A nonlinear total variation based computed tomography (CT) image reconstruction method using gradient reinforcement

Compressed sensing-based reconstruction algorithms have been proven to be more successful than analytical or iterative methods for sparse computed tomography (CT) imaging by narrowing down the solution set thanks to its ability to seek a sparser solution. Total variation (TV), one of the most popular sparsifiers, exploits spatial continuity of features by restricting variation between two neighboring pixels in each direction as using partial derivatives. When the number of projections is much fewer than the one in conventional CT, which results in much less sampling rate than the minimum required one, TV may not provide satisfactory results. In this study, a new regularizer is proposed which seeks for a sparser solution by reinforcing the gradient of TV and empowering the spatial continuity of features. The experiments are done by using both analitical phantom and real human CT images and the results are compared with conventional, four-directional, and directional TV algorithms by using contrast-to-noise ratio (CNR), signal-to-noise ratio (SNR) and Structural Similarity Index (SSIM) metrics. Both quantitative and visual evaluations show that the proposed method is promising for sparse CT image reconstruction by reducing the background noise while preserving the features and edges.

Ultrafast multiple paramagnetic species EPR imaging using a total variation based model

An EPR spectrum or an EPR sinogram for imaging contains information about all the paramagnetic species that are in the analyzed sample. When only one species is present, an image of its spatial repartition can be reconstructed from the sinogram by using the well-known Filtered Back-Projection (FBP). However, in the case of several species, the FBP does not allow the reconstruction of the images of each species from a standard acquisition. One has to use for this spectral-spatial imaging whose acquisition can be very long. A new approach, based on Total Variation minimization, is proposed in order to efficiently extract the spatial repartitions of all the species present in a sample from standard imaging data and therefore drastically reduce the acquisition time. Experiments have been carried out on Tetrathiatriarylmethyl, nitroxide and DPPH.

A spatially variant high-order variational model for Rician noise removal

Rician noise removal is an important problem in magnetic resonance (MR) imaging. Among the existing approaches, the variational method is an essential mathematical technique for Rician noise reduction. The previous variational methods mainly employ the total variation (TV) regularizer, which is a first-order term. Although the TV regularizer is able to remove noise while preserving object edges, it suffers the staircase effect. Besides, the adaptability has received little research attention. To this end, we propose a spatially variant high-order variational model (SVHOVM) for Rician noise reduction. We introduce a spatially variant TV regularizer, which can adjust the smoothing strength for each pixel depending on its characteristics. Furthermore, SVHOVM utilizes the bounded Hessian (BH) regularizer to diminish the staircase effect generated by the TV term. We develop a split Bregman algorithm to solve the proposed minimization problem. Extensive experiments are performed to demonstrate the superiority of SVHOVM over some existing variational models for Rician noise removal.

Compressed sensing reconstruction shortens the acquisition time for myocardial perfusion imaging: a simulation study

Compressed sensing (CS) has been used to improve image quality in single-photon emission tomography (SPECT) imaging. However, the effects of CS on image quality parameters in myocardial perfusion imaging (MPI) have not been investigated in detail. This preliminary study aimed to compare the performance of CS-iterative reconstruction (CS-IR) with filtered back-projection (FBP) and maximum likelihood expectation maximization (ML-EM) on their ability to reduce the acquisition time of MPI. A digital phantom that mimicked the left ventricular myocardium was created. Projection images with 120 and 30 directions (360°), and with 60 and 15 directions (180°) were generated. The SPECT images were reconstructed using FBP, ML-EM, and CS-IR. The coefficient of variation (CV) for the uniformity of myocardial accumulation, septal wall thickness, and contrast ratio (Contrast) of the defect/normal lateral wall were calculated for evaluation. The simulation was performed ten times. The CV of CS-IR was lower than that of FBP and ML-EM in both 360° and 180° acquisitions. The septal wall thickness of CS-IR at the 360° acquisition was inferior to that of ML-EM, with a difference of 2.5 mm. Contrast did not differ between ML-EM and CS-IR for the 360° and 180° acquisitions. The CV for the quarter-acquisition time in CS-IR was lower than that for the full-acquisition time in the other reconstruction methods. CS-IR has the potential to reduce the acquisition time of MPI.

A Novel Task-Based reconstruction approach for digital breast tomosynthesis

The reconstruction of a volumetric image from Digital Breast Tomosynthesis (DBT) measurements is an ill-posed inverse problem, for which existing iterative regularized approaches can provide a good solution. However, the clinical task is somehow omitted in the derivation of those techniques, although it plays a primary role in the radiologist diagnosis. In this work, we address this issue by introducing a novel variational formulation for DBT reconstruction, tailored for a specific clinical task, namely the detection of microcalcifications. Our method aims at simultaneously enhancing the detectability performance and enabling a high-quality restoration of the background breast tissues. Our contribution is threefold. First, we introduce an original task-based reconstruction framework through the proposition of a detectability function inspired from mathematical model observers. Second, we propose a novel total-variation regularizer where the gradient field accounts for the different morphological contents of the imaged breast. Third, we integrate the two developed measures into a cost function, minimized thanks to a new form of the Majorize Minimize Memory Gradient (3MG) algorithm. We conduct a numerical comparison of the convergence speed of the proposed method with those of standard convex optimization algorithms. Experimental results show the interest of our DBT reconstruction approach, qualitatively and quantitatively.

