Better than the Total Variation Regularization.

The total variation (TV) regularization is popular in iterative image reconstruction when the piecewise-constant nature of the image is encouraged. As a matter of fact, the TV regularization is not strong enough to enforce the piecewise-constant appearance. This paper suggests a different regularization function that is able to discourage some smooth transitions in the image and to encourage the piecewise-constant behavior. This new regularization function involves a Gaussian function. We use the limited-angle tomography problem to illustrate the effectiveness of this new regularization function. The limited-angle tomography situation considered in this paper uses a scanning angular range of 40 ° . For two-dimensional parallel-beam imaging, the required angular range is supposed to be 180 ° .

Comparison of two statistical methodologies for a binary classification problem of two-dimensional images.

The present work intends to compare two statistical classification methods using images as covariates and under the comparison criterion of the ROC curve. The first implemented procedure is based on exploring a mathematical-statistical model using multidimensional arrangements, frequently known as tensors. It is based on the theoretical framework of the high-dimensional generalized linear model. The second methodology is situated in the field of functional data analysis, particularly in the space of functions that have a finite measure of the total variation. A simulation study is carried out to compare both classification methodologies using the area under the ROC curve (AUC). The model based on functional data had better performance than the tensor model. A real data application using medical images is presented.

Uncertainty Quantification for Scale-Space Blob Detection.

We consider the problem of blob detection for uncertain images, such as images that have to be inferred from noisy measurements. Extending recent work motivated by astronomical applications, we propose an approach that represents the uncertainty in the position and size of a blob by a region in a three-dimensional scale space. Motivated by classic tube methods such as the taut-string algorithm, these regions are obtained from level sets of the minimizer of a total variation functional within a high-dimensional tube. The resulting non-smooth optimization problem is challenging to solve, and we compare various numerical approaches for its solution and relate them to the literature on constrained total variation denoising. Finally, the proposed methodology is illustrated on numerical experiments for deconvolution and models related to astrophysics, where it is demonstrated that it allows to represent the uncertainty in the detected blobs in a precise and physically interpretable way.

XSIM: A structural similarity index measure optimized for MRI QSM.

PURPOSE: The structural similarity index measure (SSIM) has become a popular quality metric to evaluate QSM in a way that is closer to human perception than RMS error (RMSE). However, SSIM may overpenalize errors in diamagnetic tissues and underpenalize them in paramagnetic tissues, resulting in biasing. In addition, extreme artifacts may compress the dynamic range, resulting in unrealistically high SSIM scores (hacking). To overcome biasing and hacking, we propose XSIM: SSIM implemented in the native QSM range, and with internal parameters optimized for QSM. METHODS: We used forward simulations from a COSMOS ground-truth brain susceptibility map included in the 2016 QSM Reconstruction Challenge to investigate the effect of QSM reconstruction errors on the SSIM, XSIM, and RMSE metrics. We also used these metrics to optimize QSM reconstructions of the in vivo challenge data set. We repeated this experiment with the QSM abdominal phantom. To validate the use of XSIM instead of SSIM for QSM quality assessment across a range of different reconstruction techniques/algorithms, we analyzed the reconstructions submitted to the 2019 QSM Reconstruction Challenge 2.0. RESULTS: Our experiments confirmed the biasing and hacking effects on the SSIM metric applied to QSM. The XSIM metric was robust to those effects, penalizing the presence of streaking artifacts and reconstruction errors. Using XSIM to optimize QSM reconstruction regularization weights returned less overregularization than SSIM and RMSE. CONCLUSION: XSIM is recommended over traditional SSIM to evaluate QSM reconstructions against a known ground truth, as it avoids biasing and hacking effects and provides a larger dynamic range of scores.

Adaptive orthogonal directional total variation with kernel regression for CT image denoising.

