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.

Denoising of Nifti (MRI) Images with a Regularized Neighborhood Pixel Similarity Wavelet Algorithm

The recovery of semantics from corrupted images is a significant challenge in image processing. Noise can obscure features, interfere with accurate analysis, and bias results. To address this issue, the Regularized Neighborhood Pixel Similarity Wavelet algorithm (PixSimWave) was developed for denoising Nifti (magnetic resonance imaging (MRI)). The PixSimWave algorithm uses regularized pixel similarity detection to improve the accuracy of noise reduction by creating patches to analyze the intensity of pixels and locate matching pixels, as well as adaptive neighborhood filtering to estimate noisy pixel values by allocating each pixel a weight based on its similarity. The wavelet transform breaks down the image into scales and orientations, allowing a sparse image representation to allocate a soft threshold on its similarity to the original pixels. The proposed method was evaluated on simulated and raw T1w MRIs, outperforming other methods in terms of an SSIM value of 0.9908 for a low Rician noise level of 3% and 0.9881 for a high noise level of 17%. The addition of Gaussian noise improved PSNR and SSIM, with the results indicating that the proposed method outperformed other models while preserving edges and textures. In summary, the PixSimWave algorithm is a viable noise-elimination approach that employs both sparse wavelet coefficients and regularized similarity with decreased computation time, improving the accuracy of noise reduction in images.

[Diffusion tensor field estimation based on 3D U-Net and diffusion tensor imaging model constraint]

OBJECTIVE

To propose a diffusion tensor field estimation network based on 3D U-Net and diffusion tensor imaging (DTI) model constraint (3D DTI-Unet) to accurately estimate DTI quantification parameters from a small number of diffusion-weighted (DW) images with a low signal-to-noise ratio.

METHODS

The input of 3D DTI-Unet was noisy diffusion magnetic resonance imaging (dMRI) data containing one non-DW image and 6 DW images with different diffusion coding directions. The noise-reduced non-DW image and accurate diffusion tensor field were predicted through 3D U-Net. The dMRI data were reconstructed using the DTI model and compared with the true value of dMRI data to optimize the network and ensure the consistency of the dMRI data with the physical model of the diffusion tensor field. We compared 3D DTI-Unet with two DW image denoising algorithms (MP-PCA and GL-HOSVD) to verify the effect of the proposed method.

RESULTS

The proposed method was better than MP-PCA and GL-HOSVD in terms of quantitative results and visual evaluation of DW images, diffusion tensor field and DTI quantification parameters.

CONCLUSION

The proposed method can obtain accurate DTI quantification parameters from one non-DW image and 6 DW images to reduce image acquisition time and improve the reliability of quantitative diagnosis.

TMS-Net: A segmentation network coupled with a run-time quality control method for robust cardiac image segmentation

Recently, deep networks have shown impressive performance for the segmentation of cardiac Magnetic Resonance Imaging (MRI) images. However, their achievement is proving slow to transition to widespread use in medical clinics because of robustness issues leading to low trust of clinicians to their results. Predicting run-time quality of segmentation masks can be useful to warn clinicians against poor results. Despite its importance, there are few studies on this problem. To address this gap, we propose a quality control method based on the agreement across decoders of a multi-view network, TMS-Net, measured by the cosine similarity. The network takes three view inputs resliced from the same 3D image along different axes. Different from previous multi-view networks, TMS-Net has a single encoder and three decoders, leading to better noise robustness, segmentation performance and run-time quality estimation in our experiments on the segmentation of the left atrium on STACOM 2013 and STACOM 2018 challenge datasets. We also present a way to generate poor segmentation masks by using noisy images generated with engineered noise and Rician noise to simulate undertraining, high anisotropy and poor imaging settings problems. Our run-time quality estimation method show a good classification of poor and good quality segmentation masks with an AUC reaching to 0.97 on STACOM 2018. We believe that TMS-Net and our run-time quality estimation method has a high potential to increase the thrust of clinicians to automatic image analysis tools.

[A diffusion-weighted image denoising algorithm using HOSVD combined with Rician noise corrected model]

OBJECTIVE

To propose a novel diffusion-weighted (DW) image denoising algorithm based on HOSVD to improve the signal-to-noise ratio (SNR) of DW images and the accuracy of subsequent quantization parameters.