Adaptive Total-Variation Regularized Low-Rank Representation for Analyzing Single-Cell RNA-seq Data

High-throughput sequencing of single-cell gene expression reveals a complex mechanism of individual cell's heterogeneity in a population. An important purpose for analyzing single-cell RNA sequencing (scRNA-seq) data is to identify cell subtypes and functions by cell clustering. To deal with high levels of noise and cellular heterogeneity, we introduced a new single cell data analysis model called Adaptive Total-Variation Regularized Low-Rank Representation (ATV-LRR). In scRNA-seq data, ATV-LRR can reconstruct the low-rank subspace structure to learn the similarity of cells. The low-rank representation can not only segment multiple linear subspaces, but also extract important information. Moreover, adaptive total variation also can remove cell noise and preserve cell feature details by learning the gradient information of the data. At the same time, to analyze scRNA-seq data with unknown prior information, we introduced the maximum eigenvalue method into the ATV-LRR model to automatically identify cell populations. The final clustering results show that the ATV-LRR model can detect cell types more effectively and stably.

COVID TV-Unet: Segmenting COVID-19 chest CT images using connectivity imposed Unet

The novel corona-virus disease (COVID-19) pandemic has caused a major outbreak in more than 200 countries around the world, leading to a severe impact on the health and life of many people globally. By October 2020, more than 44 million people were infected, and more than 1,000,000 deaths were reported. Computed Tomography (CT) images can be used as an alternative to the time-consuming RT-PCR test, to detect COVID-19. In this work we propose a segmentation framework to detect chest regions in CT images, which are infected by COVID-19. An architecture similar to a Unet model was employed to detect ground glass regions on a voxel level. As the infected regions tend to form connected components (rather than randomly distributed voxels), a suitable regularization term based on 2D-anisotropic total-variation was developed and added to the loss function. The proposed model is therefore called "TV-Unet". Experimental results obtained on a relatively large-scale CT segmentation dataset of around 900 images, incorporating this new regularization term leads to a 2% gain on overall segmentation performance compared to the Unet trained from scratch. Our experimental analysis, ranging from visual evaluation of the predicted segmentation results to quantitative assessment of segmentation performance (precision, recall, Dice score, and mIoU) demonstrated great ability to identify COVID-19 associated regions of the lungs, achieving a mIoU rate of over 99%, and a Dice score of around 86%.

ConvSCCS: convolutional self-controlled case series model for lagged adverse event detection

With the increased availability of large electronic health records databases comes the chance of enhancing health risks screening. Most post-marketing detection of adverse drug reaction (ADR) relies on physicians' spontaneous reports, leading to under-reporting. To take up this challenge, we develop a scalable model to estimate the effect of multiple longitudinal features (drug exposures) on a rare longitudinal outcome. Our procedure is based on a conditional Poisson regression model also known as self-controlled case series (SCCS). To overcome the need of precise risk periods specification, we model the intensity of outcomes using a convolution between exposures and step functions, which are penalized using a combination of group-Lasso and total-variation. Up to our knowledge, this is the first SCCS model with flexible intensity able to handle multiple longitudinal features in a single model. We show that this approach improves the state-of-the-art in terms of mean absolute error and computation time for the estimation of relative risks on simulated data. We apply this method on an ADR detection problem, using a cohort of diabetic patients extracted from the large French national health insurance database (SNIIRAM), a claims database containing medical reimbursements of more than 53 million people. This work has been done in the context of a research partnership between Ecole Polytechnique and CNAMTS (in charge of SNIIRAM).

Adaptive nonparametric regression with the K-nearest neighbour fused lasso

The fused lasso, also known as total-variation denoising, is a locally adaptive function estimator over a regular grid of design points. In this article, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to a method for nonparametric regression. This approach, which we call the [Formula: see text]-nearest-neighbours fused lasso, involves computing the [Formula: see text]-nearest-neighbours graph of the design points and then performing the fused lasso over this graph. We show that this procedure has a number of theoretical advantages over competing methods: specifically, it inherits local adaptivity from its connection to the fused lasso, and it inherits manifold adaptivity from its connection to the [Formula: see text]-nearest-neighbours approach. In a simulation study and an application to flu data, we show that excellent results are obtained. For completeness, we also study an estimator that makes use of an [Formula: see text]-graph rather than a [Formula: see text]-nearest-neighbours graph and contrast it with the [Formula: see text]-nearest-neighbours fused lasso.

A robust electrical conductivity imaging method with total variation and wavelet regularization

PURPOSE

This study aims to develop and evaluate a robust conductivity imaging method that combines total variation and wavelet regularization to enhance the accuracy of conductivity maps.

THEORY AND METHODS

The proposed approach is based on a gradient-based method. The central equation is derived from Maxwell's equation and describes the relationship between conductivity and the transceive phase. A linear system equation is obtained via a finite-difference method and solved using a least-squares method. Total variation and wavelet transform regularization terms are added to the minimization problem and solved using the Split Bregman method to improve reconstruction stability. The proposed approach is compared with conventional and gradient-based methods. Numerical simulations are performed to validate the accuracy of the developed method, and the effects of noise are determined. Phantom and in vivo experiments are conducted at 3 T to verify the clinical applicability of the proposed method.

RESULTS

Numerical simulations show that the proposed method is more robust than other methods and can suppress the effects of noise. The quantitative conductivity value of the phantom experiment agrees with the measured value. The in vivo experiment results present a clear structure, and the conductivity value of the tumor region is significantly higher than that around healthy tissues.

CONCLUSION

The proposed electrical conductivity imaging method can improve the quality of conductivity reconstruction, and thus, has future clinical applications.