BACKGROUND: Low-dose computed tomography (CT) has been successful in reducing radiation exposure for patients. However, the use of reconstructions from sparse angle sampling in low-dose CT often leads to severe streak artifacts in the reconstructed images. OBJECTIVE: In order to address this issue and preserve image edge details, this study proposes an adaptive orthogonal directional total variation method with kernel regression. METHODS: The CT reconstructed images are initially processed through kernel regression to obtain the N-term Taylor series, which serves as a local representation of the regression function. By expanding the series to the second order, we obtain the desired estimate of the regression function and localized information on the first and second derivatives. To mitigate the noise impact on these derivatives, kernel regression is performed again to update the first and second derivatives. Subsequently, the original reconstructed image, its local approximation, and the updated derivatives are summed using a weighting scheme to derive the image used for calculating orientation information. For further removal of stripe artifacts, the study introduces the adaptive orthogonal directional total variation (AODTV) method, which denoises along both the edge direction and the normal direction, guided by the previously obtained orientation. RESULTS: Both simulation and real experiments have obtained good results. The results of two real experiments show that the proposed method has obtained PSNR values of 34.5408 dB and 29.4634 dB, which are 1.2392-5.9333 dB and 2.828-6.7995 dB higher than the contrast denoising algorithm, respectively, indicating that the proposed method has good denoising performance. CONCLUSIONS: The study demonstrates the effectiveness of the method in eliminating strip artifacts and preserving the fine details of the images.

Extreme Few-View Tomography without Training Data.

There are fewer than 10 projection views in extreme few-view tomography. The state-of-the-art methods to reconstruct images with few-view data are compressed sensing based. Compressed sensing relies on a sparsification transformation and total variation (TV) norm minimization. However, for the extreme few-view tomography, the compressed sensing methods are not powerful enough. This paper seeks additional information as extra constraints so that extreme few-view tomography becomes possible. In transmission tomography, we roughly know the linear attenuation coefficients of the objects to be imaged. We can use these values as extra constraints. Computer simulations show that these extra constraints are helpful and improve the reconstruction quality.

Viewpoint Selection for 3D-Games with f-Divergences.

In this paper, we present a novel approach for the optimal camera selection in video games. The new approach explores the use of information theoretic metrics f-divergences, to measure the correlation between the objects as viewed in camera frustum and the ideal or target view. The f-divergences considered are the Kullback-Leibler divergence or relative entropy, the total variation and the χ2 divergence. Shannon entropy is also used for comparison purposes. The visibility is measured using the differential form factors from the camera to objects and is computed by casting rays with importance sampling Monte Carlo. Our method allows a very fast dynamic selection of the best viewpoints, which can take into account changes in the scene, in the ideal or target view, and in the objectives of the game. Our prototype is implemented in Unity engine, and our results show an efficient selection of the camera and an improved visual quality. The most discriminating results are obtained with the use of Kullback-Leibler divergence.

Model-based quantitative photoacoustic tomography with directional total variation.

In photoacoustic tomography (PAT), acoustic inversion aims to recover the spatial distribution of light energy deposition within the imaging object from the signals captured by detectors. To achieve quantitative imaging, optical inversion is further employed to derive absorption coefficient (AC) images. However, limitations such as restricted detection angles and inherent noise lead to substantial artifacts and degradation in the quality of PAT images, consequently affecting the accuracy of optical inversion results. In this study, we propose a directional total variation constrained optical inversion model to reconstruct the AC image. By incorporating anatomy prior information into the optical inversion process, our method can effectively suppress artifacts in AC images while maintaining structural integrity. Simulation, phantom, and in vivo experimental results demonstrate that our method significantly improves the reconstructed AC image quality. Our method provides a reliable foundation for achieving high-quality quantitative PAT imaging.

Dynamic Regularized Adaptive Cluster Optimization (DRACO) for Quantitative Cardiac Cine MRI in Complex Arrhythmias.