METHODS

This HOSVDbased denoising method incorporated the sparse constraint and noise-correction model. The signal expectations with Rician noise were integrated into the traditional HOSVD denoising framework for direct denoising of the DW images with Rician noise. HOSVD denoising was performed directly on each local DW image block to avoid the stripe artifacts. We compared the proposed method with 4 image denoising algorithms (LR + Edge, GL-HOSVD, BM3D and NLM) to verify the effect of the proposed method.

RESULTS

The experimental results showed that the proposed method effectively reduced the noise of DW images while preserving the image details and edge structure information. The proposed algorithm was significantly better than LR +Edge, BM3D and NLM in terms of quantitative metrics of PSNR, SSIM and FA-RMSE and in visual evaluation of denoising images and FA images. GL-HOSVD obtained good denoising results but introduced stripe artifacts at a high noise level during the denoising process. In contrast, the proposed method achieved good denoising results without causing stripe artifacts.

CONCLUSION

This HOSVD-based denoising method allows direct processing of DW images with Rician noise without introducing artifacts and can provide accurate quantitative parameters for diagnostic purposes.

T2 analysis using artificial neural networks

Quantitative analysis of magnetic resonance signal lifetimes could reveal molecular scale information. However, it is non-trivial to recover the relaxation times from MR experiments in the multi-component exponential decay analysis. Constraints are required for the ill-posed problem in conventional inversion methods, which could lead to biased solutions. Artificial neural networks (ANNs) are a series of densely connected information processing nodes which cumulatively map a set of inputs to a set of outputs. They have proven to be universal approximators and powerful tools for solving complex nonlinear problems. In this work, ANNs were trained to recover T₂ relaxation times. Both the discrete T₂ spectrum and continuous T₂ distribution were considered. Increased accuracy was achieved compared to the traditional methods. The continuous spectrum peak widths, generally not reliable in the traditional approach, could be determined accurately with ANN when the signal-to-noise ratio permitted.

An enhanced multi-fiber reconstruction technique using adaptive gradient directions coupled with MoNCW model in diffusion MRI

In this paper, we introduced a novel approach for generating unit gradient vectors named as adaptive gradient directions (AGD) for reconstructing single and decussating (crossing or kissing) white matter fibers in brain. The present study is focusing on reconstruction process of brain's white matter fibers but not dealing with data acquisition where scanning is performed. The gradient vectors used in the state-of-art methodologies for reconstruction are uniformly distributed vectors on a unit sphere but AGD, in contrary, are non-uniformly distributed points on a unit sphere. These points are uniformly distributed in some pattern on the surface of a unit sphere. For reconstruction, we have coupled the proposed AGD approach with mixture of non-central Wishart (MoNCW) model. We uphold the proposed approach with different simulations including synthetic as well as real data experiments. Resistivity to different Rician noise levels (σ=0.02-0.1) is demonstrated in simulated data for single as well as two and three decussating fibers. Our approach of using AGD dissipates the limitations that are encountered by the state-of-art technique of uniformly distributed points over the surface of unit sphere and outperforms showing significant reduction in angular errors.

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.

Sparse MR Image Reconstruction Considering Rician Noise Models: A CNN Approach

Compressive sensing (CS) provides a potential platform for acquiring slow and sequential data, as in magnetic resonance (MR) imaging. However, CS requires high computational time for reconstructing MR images from sparse k-space data, which restricts its usage for high speed online reconstruction and wireless communications. Another major challenge is removal of Rician noise from magnitude MR images which changes the image characteristics, and thus affects the clinical usefulness. The work carried out so far predominantly models MRI noise as a Gaussian type. The use of advanced noise models primarily Rician type in CS paradigm is less explored. In this work, we develop a novel framework to reconstruct MR images with high speed and visual quality from noisy sparse k-space data. The proposed algorithm employs a convolutional neural network (CNN) to denoise MR images corrupted with Rician noise. To extract local features, the algorithm exploits signal similarities by processing similar patches as a group. An imperative reduction in the run time has been achieved as the CNN has been trained on a GPU with Convolutional Architecture for Fast Feature Embedding framework making it suitable for online reconstruction. The CNN based reconstruction also eliminates the necessity of optimization and prediction of noise level while denoising, which is the major advantage over existing state-of-the-art-techniques. Analytical experiments have been carried out with various undersampling schemes and the experimental results demonstrate high accuracy and consistent peak signal to noise ratio even at 20-fold undersampling. High undersampling rates provide scope for wireless transmission of k-space data and high speed reconstruction provides applicability of our algorithm for remote health monitoring.

