Efficient and robust nonlocal means denoising of MR data based on salient features matching

Combining variational mode decomposition with regularisation techniques to denoise MRI data

In this paper, we propose a novel method for removing noise from MRI data by exploiting regularisation techniques combined with variational mode decomposition. Variational mode decomposition is a new decomposition technique for sparse decomposition of a 1D or 2D signal into a set of modes. In turn, regularisation is a method that can translate the ill-posed problem (e.g., image denoising) into a well-posed problem. The proposed method aims to remove the noise from the image in two steps. In the first step, the MR imaging data are decomposed by the 2D variational mode decomposition algorithm. In the second step, for effective suppression of Rician noise from MRI data, we used the fused lasso signal approximator with all modes acquired from the medical scan. The performance of the proposed approach was compared with state-of-the-art reference methods based on different metrics, that is, the peak signal-to-noise ratio, the structural similarity index metrics, the high-frequency error norm, the quality index based on local variance, and the sharpness index. The experiments were performed on the basis of both simulated and real images. The presented results prove the high denoising performance of the proposed algorithm; particularly under heavy noise conditions.

Structured low-rank reconstruction for navigator-free water/fat separated multi-shot diffusion-weighted EPI

PURPOSE

Multi-shot diffusion-weighted EPI allows an increase in image resolution and reduced geometric distortions and can be combined with chemical-shift encoding (Dixon) to separate water/fat signals. However, such approaches suffer from physiological motion-induced shot-to-shot phase variations. In this work, a structured low-rank-based navigator-free algorithm is proposed to address the challenge of simultaneously separating water/fat signals and correcting for physiological motion-induced shot-to-shot phase variations in multi-shot EPI-based diffusion-weighted MRI.

THEORY AND METHODS

We propose an iterative, model-based reconstruction pipeline that applies structured low-rank regularization to estimate and eliminate the shot-to-shot phase variations in a data-driven way, while separating water/fat images. The algorithm is tested in different anatomies, including head-neck, knee, brain, and prostate. The performance is validated in simulations and in-vivo experiments in comparison to existing approaches.

RESULTS

In-vivo experiments and simulations demonstrated the effectiveness of the proposed algorithm compared to extra-navigated and an alternative self-navigation approach. The proposed algorithm demonstrates the capability to reconstruct in the multi-shot/Dixon hybrid space domain under-sampled datasets, using the same number of acquired EPI shots compared to conventional fat-suppression techniques but eliminating fat signals through chemical-shift encoding. In addition, partial Fourier reconstruction can also be achieved by using the concept of virtual conjugate coils in conjunction with the proposed algorithm.

CONCLUSION

The proposed algorithm effectively eliminates the shot-to-shot phase variations and separates water/fat images, making it a promising solution for future DWI on different anatomies.

An improved method for the segmentation of roots from X-ray computed tomography 3D images: Rootine v.2

BACKGROUND

X-ray computed tomography is acknowledged as a powerful tool for the study of root system architecture of plants growing in soil. In this paper, we improved the original root segmentation algorithm "Rootine" and present its succeeding version "Rootine v.2". In addition to gray value information, Rootine algorithms are based on shape detection of cylindrical roots. Both algorithms are macros for the ImageJ software and are made freely available to the public. New features in Rootine v.2 are (i) a pot wall detection and removal step to avoid segmentation artefacts for roots growing along the pot wall, (ii) a calculation of the root average gray value based on a histogram analysis, (iii) an automatic calculation of thresholds for hysteresis thresholding of the tubeness image to reduce the number of parameters and (iv) a false negatives recovery based on shape criteria to increase root recovery. We compare the segmentation results of Rootine v.1 and Rootine v.2 with the results of root washing and subsequent analysis with WinRhizo. We use a benchmark dataset of maize roots (Zea mays L. cv. B73) grown in repacked soil for two scenarios with differing soil heterogeneity and image quality.

RESULTS

We demonstrate that Rootine v.2 outperforms its preceding version in terms of root recovery and enables to match better the root diameter distribution data obtained with root washing. Despite a longer processing time, Rootine v.2 comprises less user-defined parameters and shows an overall greater usability.