Highly accelerated 4D flow cardiovascular magnetic resonance using a pseudo-spiral Cartesian acquisition and compressed sensing reconstruction for carotid flow and wall shear stress

BACKGROUND

4D flow cardiovascular magnetic resonance (CMR) enables visualization of complex blood flow and quantification of biomarkers for vessel wall disease, such as wall shear stress (WSS). Because of the inherently long acquisition times, many efforts have been made to accelerate 4D flow acquisitions, however, no detailed analysis has been made on the effect of Cartesian compressed sensing accelerated 4D flow CMR at different undersampling rates on quantitative flow parameters and WSS.

METHODS

We implemented a retrospectively triggered 4D flow CMR acquisition with pseudo-spiral Cartesian k-space filling, which results in incoherent undersampling of k-t space. Additionally, this strategy leads to small jumps in k-space thereby minimizing eddy current related artifacts. The pseudo-spirals were rotated in a tiny golden-angle fashion, which provides optimal incoherence and a variable density sampling pattern with a fully sampled center. We evaluated this 4D flow protocol in a carotid flow phantom with accelerations of R = 2-20, as well as in carotids of 7 healthy subjects (27 ± 2 years, 4 male) for R = 10-30. Fully sampled 2D flow CMR served as a flow reference. Arteries were manually segmented and registered to enable voxel-wise comparisons of both velocity and WSS using a Bland-Altman analysis.

RESULTS

Magnitude images, velocity images, and pathline reconstructions from phantom and in vivo scans were similar for all accelerations. For the phantom data, mean differences at peak systole for the entire vessel volume in comparison to R = 2 ranged from - 2.3 to - 5.3% (WSS) and - 2.4 to - 2.2% (velocity) for acceleration factors R = 4-20. For the in vivo data, mean differences for the entire vessel volume at peak systole in comparison to R = 10 were - 9.9, - 13.4, and - 16.9% (WSS) and - 8.4, - 10.8, and - 14.0% (velocity), for R = 20, 25, and 30, respectively. Compared to single slice 2D flow CMR acquisitions, peak systolic flow rates of the phantom showed no differences, whereas peak systolic flow rates in the carotid artery in vivo became increasingly underestimated with increasing acceleration.

CONCLUSION

Acquisition of 4D flow CMR of the carotid arteries can be highly accelerated by pseudo-spiral k-space sampling and compressed sensing reconstruction, with consistent data quality facilitating velocity pathline reconstructions, as well as quantitative flow rate and WSS estimations. At an acceleration factor of R = 20 the underestimation of peak velocity and peak WSS was acceptable (< 10%) in comparison to an R = 10 accelerated 4D flow CMR reference scan. Peak flow rates were underestimated in comparison with 2D flow CMR and decreased systematically with higher acceleration factors.

Accelerated Variational PDEs for Efficient Solution of Regularized Inversion Problems

We further develop a new framework, called PDE acceleration, by applying it to calculus of variation problems defined for general functions onℝ n , obtaining efficient numerical algorithms to solve the resulting class of optimization problems based on simple discretizations of their corresponding accelerated PDEs. While the resulting family of PDEs and numerical schemes are quite general, we give special attention to their application for regularized inversion problems, with particular illustrative examples on some popular image processing applications. The method is a generalization of momentum, or accelerated, gradient descent to the PDE setting. For elliptic problems, the descent equations are a nonlinear damped wave equation, instead of a diffusion equation, and the acceleration is realized as an improvement in the CFL condition from Δt ~ Δx 2 (for diffusion) to Δt ~ Δx (for wave equations). We work out several explicit as well as a semi-implicit numerical scheme, together with their necessary stability constraints, and include recursive update formulations which allow minimal-effort adaptation of existing gradient descent PDE codes into the accelerated PDE framework. We explore these schemes more carefully for a broad class of regularized inversion applications, with special attention to quadratic, Beltrami, and total variation regularization, where the accelerated PDE takes the form of a nonlinear wave equation. Experimental examples demonstrate the application of these schemes for image denoising, deblurring, and inpainting, including comparisons against primal-dual, split Bregman, and ADMM algorithms.

Optoacoustic model-based inversion using anisotropic adaptive total-variation regularization

In optoacoustic tomography, image reconstruction is often performed with incomplete or noisy data, leading to reconstruction errors. Significant improvement in reconstruction accuracy may be achieved in such cases by using nonlinear regularization schemes, such as total-variation minimization and L ₁-based sparsity-preserving schemes. In this paper, we introduce a new framework for optoacoustic image reconstruction based on adaptive anisotropic total-variation regularization, which is more capable of preserving complex boundaries than conventional total-variation regularization. The new scheme is demonstrated in numerical simulations on blood-vessel images as well as on experimental data and is shown to be more capable than the total-variation-L ₁ scheme in enhancing image contrast.

Compressed sensing MRI based on image decomposition model and group sparsity

The image representation plays an important role in compressed sensing magnetic resonance imaging (CSMRI). However, how to adaptive sparsely represent images is a challenge for accurately reconstructing magnetic resonance (MR) images from highly undersampled data with noise. In order to further improve the reconstruction quality of the MR image, this paper first proposes tight frame-based group sparsity (TFGS) regularization that can capture the structure information of images appropriately, then TFGS regularization is employed to the image cartoon-texture decomposition model to construct CSMRI algorithm, termed cartoon-texture decomposition CSMRI algorithm (CD-MRI). CD-MRI effectively integrates the total variation and TFGS regularization into the image cartoon-texture decomposition framework, and utilizes the sparse priors of image cartoon and texture components to reconstruct MR images. Virtually, CD-MRI exploits the global sparse representations of image cartoon components by the total variation regularization, and explores group sparse representations of image texture components via the adaptive tight frame learning technique and group sparsity regularization. The alternating iterative method combining with the majorization-minimization algorithm is applied to solve the formulated optimization problem. Finally, simulation experiments demonstrate that the proposed algorithm can achieve high-quality MR image reconstruction from undersampled K-space data, and can remove noise in different sampling schemes. Compared to the previous CSMRI algorithms, the proposed approach can lead to better image reconstruction performance and better robustness to noise.