A Modified Higher-Order Singular Value Decomposition Framework With Adaptive Multilinear Tensor Rank Approximation for Three-Dimensional Magnetic Resonance Rician Noise Removal

The magnetic resonance (MR) images are acknowledged to be inevitably corrupted by Rician distributed noise, which adversely affected the image quality for diagnosis purpose. However, the traditional denoising methods may recover the images from corruptions with severe loss of detailed structure and edge information, which would affect the lesion detections and diagnostic decision making. In this study, we challenged improving the Rician noise removal from three-dimensional (3D) MR volumetric data through a modified higher-order singular value decomposition (MHOSVD) method. The proposed framework of MHOSVD involved a parameterized logarithmic nonconvex penalty function for low-rank tensor approximation (LRTA) algorithm optimization to suppress the image noise in MR dataset. Reference cubes were extracted from the noisy image volume, and block matching was performed according to nonlocal similarity for a fourth-order tensor construction. Then the LRTA problem was implemented by tensor factorization approaches, and the ranks of unfolding matrices along different modes of the tensor were estimated utilizing an adaptive nonconvex low-rank method. The denoised MR images were finally restored through aggregating all recovered cubes. We investigated the proposed algorithm MHOSVD on both the synthetic and real clinic 3D MR images for Rician noise removal, and relative results demonstrated that the MHOSVD can recover images with fine structures and detailed edge preservation with heavy noise even as high as 15% of the maximum intensity. The experimental results were also compared along with several classical denoising methods; the MHOSVD exhibited a sufficient improvement in noise-removal performance at various noise conditions in terms of different measurement indices such as peak signal-to-noise ratio and structural similarity index metrics. Based upon the comparison, the proposed MHOSVD has proved a relative state-of-the-art performance with excellent detailed structure reservation.

Impact of pulse sequence, analysis method, and signal to noise ratio on the accuracy of intervertebral disc T 2 measurement

Noninvasive assessments of intervertebral disc health and degeneration are critical for addressing disc degeneration and low back pain. Magnetic resonance imaging (MRI) is exceptionally sensitive to tissue with high water content, and measurement of the MR transverse relaxation time, T 2, has been applied as a quantitative, continuous, and objective measure of disc degeneration that is linked to the water and matrix composition of the disc. However, T 2 measurement is susceptible to inaccuracies due to Rician noise, T 1 contamination, and stimulated echo effects. These error generators can all be controlled for with proper data collection and fitting methods. The objective of this study was to identify sequence parameters to appropriately acquire MR data and to establish curve fitting methods to accurately calculate disc T 2 in the presence of noise by correcting for Rician noise. To do so, we compared T 2 calculated from the typical monoexponential (MONO) fits and noise corrected exponential (NCEXP) fits. We examined how the selected sequence parameters altered the calculated T 2 in silico and in vivo. Typical MONO fits were frequently poor due to Rician noise, and NCEXP fits were more likely to provide accurate T 2 calculations. NCEXP is particularly less biased and less uncertain at low SNR. This study showed that the NCEXP using sequences with data from 20 echoes out to echo times of ~300 ms is the best method for calculating T 2 of discs. By acquiring signal data out to longer echo times and accounting for Rician noise, the curve fitting is more robust in calculating T 2 despite the noise in the data. This is particularly important when considering degenerate discs or AF tissue because the SNR of these regions is lower.

MRI denoising using progressively distribution-based neural network

Magnetic Resonance (MR) images often suffer from noise pollution during image acquisition and transmission, which limits the accuracy of quantitative measurements from the data. Noise in magnitude MR images is usually governed by Rician distribution, due to the existence of uncorrelated Gaussian noise with zero-mean and equal variance in both the real and imaginary parts of the complex K-space data. Different from the existing MRI denoising methods that utilizing the spatial neighbor information around the pixels or patches, this work turns to capture the pixel-level distribution information by means of supervised network learning. A progressive network learning strategy is proposed via fitting the distribution of pixel-level and feature-level intensities. The proposed network consists of two residual blocks, one is used for fitting pixel domain without batch normalization layer and another one is applied for matching feature domain with batch normalization layer. Experimental results under synthetic, complex-valued and clinical MR brain images demonstrate great potential of the proposed network with substantially improved quantitative measures and visual inspections.

