Generalized total variation-based MRI Rician denoising model with spatially adaptive regularization parameters

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.

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.

Perceptually Motivated Generative Model for Magnetic Resonance Image Denoising

Image denoising is an important preprocessing step in low-level vision problems involving biomedical images. Noise removal techniques can greatly benefit raw corrupted magnetic resonance images (MRI). It has been discovered that the MR data is corrupted by a mixture of Gaussian-impulse noise caused by detector flaws and transmission errors. This paper proposes a deep generative model (GenMRIDenoiser) for dealing with this mixed noise scenario. This work makes four contributions. To begin, Wasserstein generative adversarial network (WGAN) is used in model training to mitigate the problem of vanishing gradient, mode collapse, and convergence issues encountered while training a vanilla GAN. Second, a perceptually motivated loss function is used to guide the training process in order to preserve the low-level details in the form of high-frequency components in the image. Third, batch renormalization is used between the convolutional and activation layers to prevent performance degradation under the assumption of non-independent and identically distributed (non-iid) data. Fourth, global feature attention module (GFAM) is appended at the beginning and end of the parallel ensemble blocks to capture the long-range dependencies that are often lost due to the small receptive field of convolutional filters. The experimental results over synthetic data and MRI stack obtained from real MR scanners indicate the potential utility of the proposed technique across a wide range of degradation scenarios.

MRI Reconstruction with Separate Magnitude and Phase Priors Based on Dual-Tree Complex Wavelet Transform

The methods of compressed sensing magnetic resonance imaging (CS-MRI) can be divided into two categories roughly based on the number of target variables. One group devotes to estimating the complex-valued MRI image. And the other calculates the magnitude and phase parts of the complex-valued MRI image, respectively, by enforcing separate penalties on them. We propose a new CS-based method based on dual-tree complex wavelet (DT CWT) sparsity, which is under the frame of the second class of CS-MRI. Owing to the separate regularization frame, this method reduces the impact of the phase jumps (that means the jumps or discontinuities of phase values) on magnitude reconstruction. Moreover, by virtue of the excellent features of DT CWT, such as nonoscillating envelope of coefficients and multidirectional selectivity, the proposed method is capable of capturing more details in the magnitude and phase images. The experimental results show that the proposed method recovers the image contour and edges information well and can eliminate the artifacts in magnitude results caused by phase jumps.

Denoising Diffusion MRI via Graph Total Variance in Spatioangular Domain

Diffusion MRI (DMRI) plays an essential role in diagnosing brain disorders related to white matter abnormalities. However, it suffers from heavy noise, which restricts its quantitative analysis. The total variance (TV) regularization is an effective noise reduction technique that penalizes noise-induced variances. However, existing TV-based denoising methods only focus on the spatial domain, overlooking that DMRI data lives in a combined spatioangular domain. It eventually results in an unsatisfactory noise reduction effect. To resolve this issue, we propose to remove the noise in DMRI using graph total variance (GTV) in the spatioangular domain. Expressly, we first represent the DMRI data using a graph, which encodes the geometric information of sampling points in the spatioangular domain. We then perform effective noise reduction using the powerful GTV regularization, which penalizes the noise-induced variances on the graph. GTV effectively resolves the limitation in existing methods, which only rely on spatial information for removing the noise. Extensive experiments on synthetic and real DMRI data demonstrate that GTV can remove the noise effectively and outperforms state-of-the-art methods.

Super Resolution of Magnetic Resonance Images

In this work, novel denoising and super resolution (SR) approaches for magnetic resonance (MR) images are addressed, and are integrated in a unified framework, which do not require example low resolution (LR)/high resolution (HR)/cross-modality/noise-free images and prior information of noise–noise variance. The proposed method categorizes the patches as either smooth or textured and then denoises them by deploying different denoising strategies for efficient denoising. The denoising algorithm is integrated into the SR approach, which uses a gradient profile-based constraint in a sparse representation-based framework to improve the resolution of MR images with reduced smearing of image details. This constraint regularizes the estimation of HR images such that the estimated HR image has gradient profiles similar to the gradient profiles of the original HR image. For this, the gradient profile sharpness (GPS) values of an unknown HR image are estimated using an approximated piece-wise linear relation among GPS values of LR and upsampled LR images. The experiments are performed on three different publicly available datasets. The proposed SR approach outperforms the existing unsupervised SR approach addressed for real MR images that exploits low rank and total variation (LRTV) regularization, by an average peak signal to noise ratio (PSNR) of 0.73 dB and 0.38 dB for upsampling factors 2 and 3, respectively. For the super resolution of noisy real MR images (degraded with 2% noise), the proposed approach outperforms the LRTV approach by an average PSNR of 0.54 dB and 0.46 dB for upsampling factors 2 and 3, respectively. The qualitative analysis is shown for real MR images from healthy subjects and subjects with Alzheimer’s disease and structural deformity, i.e., cavernoma.