CONCLUSION

The proposed method facilitates higher root detection accuracy than its predecessor and has the potential for improving high-throughput root phenotyping procedures based on X-ray computed tomography data analysis.

Inpainting-filtering for metal artifact reduction (IMIF-MAR) in computed tomography

The reduction of metal artifacts remains a challenge in computed tomography because they decrease image quality, and consequently might affect the medical diagnosis. The objective of this study is to present a novel method to correct metal artifacts based solely on the CT-slices. The proposed method consists of four steps. First, metal implants in the original CT-slice are segmented using an entropy based method, producing a metal image. Second, a prior image is acquired using three transformations: Gaussian filter, Parisotto and Schoenlieb inpainting method with the Mumford-Shah image model and L0 Gradient Minimization method (L0GM). Next, based on the projections from the original CT-slice, prior image and metal image, the sinogram is corrected in the traces affected by metal in the process called normalization and denormalization. Finally, the reconstructed image is obtained by FBP and a Nonlocal Means (NLM) filtering. The efficacy of the algorithm is evaluated by comparing five image quality metrics of the images and by inspecting regions of interest (ROI). Phantom data as well as clinical datasets are included. The proposed method is compared with three established metal artifact reduction (MAR) methods. The results from a phantom and clinical dataset show the visible reduction of artifacts. The conclusion is that IMIF-MAR method can reduce streak metal artifacts effectively and avoid new artifacts around metal implants, while preserving the anatomical structures. Considering both clinical and phantom studies, the proposed MAR algorithm improves the quality of clinical images affected by metal artifacts, and could be integrated in clinical setting.

Rician Denoising Based on Correlated Local Features LMMSE Approach

In this study we propose a novel correction scheme that filters Magnetic Resonance Images data, by using a modified Linear Minimum Mean Square Error (LMMSE) estimator which takes into account the joint information of the local features. A closed-form analytical solution for our estimator is presented and it proves to make the filtering process far simpler and faster than other estimation techniques that rely on iterative optimization scheme and require multiple data samples. An experimental validation of our correction scheme was carried out through large scale experiments using both clinical and synthetic MR images, artificially corrupted with rician noise of σ varying from 1 to 40. These noisy images were filtered using our proposed method against the classical LMMSE, the Non-Local Means filter and the Nonlocality-Reinforced Convolutional Neural Networks (NRCNN) techniques. The results show an outstanding performance of our proposed method, given the fact that from σ ≈ 12 onwards, the proposed method outperforms all other methods. Another attention-grabbing feature of our method is that its Structural Similarity does not vary sharply [0.87, 0.95] across the σ spectrum as the other three techniques, which implies that this method can work on a wider range of deteriorated images than the rest of the techniques.

Image Denoising Using Non-Local Means (NLM) Approach in Magnetic Resonance (MR) Imaging: A Systematic Review

The non-local means (NLM) noise reduction algorithm is well known as an excellent technique for removing noise from a magnetic resonance (MR) image to improve the diagnostic accuracy. In this study, we undertook a systematic review to determine the effectiveness of the NLM noise reduction algorithm in MR imaging. A systematic literature search was conducted of three databases of publications dating from January 2000 to March 2020; of the 82 publications reviewed, 25 were included in this study. The subjects were categorized into four major frameworks and analyzed for each research result. Research in NLM noise reduction for MR images has been increasing worldwide; however, it was found to have slightly decreased since 2016. It was found that the NLM technique was most frequently used on brain images taken using the general MR imaging technique; these were most frequently performed during simultaneous real and simulated experimental studies. In particular, comparison parameters were frequently used to evaluate the effectiveness of the algorithm on MR images. The ultimate goal is to provide an accurate method for the diagnosis of disease, and our conclusion is that the NLM noise reduction algorithm is a promising method of achieving this goal.

Detector of 3-D salient points based on the dual-tree complex wavelet transform for the positioning of hippocampi meshes in magnetic resonance images

BACKGROUND

Brain Magnetic Resonance (MR) image segmentation methods based on deformable models depend on the initial positioning to maximize the chances of successful segmentation. To minimize this limitation, salient-point based registration is used to perform the initial positioning of brain structure meshes close to their image target representation. The analysis of brain structures (such as the hippocampus) can help in the diagnosis and follow-up of neurodegenerative diseases like Alzheimer's.