Adaptive phase correction of diffusion-weighted images

Phase correction (PC) is a preprocessing technique that exploits the phase of images acquired in Magnetic Resonance Imaging (MRI) to obtain real-valued images containing tissue contrast with additive Gaussian noise, as opposed to magnitude images which follow a non-Gaussian distribution, e.g. Rician. PC finds its natural application to diffusion-weighted images (DWIs) due to their inherent low signal-to-noise ratio and consequent non-Gaussianity that induces a signal overestimation bias that propagates to the calculated diffusion indices. PC effectiveness depends upon the quality of the phase estimation, which is often performed via a regularization procedure. We show that a suboptimal regularization can produce alterations of the true image contrast in the real-valued phase-corrected images. We propose adaptive phase correction (APC), a method where the phase is estimated by using MRI noise information to perform a complex-valued image regularization that accounts for the local variance of the noise. We show, on synthetic and acquired data, that APC leads to phase-corrected real-valued DWIs that present a reduced number of alterations and a reduced bias. The substantial absence of parameters for which human input is required favors a straightforward integration of APC in MRI processing pipelines.

Laplacian Eigenmaps Network-Based Nonlocal Means Method for MR Image Denoising

Magnetic resonance (MR) images are often corrupted by Rician noise which degrades the accuracy of image-based diagnosis tasks. The nonlocal means (NLM) method is a representative filter in denoising MR images due to its competitive denoising performance. However, the existing NLM methods usually exploit the gray-level information or hand-crafted features to evaluate the similarity between image patches, which is disadvantageous for preserving the image details while smoothing out noise. In this paper, an improved nonlocal means method is proposed for removing Rician noise in MR images by using the refined similarity measures. The proposed method firstly extracts the intrinsic features from the pre-denoised image using a shallow convolutional neural network named Laplacian eigenmaps network (LEPNet). Then, the extracted features are used for computing the similarity in the NLM method to produce the denoised image. Finally, the method noise of the denoised image is utilized to further improve the denoising performance. Specifically, the LEPNet model is composed of two cascaded convolutional layers and a nonlinear output layer, in which the Laplacian eigenmaps are employed to learn the filter bank in the convolutional layers and the Leaky Rectified Linear Unit activation function is used in the final output layer to output the nonlinear features. Due to the advantage of LEPNet in recovering the geometric structure of the manifold in the low-dimension space, the features extracted by this network can facilitate characterizing the self-similarity better than the existing NLM methods. Experiments have been performed on the BrainWeb phantom and the real images. Experimental results demonstrate that among several compared denoising methods, the proposed method can provide more effective noise removal and better details preservation in terms of human vision and such objective indexes as peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM).

Denoising of MR images with Rician noise using a wider neural network and noise range division

Magnetic resonance (MR) images denoising is important in medical image analysis. Denoising methods based on deep learning have shown great promise and outperform all of the other conventional methods. However, deep-learning methods are limited by the number of training samples. In this article, using a small sample size, we applied a wider denoising neural network to MR images with Rician noise and trained several denoising models. The first model is specific to a certain noise, while the other applies to a wide range of noise levels. We considered the noise range as one interval, two sub-intervals, three sub-intervals, or even more sub-intervals to train the corresponding models. Experimental results demonstrate that for MR images, the proposed deep-learning models are efficient in terms of peak-signal-to-noise ratio, structure-similarity-index metrics and normalized mutual information. In addition, for blind noise, the effect of the three sub-intervals is better than that of the other sub-intervals.

A spatial fuzzy C-means algorithm for segmentation of brain MRI images

Brain and its structure are extremely complex with deep levels of details. Applying image processing methods of brain image can be very useful in many practical domains. Magnetic Resonance Imaging (MRI) is widely used imaging technique and has particular advantage by possessing the capability of providing highly detailed images of brain soft tissues than any other imaging techniques. The real challenge at hand for researchers is to perform precise segmentation while overcoming the effects of noise and other imaging artifacts like intensity in homogeneity introduced in medical images during image acquisition process. In this research work, a directional weighted optimized Fuzzy C-Means (dwsFCM) method has been proposed for segmentation of brain MR images. This method works by incorporating the spatial information of the pixels of the images and assigning the directional weights to the neighborhood. In order to validate the proposed segmentation framework, a comprehensive set of experiments have been performed on publically available standard simulated as well as real datasets. The experimental results showed 95% of accuracy and the performance of the proposed segmentation framework is much better and the framework suppress the sufficient amount of noise especially rician noise and reproduce good segmentation by overcoming the effect of intensity in homogeneity.