Denoising of 3D Brain MR Images with Parallel Residual Learning of Convolutional Neural Network Using Global and Local Feature Extraction

Magnetic resonance (MR) images often suffer from random noise pollution during image acquisition and transmission, which impairs disease diagnosis by doctors or automated systems. In recent years, many noise removal algorithms with impressive performances have been proposed. In this work, inspired by the idea of deep learning, we propose a denoising method named 3D-Parallel-RicianNet, which will combine global and local information to remove noise in MR images. Specifically, we introduce a powerful dilated convolution residual (DCR) module to expand the receptive field of the network and to avoid the loss of global features. Then, to extract more local information and reduce the computational complexity, we design the depthwise separable convolution residual (DSCR) module to learn the channel and position information in the image, which not only reduces parameters dramatically but also improves the local denoising performance. In addition, a parallel network is constructed by fusing the features extracted from each DCR module and DSCR module to improve the efficiency and reduce the complexity for training a denoising model. Finally, a reconstruction (REC) module aims to construct the clean image through the obtained noise deviation and the given noisy image. Due to the lack of ground-truth images in the real MR dataset, the performance of the proposed model was tested qualitatively and quantitatively on one simulated T1-weighted MR image dataset and then expanded to four real datasets. The experimental results show that the proposed 3D-Parallel-RicianNet network achieves performance superior to that of several state-of-the-art methods in terms of the peak signal-to-noise ratio, structural similarity index, and entropy metric. In particular, our method demonstrates powerful abilities in both noise suppression and structure preservation.

Joint low-rank prior and difference of Gaussian filter for magnetic resonance image denoising

The low-rank matrix approximation (LRMA) is an efficient image denoising method to reduce additive Gaussian noise. However, the existing low-rank matrix approximation does not perform well in terms of Rician noise removal for magnetic resonance imaging (MRI). To this end, we propose a novel MR image denoising approach based on the extended difference of Gaussian (DoG) filter and nonlocal low-rank regularization. In the proposed method, a novel nonlocal self-similarity evaluation with the tight frame is exploited to improve the patch matching. To remove the Rician noise and preserve the edge details, the extended DoG filter is exploited to the nonlocal low-rank regularization model. The experimental results demonstrate that the proposed method can preserve more edge and fine structures while removing noise in MR image as compared with some of the existing methods.

A Survey on State-of-the-art Denoising Techniques for Brain Magnetic Resonance Images

The accuracy of the magnetic resonance (MR) image diagnosis depends on the quality of the image, which degrades mainly due to noise and artifacts. The noise is introduced because of erroneous imaging environment or distortion in the transmission system. Therefore, denoising methods play an important role in enhancing the image quality. However, a tradeoff between denoising and preserving the structural details is required. Most of the existing surveys are conducted on a specific MR image modality or on limited denoising schemes. In this context, a comprehensive review on different MR image denoising techniques is inevitable. This survey suggests a new direction in categorizing the MR image denoising techniques. The categorization of the different image models used in medical image processing serves as the basis of our classification. This study includes recent improvements on deep learning-based denoising methods alongwith important traditional MR image denoising methods. The major challenges and their scope of improvement are also discussed. Further, many more evaluation indices are considered for a fair comparison. An elaborate discussion on selecting appropriate method and evaluation metric as per the kind of data is presented. This study may encourage researchers for further work in this domain.

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.