General regularization framework for DEER spectroscopy

Tikhonov regularization is the standard processing technique for the inversion of double electron-electron resonance (DEER) data to distance distributions without assuming a parametrized model. In other fields it has been surpassed by modern regularization methods. We analyze such alternative regularization methods based on the Tikhonov, total variation (TV) and Huber penalties with and without the use of Bregman iterations. For this, we provide a general mathematical framework and its open-source software implementation. We extend an earlier approach by Edwards and Stoll for the selection of an optimal regularization parameter to all of these penalties and use their big test data set of noisy DEER traces with known ground truth for assessment. The results indicate that regularization methods based on Bregman iterations provide an improvement upon Tikhonov regularization in recognizing features and recovering distribution width at moderate signal-to-noise ratio, provided that noise variance is known. Bregman-iterative methods are robust with respect to the method used in the choice of regularization parameter.

Noise cancellation using total variation for copy number variation detection

BACKGROUND

Due to recent advances in sequencing technologies, sequence-based analysis has been widely applied to detecting copy number variations (CNVs). There are several techniques for identifying CNVs using next generation sequencing (NGS) data, however methods employing depth of coverage or read depth (RD) have recently become a main technique to identify CNVs. The main assumption of the RD-based CNV detection methods is that the readcount value at a specific genomic location is correlated with the copy number at that location. However, readcount data's noise and biases distort the association between the readcounts and copy numbers. For more accurate CNV identification, these biases and noise need to be mitigated. In this work, to detect CNVs more precisely and efficiently we propose a novel denoising method based on the total variation approach and the Taut String algorithm.

RESULTS

To investigate the performance of the proposed denoising method, we computed sensitivities, false discovery rates and specificities of CNV detection when employing denoising, using both simulated and real data. We also compared the performance of the proposed denoising method, Taut String, with that of the commonly used approaches such as moving average (MA) and discrete wavelet transforms (DWT) in terms of sensitivity of detecting true CNVs and time complexity. The results show that Taut String works better than DWT and MA and has a better power to identify very narrow CNVs. The ability of Taut String denoising in preserving CNV segments' breakpoints and narrow CNVs increases the detection accuracy of segmentation algorithms, resulting in higher sensitivities and lower false discovery rates.

CONCLUSIONS

In this study, we proposed a new denoising method for sequence-based CNV detection based on a signal processing technique. Existing CNV detection algorithms identify many false CNV segments and fail in detecting short CNV segments due to noise and biases. Employing an effective and efficient denoising method can significantly enhance the detection accuracy of the CNV segmentation algorithms. Advanced denoising methods from the signal processing field can be employed to implement such algorithms. We showed that non-linear denoising methods that consider sparsity and piecewise constant characteristics of CNV data result in better performance in CNV detection.

Fast iteratively reweighted least squares algorithms for analysis-based sparse reconstruction

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation (TV) regularization. The proposed algorithm is based on the iterative reweighted least squares (IRLS) framework, and is accelerated by the preconditioned conjugate gradient method. The proposed method is motivated by that, the Hessian matrix for many applications is diagonally dominant. The convergence rate of the proposed algorithm is empirically shown to be almost the same as that of the traditional IRLS algorithms, that is, linear convergence. Moreover, with the specifically devised preconditioner, the computational cost for the subproblem is significantly less than that of traditional IRLS algorithms, which enables our approach to handle large scale problems. In addition to the fast convergence, it is straightforward to apply our method to standard sparsity, group sparsity, overlapping group sparsity and TV based problems. Experiments are conducted on practical applications of compressive sensing magnetic resonance imaging. Extensive results demonstrate that the proposed algorithm achieves superior performance over 14 state-of-the-art algorithms in terms of both accuracy and computational cost.

Photoacoustic imaging reconstruction using combined nonlocal patch and total-variation regularization for straight-line scanning

Background

For practical straight-line scanning in photoacoustic imaging (PAI), serious artifacts caused by missing data will occur. Traditional total variation (TV)-based algorithms fail to obtain satisfactory results, with an over-smoothed and blurred geometric structure. Therefore, it is important to develop a new algorithm to improve the quality of practical straight-line reconstructed images.

Methods

In this paper, a combined nonlocal patch and TV-based regularization model for PAI reconstruction is proposed to solve these problems. A modified adaptive nonlocal weight function is adopted to provide more reliable estimations for the similarities between patches. Similar patches are searched for throughout the entire image; thus, this model realizes adaptive search for the neighborhood of the patch. The optimization problem is simplified to a common iterative PAI reconstruction problem.

Results and conclusion

The proposed algorithm is validated by a series of numerical simulations and an in vitro experiment for straight-line scanning. The results of patch-TV are compared to those of two mainstream TV-based algorithms as well as the iterative algorithm only with patch-based regularization. Moreover, the peak signal-to-noise ratio, the noise robustness, and the convergence and calculation speeds are compared and discussed. The results show that the proposed patch-TV yields significant improvement over the other three algorithms qualitatively and quantitatively. These simulations and experiment indicate that the patch-TV algorithm successfully solves the problems of PAI reconstruction and is highly effective in practical PAI applications.