METHODS

We present a technique for detection and description of 3-D salient points, which combines filter response maps estimated for different scales and orientations of the dual-tree complex wavelet transform (DT-CWT). We apply our technique to detect salient points in volumetric brain MR images and use the detected points in a positioning methodology. To illustrate the applicability, we applied our method for the positioning of hippocampi meshes in 3-D brain MR images and assessed the results by overlapping the positioned meshes with manual annotations made by medical specialists.

RESULTS

Our method yielded mean values of normalized Dice Similarity Coefficient (nDSC) of 0.74/0.68 and Hausdorff Average Distance (HAD) of 0.73/0.75 for the left and right hippocampus, respectively.

COMPARISON WITH OTHER METHODS

The mean nDSC and HAD results of our detector were significantly better than the ones achieved by an Affine and a Phase Congruency (PC) guided positioning.

CONCLUSIONS

The detection via DT-CWT decomposition is computationally less demanding than the detection via PC and represents a robust alternative for the positioning of mesh models.

Rhesus Macaque Brain Developmental Trajectory: A Longitudinal Analysis Using Tensor-Based Structural Morphometry and Diffusion Tensor Imaging

The typical developmental trajectory of brain structure among nonhuman primates (NHPs) remains poorly understood. In this study, we characterized the normative trajectory of developmental change among a cohort of rhesus monkeys (n = 28), ranging in age from 2 to 22 months, using structural MRI datasets that were longitudinally acquired every 3-4 months. We hypothesized that NHP-specific transient intracranial volume decreases reported during late infancy would be part of the typical developmental process, which is driven by volumetric contraction of gray matter in primary functional areas. To this end, we performed multiscale analyses from the whole brain to voxel level, characterizing regional heterogeneity, hemispheric asymmetry, and sexual dimorphism in developmental patterns. The longitudinal trajectory of brain development was explained by three different regional volumetric growth patterns (exponentially decreasing, undulating, and linearly increasing), which resulted in developmental brain volume curves with transient brain volumetric decreases. White matter (WM) fractional anisotropy increased with age, corresponding to WM volume increases, while mean diffusivity (MD) showed biphasic patterns. The longitudinal trajectory of brain development in young rhesus monkeys follows typical maturation patterns seen in humans, but regional volumetric and MD changes are more dynamic in rhesus monkeys compared with humans, with marked decreases followed by "rebound-like" increases.

Roots compact the surrounding soil depending on the structures they encounter

Contradictory evidence exists regarding whether and to which extend roots change soil structure in their vicinity. Here we attempt to reconcile disparate views allowing for the two-way interaction between soil structure and root traits, i.e. changes in soil structure due to plants and changes in root growth due to soil structure. Porosity gradients extending from the root/biopore surface into the bulk soil were investigated with X-ray µCT for undisturbed soil samples from a field chronosequence as well as for a laboratory experiment with Zea mays growing into three different bulk densities. An image analysis protocol was developed, which enabled a fast analysis of the large sample pool (n > 300) at a resolution of 19 µm. Lab experiment showed that growing roots only compact the surrounding soil if macroporosity is low and dominated by isolated pores. When roots can grow into a highly connected macropore system showing high connectivity the rhizosphere is more porous compared to the bulk soil. A compaction around roots/biopores in the field chronosequence was only observed in combination with high root/biopore length densities. We conclude that roots compact the rhizosphere only if the initial soil structure does not offer a sufficient volume of well-connected macropores.