A sparse representation and dictionary learning based algorithm for image restoration in the presence of Rician noise

Rician noise removal for Magnetic Resonance Imaging (MRI) is very important because the MRI has been widely used in various clinical applications and the associated Rician noise deteriorates the image quality and causes errors in interpreting the images. Great efforts have recently been devoted to develop the corresponding noise-removal algorithms, particularly the development based on the newly-established Total Variation (TV) theorem. However, all the TV-based algorithms depend mainly on the gradient information and have been shown to produce the so called "blocky" artifact, which also deteriorates the image quality and causes image interpretation errors. In order to avoid producing the artifact, this paper presents a new de-noising model based on sparse representation and dictionary learning. The Split Bregman Iteration strategy is employed to implement the model. Furthermore, an appropriate dictionary is designed by the use of the Kernel Singular Value Decomposition method, resulting in a new Rician noise removal algorithm. Compared with other de-noising algorithms, the presented new algorithm can achieve superior performance, in terms of quantitative measures of the Structural Similarity Index and Peak Signal to Noise Ratio, by a series of experiments using different images in the presence of Rician noise.

Denoising of 3D magnetic resonance images with multi-channel residual learning of convolutional neural network

PURPOSE

To test if the proposed deep learning based denoising method denoising convolutional neural networks (DnCNN) with residual learning and multi-channel strategy can denoise three dimensional MR images with Rician noise robustly.

MATERIALS AND METHODS

Multi-channel DnCNN (MCDnCNN) method with two training strategies was developed to denoise MR images with and without a specific noise level, respectively. To evaluate our method, three datasets from two public data sources of IXI dataset and Brainweb, including T1 weighted MR images acquired at 1.5 and 3 T as well as MR images simulated with a widely used MR simulator, were randomly selected and artificially added with different noise levels ranging from 1 to 15%. For comparison, four other state-of-the-art denoising methods were also tested using these datasets.

RESULTS

In terms of the highest peak-signal-to-noise-ratio and global of structure similarity index, our proposed MCDnCNN model for a specific noise level showed the most robust denoising performance in all three datasets. Next to that, our general noise-applicable model also performed better than the rest four methods in two datasets. Furthermore, our training model showed good general applicability.

CONCLUSION

Our proposed MCDnCNN model has been demonstrated to robustly denoise three dimensional MR images with Rician noise.

Wavelet-domain TI Wiener-like filtering for complex MR data denoising

Magnetic resonance (MR) images are affected by random noises, which degrade many image processing and analysis tasks. It has been shown that the noise in magnitude MR images follows a Rician distribution. Unlike additive Gaussian noise, the noise is signal-dependent, and consequently difficult to reduce, especially in low signal-to-noise ratio (SNR) images. Wirestam et al. in [20] proposed a Wiener-like filtering technique in wavelet-domain to reduce noise before construction of the magnitude MR image. Based on Wirestam's study, we propose a wavelet-domain translation-invariant (TI) Wiener-like filtering algorithm for noise reduction in complex MR data. The proposed denoising algorithm shows the following improvements compared with Wirestam's method: (1) we introduce TI property into the Wiener-like filtering in wavelet-domain to suppress artifacts caused by translations of the signal; (2) we integrate one Stein's Unbiased Risk Estimator (SURE) thresholding with two Wiener-like filters to make the hard-thresholding scale adaptive; and (3) the first Wiener-like filtering is used to filter the original noisy image in which the noise obeys Gaussian distribution and it provides more reasonable results. The proposed algorithm is applied to denoise the real and imaginary parts of complex MR images. To evaluate our proposed algorithm, we conduct extensive denoising experiments using T1-weighted simulated MR images, diffusion-weighted (DW) phantom and in vivo data. We compare our algorithm with other popular denoising methods. The results demonstrate that our algorithm outperforms others in term of both efficiency and robustness.

Efficient 2D MRI relaxometry using compressed sensing

Potential applications of 2D relaxation spectrum NMR and MRI to characterize complex water dynamics (e.g., compartmental exchange) in biology and other disciplines have increased in recent years. However, the large amount of data and long MR acquisition times required for conventional 2D MR relaxometry limits its applicability for in vivo preclinical and clinical MRI. We present a new MR pipeline for 2D relaxometry that incorporates compressed sensing (CS) as a means to vastly reduce the amount of 2D relaxation data needed for material and tissue characterization without compromising data quality. Unlike the conventional CS reconstruction in the Fourier space (k-space), the proposed CS algorithm is directly applied onto the Laplace space (the joint 2D relaxation data) without compressing k-space to reduce the amount of data required for 2D relaxation spectra. This framework is validated using synthetic data, with NMR data acquired in a well-characterized urea/water phantom, and on fixed porcine spinal cord tissue. The quality of the CS-reconstructed spectra was comparable to that of the conventional 2D relaxation spectra, as assessed using global correlation, local contrast between peaks, peak amplitude and relaxation parameters, etc. This result brings this important type of contrast closer to being realized in preclinical, clinical, and other applications.