BACKGROUND: Irregular cardiac motion can render conventional segmented cine MRI nondiagnostic. Clustering has been proposed for cardiac motion binning and may be optimized for complex arrhythmias. PURPOSE: To develop an adaptive cluster optimization method for irregular cardiac motion, and to generate the corresponding time-resolved cine images. STUDY TYPE: Prospective. SUBJECTS: Thirteen with atrial fibrillation, four with premature ventricular contractions, and one patient in sinus rhythm. FIELD STRENGTH/SEQUENCE: Free-running balanced steady state free precession (bSSFP) with sorted golden-step, reference real-time sequence. ASSESSMENT: Each subject underwent both the sorted golden-step bSSFP and the reference Cartesian real-time imaging. Golden-step bSSFP images were reconstructed using the dynamic regularized adaptive cluster optimization (DRACO) method and k-means clustering. Image quality (4-point Likert scale), signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), edge sharpness, and ventricular function were assessed. STATISTICAL TESTS: Paired t-tests, Friedman test, regression analysis, Fleiss' Kappa, Bland-Altman analysis. Significance level P < 0.05. RESULTS: The DRACO method had the highest percent of images with scores ≥3 (96% for diastolic frame, 93% for systolic frame, and 93% for multiphase cine) and the percentages were significantly higher compared with both the k-means and real-time methods. Image quality scores, SNR, and CNR were significantly different between DRACO vs. k-means and between DRACO vs. real-time. Cardiac function analysis showed no significant differences between DRACO vs. the reference real-time. CONCLUSION: DRACO with time-resolved reconstruction generated high quality images and has early promise for quantitative cine cardiac MRI in patients with complex arrhythmias including atrial fibrillation. TECHNICAL EFFICACY: Stage 2.

Total variation regularized tensor ring decomposition for OCT image denoising and super-resolution.

This paper suggests a novel hybrid tensor-ring (TR) decomposition and first-order tensor-based total variation (FOTTV) model, known as the TRFOTTV model, for super-resolution and noise suppression of optical coherence tomography (OCT) images. OCT imaging faces two fundamental problems undermining correct OCT-based diagnosis: significant noise levels and low sampling rates to speed up the capturing process. Inspired by the effectiveness of TR decomposition in analyzing complicated data structures, we suggest the TRFOTTV model for noise suppression and super-resolution of OCT images. Initially, we extract the nonlocal 3D patches from OCT data and group them to create a third-order low-rank tensor. Subsequently, using TR decomposition, we extract the correlations among all modes of the grouped OCT tensor. Finally, FOTTV is integrated into the TR model to enhance spatial smoothness in OCT images and conserve layer structures more effectively. The proximal alternating minimization and alternative direction method of multipliers are applied to solve the obtained optimization problem. The effectiveness of the suggested method is verified by four OCT datasets, demonstrating superior visual and numerical outcomes compared to state-of-the-art procedures.

Directional TV algorithm for image reconstruction from sparse-view projections in EPR imaging.

Objective.Electron paramagnetic resonance (EPR) imaging is an advanced in vivo oxygen imaging modality. The main drawback of EPR imaging is the long scanning time. Sparse-view projections collection is an effective fast scanning pattern. However, the commonly-used filtered back projection (FBP) algorithm is not competent to accurately reconstruct images from sparse-view projections because of the severe streak artifacts. The aim of this work is to develop an advanced algorithm for sparse reconstruction of 3D EPR imaging.Methods.The optimization based algorithms including the total variation (TV) algorithm have proven to be effective in sparse reconstruction in EPR imaging. To further improve the reconstruction accuracy, we propose the directional TV (DTV) model and derive its Chambolle-Pock solving algorithm.Results.After the algorithm correctness validation on simulation data, we explore the sparse reconstruction capability of the DTV algorithm via a simulated six-sphere phantom and two real bottle phantoms filled with OX063 trityl solution and scanned by an EPR imager with a magnetic field strength of 250 G.Conclusion.Both the simulated and real data experiments show that the DTV algorithm is superior to the existing FBP and TV-type algorithms and a deep learning based method according to visual inspection and quantitative evaluations in sparse reconstruction of EPR imaging.Significance.These insights gained in this work may be used in the development of fast EPR imaging workflow of practical significance.

Magnetic resonance image reconstruction based on image decomposition constrained by total variation and tight frame.