Separate Memory-Enhancing Effects of Reward and Strategic Encoding

Memory encoding for important information can be enhanced both by reward anticipation and by intentional strategies. These effects are hypothesized to depend on distinct neural mechanisms, yet prior work has provided only limited evidence for their separability. We aimed to determine whether reward-driven and strategic mechanisms for prioritizing important information are separable, even if they may also interact. We examined the joint operation of both mechanisms using fMRI measures of brain activity. Participants learned abstract visual images in a value-directed recognition paradigm. On each trial, two novel images were presented simultaneously in different screen quadrants, one arbitrarily designated as high point value and one as low value. Immediately after each block of 16 study trials, the corresponding point rewards could be obtained in a test of item recognition and spatial location memory. During encoding trials leading to successful subsequent memory, especially of high-value images, increased activity was observed in dorsal frontoparietal and lateral occipitotemporal cortex. Furthermore, activity in a network associated with reward was higher during encoding when any image, of high or low value, was subsequently remembered. Functional connectivity between right medial temporal lobe and right ventral tegmental area, measured via psychophysiological interaction, was also greater during successful encoding regardless of value. Strategic control of memory, as indexed by successful prioritization of the high-value image, affected activity in dorsal posterior parietal cortex as well as connectivity between this area and right lateral temporal cortex. These results demonstrate that memory can be strengthened by separate neurocognitive mechanisms for strategic control versus reward-based enhancement of processing.

Integrated datasets of normalized brain with functional localization using intra-operative electrical stimulation

PURPOSE

The purpose of this study was to transform brain mapping data into a digitized intra-operative MRI and integrated brain function dataset for predictive glioma surgery considering tumor resection volume, as well as the intra-operative and postoperative complication rates.

METHODS

Brain function data were transformed into digitized localizations on a normalized brain using a modified electric stimulus probe after brain mapping. This normalized brain image with functional information was then projected onto individual patient's brain images including predictive brain function data.

RESULTS

Log data were successfully acquired using a medical device integrated into intra-operative MR images, and digitized brain function was converted to a normalized brain data format in 13 cases. For the electrical stimulation positions in which patients showed speech arrest (SA), speech impairment (SI), motor and sensory responses during cortical mapping processes in awake craniotomy, the data were tagged, and the testing task and electric current for the stimulus were recorded. There were 13 SA, 7 SI, 8 motor and 4 sensory responses (32 responses) in total. After evaluation of transformation accuracy in 3 subjects, the first transformation from intra- to pre-operative MRI using non-rigid registration was calculated as 2.6 ± 1.5 and 2.1 ± 0.9 mm, examining neighboring sulci on the electro-stimulator position and the cortex surface near each tumor, respectively; the second transformation from pre-operative to normalized brain was 1.7 ± 0.8 and 1.4 ± 0.5 mm, respectively, representing acceptable accuracy.

CONCLUSION

This image integration and transformation method for brain normalization should facilitate practical intra-operative brain mapping. In the future, this method may be helpful for pre-operatively or intra-operatively predicting brain function.

Denoising high angular resolution diffusion imaging data by combining singular value decomposition and non-local means filter

BACKGROUND

High angular resolution diffusion imaging (HARDI) data is typically corrupted with Rician noise. Although larger b-values help to retrieve more accurate angular diffusivity information, they also lead to an increase in noise generation.

NEW METHOD

In order to sufficiently reduce noise in HARDI images and improve the construction of orientation distribution function (ODF) fields, a novel denoising method was developed in this study by combining the singular value decomposition (SVD) and non-local means (NLM) filter. Similar 3D patches were first recruited into a matrix from a search volume. HARDI signals in the matrix were then re-estimated using the SVD low rank approximation, and a NLM filter was employed to filter out any residual noise.

RESULTS

The performance of the proposed method was evaluated against the state-of-the-art denoising methods based on both synthetic and real HARDI datasets. Results demonstrated the superior performance of the developed SVD-NLM method in denoising HARDI data through preserving fine angular structural details and estimating diffusion orientations from improved ODF fields.

CONCLUSION

The proposed SVD-NLM method can improve HARDI quantitative computations, such as MRI brain tissue segmentation and diffusion profile estimation, that rely on the quality of imaging data.