Quantitative R2* MRI of the liver with rician noise models for evaluation of hepatic iron overload: Simulation, phantom, and early clinical experience

PURPOSE

To compare Rician and non-Rician noise models for quantitative R2 * magnetic resonance imaging (MRI), in a simulation, phantom, and human study.

MATERIALS AND METHODS

Synthetic 12-echo spoiled GRE (SGRE) datasets were generated with various R2 * rates (0-2000 sec(-1) ) at a signal-to-noise ratio (SNR) of 50, 20, 10, and 5. Phantoms of different MnCl2 concentrations (0-25 mM) were constructed and imaged using a 12-echo 3D SGRE sequence at 1.5T. Increasing levels of synthetic noise was added to the original data to simulate sequentially lower SNR conditions. Sixteen patients with suspected or known iron overload were imaged using 12-echo 3D SGRE at 1.5T. Various R2 * quantification methods, based on Rician and non-Rician noise models, were compared in the simulation, phantom, and human datasets.

RESULTS

Non-Rician R2 * estimates were variably inaccurate in the high R2 * range (>500 sec(-1) ), with SNR-dependent linear goodness-of-fit statistic (R(2) ) of 0.373-0.999. Rician R2 * estimates were accurate even in the high R2 * range, with high R(2) of 0.940-0.999 regardless of SNR. Non-Rician R2 * estimates were variably nonlinear at high MnCl2 concentrations, with SNR-dependent R(2) of 0.345-0.994. Rician R2 * estimates were linear even at high MnCl2 concentrations, with high R(2) of 0.923-0.994 regardless of SNR. Between-method agreement of the R2 * estimates was excellent in patients with low ferritin but poor in patients with high ferritin. Rician R2 * estimates had excellent correlation with ferritin (r = 0.966 P < 0.001).

CONCLUSION

Rician R2 * estimates were most consistent in the high R2 * conditions and under varying SNR, and may be more reliable when high iron load is suspected.

Bayesian analysis of transverse signal decay with application to human brain

PURPOSE

Transverse relaxation analysis with several signal models has been used extensively to determine tissue and material properties. However, the derivation of corresponding parameter values is notoriously unreliable. We evaluate improvements in the quality of parameter estimation using Bayesian analysis and incorporating the Rician noise model, as appropriate for magnitude MR images.

THEORY AND METHODS

Monoexponential, stretched exponential, and biexponential signal models were analyzed using nonlinear least squares (NLLS) and Bayesian approaches. Simulations and phantom and human brain data were analyzed using three different approaches to account for noise. Parameter estimation bias (reflecting accuracy) and dispersion (reflecting precision) were derived for a range of signal-to-noise ratios (SNR) and relaxation parameters.

RESULTS

All methods performed well at high SNR. At lower SNR, the Bayesian approach yielded parameter estimates of considerably greater precision, as well as greater accuracy, than did NLLS. Incorporation of the Rician noise model greatly improved accuracy and, to a somewhat lesser extent, precision, in derived transverse relaxation parameters. Analyses of data obtained from solution phantoms and from brain were consistent with simulations.

CONCLUSION

Overall, estimation of parameters characterizing several different transverse relaxation models was markedly improved through use of Bayesian analysis and through incorporation of the Rician noise model.

Laplacian based non-local means denoising of MR images with Rician noise

Magnetic Resonance (MR) image is often corrupted with a complex white Gaussian noise (Rician noise) which is signal dependent. Considering the special characteristics of Rician noise, we carry out nonlocal means denoising on squared magnitude images and compensate the introduced bias. In this paper, we propose an algorithm which not only preserves the edges and fine structures but also performs efficient denoising. For this purpose we have used a Laplacian of Gaussian (LoG) filter in conjunction with a nonlocal means filter (NLM). Further, to enhance the edges and to accelerate the filtering process, only a few similar patches have been preselected on the basis of closeness in edge and inverted mean values. Experiments have been conducted on both simulated and clinical data sets. The qualitative and quantitative measures demonstrate the efficacy of the proposed method.