OBJECTIVES: Magnetic resonance imaging (MRI) is a commonly used tool in clinical medicine, but it suffers from the disadvantage of slow imaging speed. To address this, we propose a novel MRI reconstruction algorithm based on image decomposition to realize accurate image reconstruction with undersampled k-space data. METHODS: In our algorithm, the MR images to be recovered are split into cartoon and texture components utilizing image decomposition theory. Different sparse transform constraints are applied to each component based on their morphological structure characteristics. The total variation transform constraint is used for the smooth cartoon component, while the L0 norm constraint of tight frame redundant transform is used for the oscillatory texture component. Finally, an alternating iterative minimization approach is adopted to complete the reconstruction. RESULTS: Numerous numerical experiments are conducted on several MR images and the results consistently show that, compared with the existing classical compressed sensing algorithm, our algorithm significantly improves the peak signal-to-noise ratio of the reconstructed images and preserves more image details. CONCLUSIONS: Our algorithm harnesses the sparse characteristics of different image components to reconstruct MR images accurately with highly undersampled data. It can greatly accelerate MRI speed and be extended to other imaging reconstruction fields.

TENSOR QUANTILE REGRESSION WITH LOW-RANK TENSOR TRAIN ESTIMATION.

Neuroimaging studies often involve predicting a scalar outcome from an array of images collectively called tensor. The use of magnetic resonance imaging (MRI) provides a unique opportunity to investigate the structures of the brain. To learn the association between MRI images and human intelligence, we formulate a scalar-on-image quantile regression framework. However, the high dimensionality of the tensor makes estimating the coefficients for all elements computationally challenging. To address this, we propose a low-rank coefficient array estimation algorithm based on tensor train (TT) decomposition which we demonstrate can effectively reduce the dimensionality of the coefficient tensor to a feasible level while ensuring adequacy to the data. Our method is more stable and efficient compared to the commonly used, Canonic Polyadic rank approximation-based method. We also propose a generalized Lasso penalty on the coefficient tensor to take advantage of the spatial structure of the tensor, further reduce the dimensionality of the coefficient tensor, and improve the interpretability of the model. The consistency and asymptotic normality of the TT estimator are established under some mild conditions on the covariates and random errors in quantile regression models. The rate of convergence is obtained with regularization under the total variation penalty. Extensive numerical studies, including both synthetic and real MRI imaging data, are conducted to examine the empirical performance of the proposed method and its competitors.

Intravoxel incoherent motion and diffusion kurtosis imaging and their machine-learning-based texture analysis for detection and assessment of prostate cancer severity at 3 T.

OBJECTIVES: To evaluate the role of combined intravoxel incoherent motion and diffusion kurtosis imaging (IVIM-DKI) and their machine-learning-based texture analysis for the detection and assessment of severity in prostate cancer (PCa). MATERIALS AND METHODS: Eighty-eight patients underwent MRI on a 3 T scanner after giving informed consent. IVIM-DKI data were acquired using 13 b values (0-2000 s/mm2) and analyzed using the IVIM-DKI model with the total variation (TV) method. PCa patients were categorized into two groups: clinically insignificant prostate cancer (CISPCa) (Gleason grade ≤ 6) and clinically significant prostate cancer (CSPCa) (Gleason grade ≥ 7). One-way analysis-of-variance, t test, and receiver operating characteristic analysis was performed to measure the discriminative ability to detect PCa using IVIM-DKI parameters. A chi-square test was used to select important texture features of apparent diffusion coefficient (ADC) and IVIM-DKI parameters. These selected texture features were used in an artificial neural network for PCa detection. RESULTS: ADC and diffusion coefficient (D) were significantly lower (p < 0.001), and kurtosis (k) was significantly higher (p < 0.001), in PCa as compared with benign prostatic hyperplasia (BPH) and normal peripheral zone (PZ). ADC, D, and k showed high areas under the curves (AUCs) of 0.92, 0.89, and 0.88, respectively, in PCa detection. ADC and D were significantly lower (p < 0.05) as compared with CISPCa versus CSPCa. D for detecting CSPCa was high, with an AUC of 0.63. A negative correlation of ADC and D with GS (ADC, ρ = -0.33; D, ρ = -0.35, p < 0.05) and a positive correlation of k with GS (ρ = 0.22, p < 0.05) were observed. Combined IVIM-DKI texture showed high AUC of 0.83 for classification of PCa, BPH, and normal PZ. CONCLUSION: D, f, and k computed using the IVIM-DKI model with the TV method were able to differentiate PCa from BPH and normal PZ. Texture features of combined IVIM-DKI parameters showed high accuracy and AUC in PCa detection.