Denoising of MR images using Kolmogorov-Smirnov distance in a Non Local framework

Data coming from any acquisition system, such as Magnetic Resonance Imaging ones, are affected by noise. Although modern high field scanners can reach high Signal to Noise Ratios, in some circumstances, for example in case of very weak signals due to a specific acquisition sequence, noise becomes a critical issue that has to be properly handled. In the last years methods based on the so called Non Local Mean have proven to be very effective in denoising tasks. The idea of these filters is to find similar patches across the image and to jointly exploit them to obtain the restored image. A critical point is the distance metric adopted for measuring similarity. Within this manuscript, we propose a filtering technique based on the Kolmogorov-Smirnov distance. The main innovative aspect of the proposed method consists of the criteria adopted for finding similar pixels across the image: it is based on the statistics of the points rather than the widely adopted weighted Euclidean distance. More in details, the Cumulative Distribution Functions of different pixels are evaluated and compared in order to measure their similarities, exploiting a stack of images of the same slice acquired with different acquisition parameters. To quantitatively and qualitatively assess the performances of the approach, a comparison with other widely adopted denoising filters in case of both simulated and real datasets has been carried out. The obtained results confirm the validity of the proposed solution.

A CT Scan Harmonization Technique to Detect Emphysema and Small Airway Diseases

Recent studies have suggested the central role of small airway destruction in the pathogenesis of COPD leading to further parenchymal destruction. This evidence has sparked the interest in in-vivo assessment of small airway disease overall at the early onset of the disease. The parametric response mapping (PRM) technique has been proposed to distinguish gas trapping due to small airway disease from low attenuation areas due to emphysema. Despite its success, the PRM technique shows some limitations that are precluding the interpretation of its results. The density value used to assess gas trapping highly depends on acquisition parameters, such as dose and reconstruction kernel, and changes in body size, that introduce inhomogeneous photon absorption patterns. In particular, many studies using PRM employ inspiratory and expiratory images that are obtained at different dose levels. Emphysema impact in early disease may be confounded with the gas trapping due to the noise introduced by differences in the acquisition during the PRM. In this work, we propose a CT harmonization technique to remove the nuisance factors to distinguish between small airway disease and emphysema. Our results show that the measurements based on CT harmonization provide an increase in the detection of both emphysema and airway disease, resulting in a statistically significant impact of both components and a better association with lung function measures.

De-noising of 3D multiple-coil MR images using modified LMMSE estimator

De-noising is a crucial topic in Magnetic Resonance Imaging (MRI) which focuses on less loss of Magnetic Resonance (MR) image information and details preservation during the noise suppression. Nowadays multiple-coil MRI system is preferred to single one due to its acceleration in the imaging process. Due to the fact that the model of noise in single-coil and multiple-coil MRI systems are different, the de-noising methods that mostly are adapted to single-coil MRI systems, do not work appropriately with multiple-coil one. The model of noise in single-coil MRI systems is Rician while in multiple-coil one (if no subsampling occurs in k-space or GRAPPA reconstruction process is being done in the coils), it obeys noncentral Chi (nc-χ). In this paper, a new filtering method based on the Linear Minimum Mean Square Error (LMMSE) estimator is proposed for multiple-coil MR Images ruined by nc-χ noise. In the presented method, to have an optimum similarity selection of voxels, the Bayesian Mean Square Error (BMSE) criterion is used and proved for nc-χ noise model and also a nonlocal voxel selection methodology is proposed for nc-χ distribution. The results illustrate robust and accurate performance compared to the related state-of-the-art methods, either on ideal nc-χ images or GRAPPA reconstructed ones.

Joint Intensity Fusion Image Synthesis Applied to Multiple Sclerosis Lesion Segmentation

We propose a new approach to Multiple Sclerosis lesion segmentation that utilizes synthesized images. A new method of image synthesis is considered: joint intensity fusion (JIF). JIF synthesizes an image from a library of deformably registered and intensity normalized atlases. Each location in the synthesized image is a weighted average of the registered atlases; atlas weights vary spatially. The weights are determined using the joint label fusion (JLF) framework. The primary methodological contribution is the application of JLF to MRI signal directly rather than labels. Synthesized images are then used as additional features in a lesion segmentation task using the OASIS classifier, a logistic regression model on intensities from multiple modalities. The addition of JIF synthesized images improved the Dice-Sorensen coefficient (relative to manually drawn gold standards) of lesion segmentations over the standard model segmentations by 0.0462 ± 0.0050 (mean ± standard deviation) at optimal threshold over all subjects and 10 separate training/testing folds.