An efficient algorithm for dynamic MRI using low-rank and total variation regularizations

In this paper, we propose an efficient algorithm for dynamic magnetic resonance (MR) image reconstruction. With the total variation (TV) and the nuclear norm (NN) regularization, the TVNNR model can utilize both spatial and temporal redundancy in dynamic MR images. Such prior knowledge can help model dynamic MRI data significantly better than a low-rank or a sparse model alone. However, it is very challenging to efficiently minimize the energy function due to the non-smoothness and non-separability of both TV and NN terms. To address this issue, we propose an efficient algorithm by solving a primal-dual form of the original problem. We theoretically prove that the proposed algorithm achieves a convergence rate of O(1/N) for N iterations. In comparison with state-of-the-art methods, extensive experiments on single-coil and multi-coil dynamic MR data demonstrate the superior performance of the proposed method in terms of both reconstruction accuracy and time complexity.

Subsampling and inpainting approaches for electron tomography

With the aim of addressing the issue of sample damage during electron tomography data acquisition, we propose a number of new reconstruction strategies based on subsampling (which uses only a subset of a full image) and inpainting (recovery of a full image from subsampled one). We point out that the total-variation (TV) inpainting model commonly used to inpaint subsampled images may be inappropriate for 2D projection images of typical TEM specimens. Thus, we propose higher-order TV (HOTV) inpainting, which accommodates the fact that projection images may be inherently smooth, as a more suitable image inpainting scheme. We also describe how the HOTV method can be extended to 3D, a scheme which makes use of both image data and sinogram data. Additionally, we propose gradient subsampling as a more efficient scheme than random subsampling. We make a rigorous comparison of our proposed new reconstruction schemes with existing ones. The new schemes are demonstrated to perform better than or as well as existing schemes, and we show that they outperform existing schemes at low subsampling rates.

Compressed sensing MRI via fast linearized preconditioned alternating direction method of multipliers

Background

The challenge of reconstructing a sparse medical magnetic resonance image based on compressed sensing from undersampled k-space data has been investigated within recent years. As total variation (TV) performs well in preserving edge, one type of approach considers TV-regularization as a sparse structure to solve a convex optimization problem. Nevertheless, this convex optimization problem is both nonlinear and nonsmooth, and thus difficult to handle, especially for a large-scale problem. Therefore, it is essential to develop efficient algorithms to solve a very broad class of TV-regularized problems.

Methods

In this paper, we propose an efficient algorithm referred to as the fast linearized preconditioned alternating direction method of multipliers (FLPADMM), to solve an augmented TV-regularized model that adds a quadratic term to enforce image smoothness. Because of the separable structure of this model, FLPADMM decomposes the convex problem into two subproblems. Each subproblem can be alternatively minimized by augmented Lagrangian function. Furthermore, a linearized strategy and multistep weighted scheme can be easily combined for more effective image recovery.

Results

The method of the present study showed improved accuracy and efficiency, in comparison to other methods. Furthermore, the experiments conducted on in vivo data showed that our algorithm achieved a higher signal-to-noise ratio (SNR), lower relative error (Rel.Err), and better structural similarity (SSIM) index in comparison to other state-of-the-art algorithms.

Conclusions

Extensive experiments demonstrate that the proposed algorithm exhibits superior performance in accuracy and efficiency than conventional compressed sensing MRI algorithms.

Generalized Scalar-on-Image Regression Models via Total Variation

The use of imaging markers to predict clinical outcomes can have a great impact in public health. The aim of this paper is to develop a class of generalized scalar-on-image regression models via total variation (GSIRM-TV), in the sense of generalized linear models, for scalar response and imaging predictor with the presence of scalar covariates. A key novelty of GSIRM-TV is that it is assumed that the slope function (or image) of GSIRM-TV belongs to the space of bounded total variation in order to explicitly account for the piecewise smooth nature of most imaging data. We develop an efficient penalized total variation optimization to estimate the unknown slope function and other parameters. We also establish nonasymptotic error bounds on the excess risk. These bounds are explicitly specified in terms of sample size, image size, and image smoothness. Our simulations demonstrate a superior performance of GSIRM-TV against many existing approaches. We apply GSIRM-TV to the analysis of hippocampus data obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset.

Total variation for the analysis of event-related potentials

BACKGROUND

Event-related potential waveforms are often analysed in the time-domain for changes of striking morphological features, like amplitudes or latencies of extrema, at the expense of missing less obvious changes in overall morphology.

NEW METHOD

The measure of total variation can capture a variety of changes in curve morphology. We show analytical examples, and the application to two sets of EEG data (n₁=41, n₂=19) difficult to analyse with more traditional methods.

RESULTS

Total variation can be used to identify the effects of experimental manipulations on event-related potential waveforms, and can additionally be used to identify the respective time windows by means of hierarchical subdivision of longer signals.

COMPARISON WITH EXISTING METHODS

The ANOVA of total variation provided additional insights into effects already hinted at by the ANOVA of global field power in the first experiment, and identified a number of interactions missed by an ANOVA of amplitude as well as a topographic ANOVA in the second one.

CONCLUSIONS

The analysis of total variation can be an interesting complement to more traditional analyses, especially when changes are hard to assess with traditional methods, e.g. in the absence of pronounced extrema, or the presence of noise or large interindividual variations of latency.