An analytical form of ring artifact correction for computed tomography based on directional gradient domain optimization.

BACKGROUND: Ring artifact is a common problem in Computed Tomography (CT), which can lead to inaccurate diagnoses and treatment plans. It can be caused by various factors such as detector imperfections, anti-scatter grids, or other nonuniform filters placed in the x-ray beam. Physics-based corrections for these x-ray source and detector non-uniformity, in general cannot completely get rid of the ring artifacts. Therefore, there is a need for a robust method that can effectively remove ring artifacts in the image domain while preserving details. PURPOSE: This study aims to develop an effective method for removing ring artifacts from reconstructed CT images. METHODS: The proposed method starts by converting the reconstructed CT image containing ring artifacts into polar coordinates, thereby transforming these artifacts into stripes. Relative Total Variation is used to extract the image's overall structural information. For the efficient restoration of intricate details, we introduce Directional Gradient Domain Optimization (DGDO) and design objective functions that make use of both the image's gradient and its overall structure. Subsequently, we present an efficient analytical algorithm to minimize these objective functions. The image obtained through DGDO is then transformed back into Cartesian coordinates, finalizing the ring artifact correction process. RESULTS: Through a series of synthetic and real-world experiments, we have effectively demonstrated the prowess of our proposed method in the correction of ring artifacts while preserving intricate details in reconstructed CT images. In a direct comparison, our method has exhibited superior visual quality compared to several previous approaches. These results underscore the remarkable potential of our approach for enhancing the overall quality and clinical utility of CT imaging. CONCLUSIONS: The proposed method offers an analytical solution for removing ring artifacts from CT images while preserving details. As ring artifacts are a common problem in CT imaging, this method has high practical value in the medical field. The proposed method can improve image quality and reduce the difficulty of disease diagnosis, thereby contributing to better patient care.

Directional TV algorithm for fast EPR imaging.

Precise radiation guided by oxygen images has demonstrated superiority over the traditional radiation methods. Electron paramagnetic resonance (EPR) imaging has proven to be the most advanced oxygen imaging modality. However, the main drawback of EPR imaging is the long scan time. For each projection, we usually need to collect the projection many times and then average them to achieve high signal-to-noise ratio (SNR). One approach to fast scan is to reduce the repeating time for each projection. While the projections would be noisy and thus the traditional commonly-use filtered backprojection (FBP) algorithm would not be capable of accurately reconstructing images. Optimization-based iterative algorithms may accurately reconstruct images from noisy projections for they may incorporate prior information into optimization models. Based on the total variation (TV) algorithms for EPR imaging, in this work, we propose a directional TV (DTV) algorithm to further improve the reconstruction accuracy. We construct the DTV constrained, data divergence minimization (DTVcDM) model, derive its Chambolle-Pock (CP) solving algorithm, validate the correctness of the whole algorithm, and perform evaluations via simulated and real data. The experimental results show that the DTV algorithm outperforms the existing TV and FBP algorithms in fast EPR imaging. Compared to the standard FBP algorithm, the proposed algorithm may achieve 10 times of acceleration.

Efficient EEG motion artifact elimination framework for ambulatory epileptic seizure detection application.