Segmentation of tongue shapes during vowel production in magnetic resonance images based on statistical modelling

Quantification of the anatomic and functional aspects of the tongue is pertinent to analyse the mechanisms involved in speech production. Speech requires dynamic and complex articulation of the vocal tract organs, and the tongue is one of the main articulators during speech production. Magnetic resonance imaging has been widely used in speech-related studies. Moreover, the segmentation of such images of speech organs is required to extract reliable statistical data. However, standard solutions to analyse a large set of articulatory images have not yet been established. Therefore, this article presents an approach to segment the tongue in two-dimensional magnetic resonance images and statistically model the segmented tongue shapes. The proposed approach assesses the articulator morphology based on an active shape model, which captures the shape variability of the tongue during speech production. To validate this new approach, a dataset of mid-sagittal magnetic resonance images acquired from four subjects was used, and key aspects of the shape of the tongue during the vocal production of relevant European Portuguese vowels were evaluated.

Gradient Boosted Trees for Corrective Learning

Random forests (RF) have long been a widely popular method in medical image analysis. Meanwhile, the closely related gradient boosted trees (GBT) have not become a mainstream tool in medical imaging despite their attractive performance, perhaps due to their computational cost. In this paper, we leverage the recent availability of an efficient open-source GBT implementation to illustrate the GBT method in a corrective learning framework, in application to the segmentation of the caudate nucleus, putamen and hippocampus. The size and shape of these structures are used to derive important biomarkers in many neurological and psychiatric conditions. However, the large variability in deep gray matter appearance makes their automated segmentation from MRI scans a challenging task. We propose using GBT to improve existing segmentation methods. We begin with an existing 'host' segmentation method to create an estimate surface. Based on this estimate, a surface-based sampling scheme is used to construct a set of candidate locations. GBT models are trained on features derived from the candidate locations, including spatial coordinates, image intensity, texture, and gradient magnitude. The classification probabilities from the GBT models are used to calculate a final surface estimate. The method is evaluated on a public dataset, with a 2-fold cross-validation. We use a multi-atlas approach and FreeSurfer as host segmentation methods. The mean reduction in surface distance error metric for FreeSurfer was 0.2 - 0.3 mm, whereas for multi-atlas segmentation, it was 0.1mm for each of caudate, putamen and hippocampus. Importantly, our approach outperformed an RF model trained on the same features (p < 0.05 on all measures). Our method is readily generalizable and can be applied to a wide range of medical image segmentation problems and allows any segmentation method to be used as input.

Real-Time Nonlocal Means-Based Despeckling

In this paper, we propose a multiscale nonlocal means-based despeckling method for medical ultrasound. The multiscale approach leads to large computational savings and improves despeckling results over single-scale iterative approaches. We present two variants of the method. The first, denoted multiscale nonlocal means (MNLM), yields uniform robust filtering of speckle both in structured and homogeneous regions. The second, denoted unnormalized MNLM (UMNLM), is more conservative in regions of structure assuring minimal disruption of salient image details. Due to the popularity of anisotropic diffusion-based methods in the despeckling literature, we review the connection between anisotropic diffusion and iterative variants of NLM. These iterative variants in turn relate to our multiscale variant. As part of our evaluation, we conduct a simulation study making use of ground truth phantoms generated from clinical B-mode ultrasound images. We evaluate our method against a set of popular methods from the despeckling literature on both fine and coarse speckle noise. In terms of computational efficiency, our method outperforms the other considered methods. Quantitatively on simulations and on a tissue-mimicking phantom, our method is found to be competitive with the state-of-the-art. On clinical B-mode images, our method is found to effectively smooth speckle while preserving low-contrast and highly localized salient image detail.

Impact of denoising on precision and accuracy of saturation-recovery-based myocardial T1 mapping

PURPOSE

To evaluate the impact of a novel postprocessing denoising technique on accuracy and precision in myocardial T₁ mapping.