TENDER: Tensor non-local deconvolution enabled radiation reduction in CT perfusion

Stroke is the leading cause of long-term disability and the second leading cause of mortality in the world, and exerts an enormous burden on the public health. Computed Tomography (CT) remains one of the most widely used imaging modality for acute stroke diagnosis. However when coupled with CT perfusion, the excessive radiation exposure in repetitive imaging to assess treatment response and prognosis has raised significant public concerns regarding its potential hazards to both short- and long-term health outcomes. Tensor total variation has been proposed to reduce the necessary radiation dose in CT perfusion without comprising the image quality by fusing the information of the local anatomical structure with the temporal blood flow model. However the local search in the TTV framework fails to leverage the non-local information in the spatio-temporal data. In this paper, we propose TENDER, an efficient framework of non-local tensor deconvolution to maintain the accuracy of the hemodynamic parameters and the diagnostic reliability in low radiation dose CT perfusion. The tensor total variation is extended using non-local spatio-temporal cubics for regularization, and an efficient algorithm is proposed to reduce the time complexity with speedy similarity computation. Evaluations on clinical data of patients subjects with cerebrovascular disease and normal subjects demonstrate the advantage of non-local tensor deconvolution for reducing radiation dose in CT perfusion.

Hybrid regularizers-based adaptive anisotropic diffusion for image denoising

To eliminate the staircasing effect for total variation filter and synchronously avoid the edges blurring for fourth-order PDE filter, a hybrid regularizers-based adaptive anisotropic diffusion is proposed for image denoising. In the proposed model, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{-1}$$\end{document}H-1-norm is considered as the fidelity term and the regularization term is composed of a total variation regularization and a fourth-order filter. The two filters can be adaptively selected according to the diffusion function. When the pixels locate at the edges, the total variation filter is selected to filter the image, which can preserve the edges. When the pixels belong to the flat regions, the fourth-order filter is adopted to smooth the image, which can eliminate the staircase artifacts. In addition, the split Bregman and relaxation approach are employed in our numerical algorithm to speed up the computation. Experimental results demonstrate that our proposed model outperforms the state-of-the-art models cited in the paper in both the qualitative and quantitative evaluations.

Low-dose cerebral perfusion computed tomography image restoration via low-rank and total variation regularizations

Cerebral perfusion x-ray computed tomography (PCT) is an important functional imaging modality for evaluating cerebrovascular diseases and has been widely used in clinics over the past decades. However, due to the protocol of PCT imaging with repeated dynamic sequential scans, the associative radiation dose unavoidably increases as compared with that used in conventional CT examinations. Minimizing the radiation exposure in PCT examination is a major task in the CT field. In this paper, considering the rich similarity redundancy information among enhanced sequential PCT images, we propose a low-dose PCT image restoration model by incorporating the low-rank and sparse matrix characteristic of sequential PCT images. Specifically, the sequential PCT images were first stacked into a matrix (i.e., low-rank matrix), and then a non-convex spectral norm/regularization and a spatio-temporal total variation norm/regularization were then built on the low-rank matrix to describe the low rank and sparsity of the sequential PCT images, respectively. Subsequently, an improved split Bregman method was adopted to minimize the associative objective function with a reasonable convergence rate. Both qualitative and quantitative studies were conducted using a digital phantom and clinical cerebral PCT datasets to evaluate the present method. Experimental results show that the presented method can achieve images with several noticeable advantages over the existing methods in terms of noise reduction and universal quality index. More importantly, the present method can produce more accurate kinetic enhanced details and diagnostic hemodynamic parameter maps.

Quantitative mapping of chemical compositions with MRI using compressed sensing

In this work, a magnetic resonance (MR) imaging method for accelerating the acquisition time of two dimensional concentration maps of different chemical species in mixtures by the use of compressed sensing (CS) is presented. Whilst 2D-concentration maps with a high spatial resolution are prohibitively time-consuming to acquire using full k-space sampling techniques, CS enables the reconstruction of quantitative concentration maps from sub-sampled k-space data. First, the method was tested by reconstructing simulated data. Then, the CS algorithm was used to reconstruct concentration maps of binary mixtures of 1,4-dioxane and cyclooctane in different samples with a field-of-view of 22mm and a spatial resolution of 344μm×344μm. Spiral based trajectories were used as sampling schemes. For the data acquisition, eight scans with slightly different trajectories were applied resulting in a total acquisition time of about 8min. In contrast, a conventional chemical shift imaging experiment at the same resolution would require about 17h. To get quantitative results, a careful weighting of the regularisation parameter (via the L-curve approach) or contrast-enhancing Bregman iterations are applied for the reconstruction of the concentration maps. Both approaches yield relative errors of the concentration map of less than 2mol-% without any calibration prior to the measurement. The accuracy of the reconstructed concentration maps deteriorates when the reconstruction model is biased by systematic errors such as large inhomogeneities in the static magnetic field. The presented method is a powerful tool for the fast acquisition of concentration maps that can provide valuable information for the investigation of many phenomena in chemical engineering applications.