Motion artifacts are a pervasive challenge in EEG ambulatory monitoring, often obscuring critical neurological signals and impeding accurate seizure detection. In this study, we propose a new approach of outlier based grouping of two level Singular Spectrum Analysis (SSA) decomposition combined with Relative Total Variation (RTV) filter for the effective removal of motion-induced noise from ambulatory EEG data. A two-stage SSA method was employed to decompose single-channel EEG signal, which had been interfered with, into various fre quency bands. The affected sub-band signal was then subjected to an RTV filter to estimate the artifact signal. Subtracting this estimated artifact signal from the contaminated sub-band signal yielded the filtered sub-band signal. Subse quently, the filtered sub-band signal was reintegrated with the other decomposed components from noise-free bands, culminating in the generation of the ultimate denoised EEG signal. Based on the comprehensive set of simulation results, it can be deduced that the algorithm described in the paper outperforms existing methods. It demonstrates superior metrics evaluation in terms of ΔSNR,η,MAE, andPSNRwhen compared to these alternatives. Our framework sig- nificantly enhances the quality of EEG data by successfully eliminating motion artifacts while preserving crucial brainwave information. To evaluate the prac tical impact of this noise reduction technique, we assess its performance in the context of seizure detection. The results reveal a substantial improvement in the accuracy and reliability of seizure detection algorithms when applied to EEG data preprocessed with proposed method.

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.

Prototyping optimization-based image reconstructions from limited-angular-range data in dual-energy CT.

Image reconstruction from data collected over full-angular range (FAR) in dual-energy CT (DECT) is well-studied. There exists interest in DECT with advanced scan configurations in which data are collected only over limited-angular ranges (LARs) for meeting unique workflow needs in certain practical imaging applications, and thus in the algorithm development for image reconstruction from such LAR data. The objective of the work is to investigate and prototype image reconstructions in DECT with LAR scans. We investigate and prototype optimization programs with various designs of constraints on the directional-total-variations (DTVs) of virtual monochromatic images and/or basis images, and derive the DTV algorithms to numerically solve the optimization programs for achieving accurate image reconstruction from data collected in a slew of different LAR scans. Using simulated and real data acquired with low- and high-kV spectra over LARs, we conduct quantitative studies to demonstrate and evaluate the optimization programs and their DTV algorithms developed. As the results of the numerical studies reveal, while the DTV algorithms yield images of visual quality and quantitative accuracy comparable to that of the existing algorithms from FAR data, the former reconstruct images with improved visualization, reduced artifacts, and also enhanced quantitative accuracy when applied to LAR data in DECT. Optimization-based, one-step algorithms, including the DTV algorithms demonstrated, can be developed for quantitative image reconstruction from spectral data collected over LARs of extents that are considerably smaller than the FAR in DECT. The theoretical and numerical results obtained can be exploited for prototyping designs of optimization-based reconstructions and LAR scans in DECT, and they may also yield insights into the development of reconstruction procedures in practical DECT applications. The approach and algorithms developed can naturally be applied to investigating image reconstruction from LAR data in multi-spectral and photon-counting CT.

Reconstruction of Sparse-View X-ray Computed Tomography Based on Adaptive Total Variation Minimization.

Sparse-view reconstruction has garnered significant interest in X-ray computed tomography (CT) imaging owing to its ability to lower radiation doses and enhance detection efficiency. Among current methods for sparse-view CT reconstruction, an algorithm utilizing iterative reconstruction based on full variational regularization demonstrates good performance. The optimized direction and number of computations for the gradient operator of the regularization term play a crucial role in determining not only the reconstructed image quality but also the convergence speed of the iteration process. The conventional TV approach solely accounts for the vertical and horizontal directions of the two-dimensional plane in the gradient direction. When projection data decrease, the edges of the reconstructed image become blurred. Exploring too many gradient directions for TV terms often comes at the expense of more computational costs. To enhance the balance of computational cost and reconstruction quality, this study suggests a novel TV computation model that is founded on a four-direction gradient operator. In addition, selecting appropriate iteration parameters significantly impacts the quality of the reconstructed image. We propose a nonparametric control method utilizing the improved TV approach as a solution to the tedious manual parameter optimization issue. The relaxation parameters of projection onto convex sets (POCS) are determined according to the scanning number and numerical proportion of the projection data; according to the image error before and after iterations, the gradient descent step of the TV item is adaptively adjusted. Compared with several representative iterative reconstruction algorithms, the experimental results show that the algorithm can effectively preserve edges and suppress noise in sparse-view CT reconstruction.