MATERIALS AND METHODS

This study introduces a fast and robust denoising method developed for magnetic resonance T₁ mapping. The technique imposes edge-preserving regularity and exploits the co-occurence of spatial gradients in the acquired T₁ -weighted images. The proposed approach was assessed in simulations, ex vivo data and in vivo imaging on a cohort of 16 healthy volunteers (12 males, average age 39 ± 8 years, 62 ± 9 bpm) both in pre- and postcontrast injection. The method was evaluated in myocardial T₁ mapping at 3T with a saturation-recovery technique that is accurate but sensitive to noise. ROIs in the myocardium and left-ventricle blood pool were analyzed by an experienced reader. Mean T₁ values and standard deviation were extracted and compared in all studies.

RESULTS

Simulations on synthetic phantom showed signal-to-noise ratio and sharpness improvement with the proposed method in comparison with conventional denoising. In vivo results demonstrated that our method preserves accuracy, as no difference in mean T₁ values was observed in the myocardium (precontrast: 1433/1426 msec, 95%CI: [-40.7, 55.9], p = 0.75, postcontrast: 766/759 msec, 95%CI: [-60.7, 77.2], p = 0.8). Meanwhile, precision was improved with standard deviations of T₁ values being significantly decreased (precontrast: 223/151 msec, 95%CI: [27.3, 116.5], p = 0.003, postcontrast: 176/135 msec, 95%CI: [5.5, 77.1], p = 0.03).

CONCLUSION

The proposed denoising method preserves accuracy and improves precision in myocardial T₁ mapping, with the potential to offer better map visualization and analysis.

LEVEL OF EVIDENCE

3 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2017;46:1377-1388.

Spatially variant noise estimation in MRI: a homomorphic approach

The reliable estimation of noise characteristics in MRI is a task of great importance due to the influence of noise features in extensively used post-processing algorithms. Many methods have been proposed in the literature to retrieve noise features from the magnitude signal. However, most of them assume a stationary noise model, i.e., the features of noise do not vary with the position inside the image. This assumption does not hold when modern scanning techniques are considered, e.g., in the case of parallel reconstruction and intensity correction. Therefore, new noise estimators must be found to cope with non-stationary noise. Some methods have been recently proposed in the literature. However, they require multiple acquisitions or extra information which is usually not available (biophysical models, sensitivity of coils). In this work we overcome this drawback by proposing a new method that can accurately estimate the non-stationary parameters of noise from just a single magnitude image. In the derivation, we considered the noise to follow a non-stationary Rician distribution, since it is the most common model in real acquisitions (e.g., SENSE reconstruction), though it can be easily generalized to other models. The proposed approach makes use of a homomorphic separation of the spatially variant noise in two terms: a stationary noise term and one low frequency signal that correspond to the x-dependent variance of noise. The non-stationary variance of noise is then estimated by a low pass filtering with a Rician bias correction. Results in real and synthetic experiments evidence the better performance and the lowest error variance of the proposed methodology when compared to the state-of-the-art methods.

Noise estimation in magnetic resonance SENSE reconstructed data

Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k-space. SENSE is one of the most popular reconstruction methods proposed in order to suppress the artifacts created by this subsampling. However, the SENSE reconstruction process yields to a variance of noise value which is dependent on the position within the image. Hence, the traditional noise estimation methods based on a single noise level for the whole image fail. Accordingly, we propose a novel method to recover the complete spatial pattern of the variance of noise in SENSE reconstructed images up from the sensitivity maps of each receiver coil. Our method fits applications in statistical image processing tasks such as image denoising.

BHATTACHARYYA MEDIAN OF SYMMETRIC POSITIVE-DEFINITE MATRICES AND APPLICATION TO THE DENOISING OF DIFFUSION-TENSOR FIELDS

In this paper, we present algorithms for the computation of the median of a set of symmetric positive-definite matrices using different distances/divergences. The novelty of this paper lies in the median computation using the Bhattacharya distance on diffusion tensors. The numerical computation of the median is achieved using the gradient descent algorithm and the fixed point algorithm. We present an application namely, one of denoising tensor-valued data using median filters constructed using several distance/divergences and compare their performance.