An efficient total variation algorithm for super-resolution in fetal brain MRI with adaptive regularization

Although fetal anatomy can be adequately viewed in new multi-slice MR images, many critical limitations remain for quantitative data analysis. To this end, several research groups have recently developed advanced image processing methods, often denoted by super-resolution (SR) techniques, to reconstruct from a set of clinical low-resolution (LR) images, a high-resolution (HR) motion-free volume. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has been quite attracted by Total Variation energies because of their ability in edge preserving but only standard explicit steepest gradient techniques have been applied for optimization. In a preliminary work, it has been shown that novel fast convex optimization techniques could be successfully applied to design an efficient Total Variation optimization algorithm for the super-resolution problem. In this work, two major contributions are presented. Firstly, we will briefly review the Bayesian and Variational dual formulations of current state-of-the-art methods dedicated to fetal MRI reconstruction. Secondly, we present an extensive quantitative evaluation of our SR algorithm previously introduced on both simulated fetal and real clinical data (with both normal and pathological subjects). Specifically, we study the robustness of regularization terms in front of residual registration errors and we also present a novel strategy for automatically select the weight of the regularization as regards the data fidelity term. Our results show that our TV implementation is highly robust in front of motion artifacts and that it offers the best trade-off between speed and accuracy for fetal MRI recovery as in comparison with state-of-the art methods.

Median prior constrained TV algorithm for sparse view low-dose CT reconstruction

It is known that lowering the X-ray tube current (mAs) or tube voltage (kVp) and simultaneously reducing the total number of X-ray views (sparse view) is an effective means to achieve low-dose in computed tomography (CT) scan. However, the associated image quality by the conventional filtered back-projection (FBP) usually degrades due to the excessive quantum noise. Although sparse-view CT reconstruction algorithm via total variation (TV), in the scanning protocol of reducing X-ray tube current, has been demonstrated to be able to result in significant radiation dose reduction while maintain image quality, noticeable patchy artifacts still exist in reconstructed images. In this study, to address the problem of patchy artifacts, we proposed a median prior constrained TV regularization to retain the image quality by introducing an auxiliary vector m in register with the object. Specifically, the approximate action of m is to draw, in each iteration, an object voxel toward its own local median, aiming to improve low-dose image quality with sparse-view projection measurements. Subsequently, an alternating optimization algorithm is adopted to optimize the associative objective function. We refer to the median prior constrained TV regularization as "TV_MP" for simplicity. Experimental results on digital phantoms and clinical phantom demonstrated that the proposed TV_MP with appropriate control parameters can not only ensure a higher signal to noise ratio (SNR) of the reconstructed image, but also its resolution compared with the original TV method.

A Laplacian based image filtering using switching noise detector

This paper presents a Laplacian-based image filtering method. Using a local noise estimator function in an energy functional minimizing scheme we show that Laplacian that has been known as an edge detection function can be used for noise removal applications. The algorithm can be implemented on a 3x3 window and easily tuned by number of iterations. Image denoising is simplified to the reduction of the pixels value with their related Laplacian value weighted by local noise estimator. The only parameter which controls smoothness is the number of iterations. Noise reduction quality of the introduced method is evaluated and compared with some classic algorithms like Wiener and Total Variation based filters for Gaussian noise. And also the method compared with the state-of-the-art method BM3D for some images. The algorithm appears to be easy, fast and comparable with many classic denoising algorithms for Gaussian noise.

Fast quantitative susceptibility mapping using 3D EPI and total generalized variation

Quantitative susceptibility mapping (QSM) allows new insights into tissue composition and organization by assessing its magnetic property. Previous QSM studies have already demonstrated that magnetic susceptibility is highly sensitive to myelin density and fiber orientation as well as to para- and diamagnetic trace elements. Image resolution in QSM with current approaches is limited by the long acquisition time of 3D scans and the need for high signal to noise ratio (SNR) to solve the dipole inversion problem. We here propose a new total-generalized-variation (TGV) based method for QSM reconstruction, which incorporates individual steps of phase unwrapping, background field removal and dipole inversion in a single iteration, thus yielding a robust solution to the reconstruction problem. This approach has beneficial characteristics for low SNR data, allowing for phase data to be rapidly acquired with a 3D echo planar imaging (EPI) sequence. The proposed method was evaluated with a numerical phantom and in vivo at 3 and 7 T. Compared to total variation (TV), TGV-QSM enforced higher order smoothness which yielded solutions closer to the ground truth and prevented stair-casing artifacts. The acquisition time for images with 1mm isotropic resolution and whole brain coverage was 10s on a clinical 3 Tesla scanner. In conclusion, 3D EPI acquisition combined with single-step TGV reconstruction yields reliable QSM images of the entire brain with 1mm isotropic resolution in seconds. The short acquisition time combined with the robust reconstruction may enable new QSM applications in less compliant populations, clinical susceptibility tensor imaging, and functional resting state examinations.

Anatomically weighted second-order total variation reconstruction of 23Na MRI using prior information from 1H MRI

Sodium ((23)Na) MRI is a noninvasive tool to assess cell viability, which is linked to the total tissue sodium concentration (TSC). However, due to low in vivo concentrations, (23)Na MRI suffers from low signal-to-noise ratio (SNR) and limited spatial resolution. As a result, image quality is compromised by Gibbs ringing artifacts and partial volume effects. An iterative reconstruction algorithm that incorporates prior information from (1)H MRI is developed to reduce partial volume effects and to increase the SNR in non-proton MRI. Anatomically weighted second-order total variation (AnaWeTV) is proposed as a constraint for compressed sensing reconstruction of 3D projection reconstruction (3DPR) data. The method is evaluated in simulations and a MR measurement of a multiple sclerosis (MS) patient by comparing it to gridding and other reconstruction techniques. AnaWeTV increases resolution of known structures and reduces partial volume effects. In simulated MR brain data (nominal resolution Δx(3) = 3 × 3 × 3 mm(3)), the intensity error of four small MS lesions was reduced from (6.9 ± 3.8)% (gridding) to (2.8 ± 1.4)% (AnaWeTV with T2-weighted reference images). Compared to gridding, a substantial SNR increase of 130% was found in the white matter of the MS patient. The algorithm is robust against misalignment of the prior information on the order of the (23)Na image resolution. Features without prior information are still reconstructed with high contrast. AnaWeTV allows a more precise quantification of TSC in structures with prior knowledge. Thus, the AnaWeTV algorithm is in particular beneficial for the assessment of tissue structures that are visible in both (23)Na and (1)H MRI.

