poisson-TV and LS-TV can provide a high visual quality at a low dose level. The bias and variance of the proposed LS-TV and Poisson-TV methods are 20% to 74% less at all counting levels than those of the EM method. Poisson-TV gives the best performance in terms of high-accuracy reconstruction with the lowest bias and variance as compared to the ground truth (14.3% less bias and 21.9% less variance). In contrast, LS-TV gives the best performance in terms of the high contrast of the reconstruction with the highest CRC.