Merging squared-magnitude approaches to DWI denoising: An adaptive Wiener filter tuned to the anatomical contents of the image

We present a new method for denoising of Diffusion Weighted Images (DWI) that shares several desirable features of state-of-the-art proposals: 1) it works with the squared-magnitude signal, allowing for a closed-form formulation as a Linear Minimum Mean Squared Error (LMMSE) estimator, a.k.a. Wiener filter; 2) it jointly accounts for the DWI channels altogether, being able to unveil anatomical structures that remain hidden in each separated channel; 3) it uses a Non-Local Means (NLM)-like scheme to discriminate voxels corresponding to different fiber bundles, being able to enhance the anatomical structures of the DWI. We report extensive experiments evidencing the new approach outperforms several related methods for all the range of input signal-to-noise ratios (SNR). An open-source C++ implementation of the algorithm is also provided for the sake of reproducibility.

Effective noise estimation and filtering from correlated multiple-coil MR data

Modern magnetic resonance (MR) imaging protocols based on multiple-coil acquisitions have carried on a new attention to noise and signal statistical modeling, as long as most of the existing techniques for data processing are model based. In particular, nonaccelerated multiple-coil and GeneRalized Autocalibrated Partially Parallel Acquisitions (GRAPPA) have brought noncentral-χ (nc-χ) statistics into stake as a suitable substitute for traditional Rician distributions. However, this model is only valid when the signals received by each coil are roughly uncorrelated. The recent literature on this topic suggests that this is often not the case, so nc-χ statistics are in principle not adequate. Fortunately, such model can be adapted through the definition of a set of effective parameters, namely, an effective noise power (greater than the actual power of thermal noise in the Radio Frequency receiver) and an effective number of coils (smaller than the actual number of RF receiving coils in the system). The implications of these artifacts in practical algorithms have not been discussed elsewhere. In the present paper, we aim to study their actual impact and suggest practical rules to cope with them. We define the main noise parameters in this context, introducing a new expression for the effective variance of noise which is of capital importance for the two image processing problems studied: first, we propose a new method to estimate the effective variance of noise from the composite magnitude signal of MR data when correlations are assumed. Second, we adapt several model-based image denoising techniques to the correlated case using the noise estimation techniques proposed. We show, through a number of experiments with synthetic, phantom, and in vivo data, that neglecting the correlated nature of noise in multiple-coil systems implies important errors even in the simplest cases. At the same time, the proper statistical characterization of noise through effective parameters drives to improved accuracy (both qualitatively and quantitatively) for both of the problems studied.

Least squares for diffusion tensor estimation revisited: propagation of uncertainty with Rician and non-Rician signals

Least Squares (LS) and its minimum variance counterpart, Weighted Least Squares (WLS), have become very popular when estimating the Diffusion Tensor (DT), to the point that they are the standard in most of the existing software for diffusion MRI. They are based on the linearization of the Stejskal-Tanner equation by means of the logarithmic compression of the diffusion signal. Due to the Rician nature of noise in traditional systems, a certain bias in the estimation is known to exist. This artifact has been made patent through some experimental set-ups, but it is not clear how the distortion translates in the reconstructed DT, and how important it is when compared to the other source of error contributing to the Mean Squared Error (MSE) in the estimate, i.e. the variance. In this paper we propose the analytical characterization of log-Rician noise and its propagation to the components of the DT through power series expansions. We conclude that even in highly noisy scenarios the bias for log-Rician signals remains moderate when compared to the corresponding variance. Yet, with the advent of Parallel Imaging (pMRI), the Rician model is not always valid. We make our analysis extensive to a number of modern acquisition techniques through the study of a more general Non Central-Chi (nc-χ) model. Since WLS techniques were initially designed bearing in mind Rician noise, it is not clear whether or not they still apply to pMRI. An important finding in our work is that the common implementation of WLS is nearly optimal when nc-χ noise is considered. Unfortunately, the bias in the estimation becomes far more important in this case, to the point that it may nearly overwhelm the variance in given situations. Furthermore, we evidence that such bias cannot be removed by increasing the number of acquired gradient directions. A number of experiments have been conducted that corroborate our analytical findings, while in vivo data have been used to test the actual relevance of the bias in the estimation.