Fast quantitative susceptibility mapping with L1-regularization and automatic parameter selection

PURPOSE

To enable fast reconstruction of quantitative susceptibility maps with total variation penalty and automatic regularization parameter selection.

METHODS

ℓ(1) -Regularized susceptibility mapping is accelerated by variable splitting, which allows closed-form evaluation of each iteration of the algorithm by soft thresholding and fast Fourier transforms. This fast algorithm also renders automatic regularization parameter estimation practical. A weighting mask derived from the magnitude signal can be incorporated to allow edge-aware regularization.

RESULTS

Compared with the nonlinear conjugate gradient (CG) solver, the proposed method is 20 times faster. A complete pipeline including Laplacian phase unwrapping, background phase removal with SHARP filtering, and ℓ(1) -regularized dipole inversion at 0.6 mm isotropic resolution is completed in 1.2 min using MATLAB on a standard workstation compared with 22 min using the CG solver. This fast reconstruction allows estimation of regularization parameters with the L-curve method in 13 min, which would have taken 4 h with the CG algorithm. The proposed method also permits magnitude-weighted regularization, which prevents smoothing across edges identified on the magnitude signal. This more complicated optimization problem is solved 5 times faster than the nonlinear CG approach. Utility of the proposed method is also demonstrated in functional blood oxygen level-dependent susceptibility mapping, where processing of the massive time series dataset would otherwise be prohibitive with the CG solver.

CONCLUSION

Online reconstruction of regularized susceptibility maps may become feasible with the proposed dipole inversion.

Compressed sensing MRI exploiting complementary dual decomposition

Compressed sensing (CS) MRI exploits the sparsity of an image in a transform domain to reconstruct the image from incoherently under-sampled k-space data. However, it has been shown that CS suffers particularly from loss of low-contrast image features with increasing reduction factors. To retain image details in such degraded experimental conditions, in this work we introduce a novel CS reconstruction method exploiting feature-based complementary dual decomposition with joint estimation of local scale mixture (LSM) model and images. Images are decomposed into dual block sparse components: total variation for piecewise smooth parts and wavelets for residuals. The LSM model parameters of residuals in the wavelet domain are estimated and then employed as a regional constraint in spatially adaptive reconstruction of high frequency subbands to restore image details missing in piecewise smooth parts. Alternating minimization of the dual image components subject to data consistency is performed to extract image details from residuals and add them back to their complementary counterparts while the LSM model parameters and images are jointly estimated in a sequential fashion. Simulations and experiments demonstrate the superior performance of the proposed method in preserving low-contrast image features even at high reduction factors.

Phase reconstruction from velocity-encoded MRI measurements--a survey of sparsity-promoting variational approaches

In recent years there has been significant developments in the reconstruction of magnetic resonance velocity images from sub-sampled k-space data. While showing a strong improvement in reconstruction quality compared to classical approaches, the vast number of different methods, and the challenges in setting them up, often leaves the user with the difficult task of choosing the correct approach, or more importantly, not selecting a poor approach. In this paper, we survey variational approaches for the reconstruction of phase-encoded magnetic resonance velocity images from sub-sampled k-space data. We are particularly interested in regularisers that correctly treat both smooth and geometric features of the image. These features are common to velocity imaging, where the flow field will be smooth but interfaces between the fluid and surrounding material will be sharp, but are challenging to represent sparsely. As an example we demonstrate the variational approaches on velocity imaging of water flowing through a packed bed of solid particles. We evaluate Wavelet regularisation against Total Variation and the relatively recent second order Total Generalised Variation regularisation. We combine these regularisation schemes with a contrast enhancement approach called Bregman iteration. We verify for a variety of sampling patterns that Morozov's discrepancy principle provides a good criterion for stopping the iterations. Therefore, given only the noise level, we present a robust guideline for setting up a variational reconstruction scheme for MR velocity imaging.

Assessment of regularization techniques for electrocardiographic imaging

A widely used approach to solving the inverse problem in electrocardiography involves computing potentials on the epicardium from measured electrocardiograms (ECGs) on the torso surface. The main challenge of solving this electrocardiographic imaging (ECGI) problem lies in its intrinsic ill-posedness. While many regularization techniques have been developed to control wild oscillations of the solution, the choice of proper regularization methods for obtaining clinically acceptable solutions is still a subject of ongoing research. However there has been little rigorous comparison across methods proposed by different groups. This study systematically compared various regularization techniques for solving the ECGI problem under a unified simulation framework, consisting of both 1) progressively more complex idealized source models (from single dipole to triplet of dipoles), and 2) an electrolytic human torso tank containing a live canine heart, with the cardiac source being modeled by potentials measured on a cylindrical cage placed around the heart. We tested 13 different regularization techniques to solve the inverse problem of recovering epicardial potentials, and found that non-quadratic methods (total variation algorithms) and first-order and second-order Tikhonov regularizations outperformed other methodologies and resulted in similar average reconstruction errors.