Removal of high density Gaussian noise in compressed sensing MRI reconstruction through modified total variation image denoising method

A modified total variation MRI image denoising method is proposed in this paper. First, the proposed method removes the noise in K-space in compressed sensing MRI reconstruction. Then, the removed K-space data is used as a partial frequency observation in compressed sensing MRI model. The proposed method shows better results than RecPF method, LDP method, TVCMRI method, and FCSA method in sparse MRI reconstruction. The proposed method is tested against Shepp-Logan phantom and real MR images corrupted by noise of different intensity level, and it gives better Signal-to-Noise Ratio (SNR), the relative error (ReErr), and the structural similarity (SSIM) than RecPF, LDP, TVCMRI, and FCSA.

Computer-Aided Design and Manufacturing (CAD/CAM) for Bioprinting

Three-dimensional (3D) printing of human tissues and organs has been an exciting area of research for almost three decades [Bonassar and Vacanti. J Cell Biochem. 72(Suppl 30-31):297-303 (1998)]. The primary goal of bioprinting, presently, is achieving printed constructs with the overarching aim toward fully functional tissues and organs. Technology, in hand with the development of bioinks, has been identified as the key to this success. As a result, the place of computer-aided systems (design and manufacturing-CAD/CAM) cannot be underestimated and plays a significant role in this area. Unlike many reviews in this field, this chapter focuses on the technology required for 3D bioprinting from an initial background followed by the exciting area of medical imaging and how it plays a role in bioprinting. Extraction and classification of tissue types from 3D scans is discussed in addition to modeling and simulation capabilities of scanned systems. After that, the necessary area of transferring the 3D model to the printer is explored. The chapter closes with a discussion of the current state-of-the-art and inherent challenges facing the research domain to achieve 3D tissue and organ printing.

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).

Weighted Schatten p-norm minimization for 3D magnetic resonance images denoising

Magnetic resonance (MR) imaging plays an important role in clinical diagnosis and scientific research. A clean MR image can better provide patient's information to doctors or researchers for further treatment. However, in real life, MR images are inevitably corrupted by annoying Rician noise in the process of imaging. Aiming at the Rician noise of 3D MR images, a framework is proposed to suppress noise by low-rank matrix approximation (LRMA) with weighted Schatten p-norm minimization regularization (WSNMD-3D). The proposed method not only considers the importance of different rank components, but can also approximate the true rank of the latent low-rank matrix. This approach first groups similar non-local cubic patches extracted from the noisy 3D MR image into a matrix whose columns are vectorized patches. The above matrix can be modeled as a low-rank matrix approximate model. Then weighted Schatten p-norm minimization (WSNM) is applied to the model, which shrinks different rank components with different treatments. Finally, the denoised 3D MR image is acquired by aggregating all denoised patches with weighted averaging. Experimental results on synthetic and real 3D MR data show that the proposed method obtains better results than state-of-the-art methods, both visually and quantitatively.

Simultaneous magnetic resonance diffusion and pseudo-diffusion tensor imaging

PURPOSE

An emerging topic in diffusion magnetic resonance is imaging blood microcirculation alongside water diffusion using the intravoxel incoherent motion (IVIM) model. Recently, a combined IVIM diffusion tensor imaging (IVIM-DTI) model was proposed, which accounts for both anisotropic pseudo-diffusion due to blood microcirculation and anisotropic diffusion due to tissue microstructures. In this article, we propose a robust IVIM-DTI approach for simultaneous diffusion and pseudo-diffusion tensor imaging.

METHODS

Conventional IVIM estimation methods can be broadly divided into two-step (diffusion and pseudo-diffusion estimated separately) and one-step (diffusion and pseudo-diffusion estimated simultaneously) methods. Here, both methods were applied on the IVIM-DTI model. An improved one-step method based on damped Gauss-Newton algorithm and a Gaussian prior for the model parameters was also introduced. The sensitivities of these methods to different parameter initializations were tested with realistic in silico simulations and experimental in vivo data.

RESULTS

The one-step damped Gauss-Newton method with a Gaussian prior was less sensitive to noise and the choice of initial parameters and delivered more accurate estimates of IVIM-DTI parameters compared to the other methods.

CONCLUSION

One-step estimation using damped Gauss-Newton and a Gaussian prior is a robust method for simultaneous diffusion and pseudo-diffusion tensor imaging using IVIM-DTI model. Magn Reson Med 79:2367-2378, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Non-Stationary Rician Noise Estimation in Parallel MRI Using a Single Image: A Variance-Stabilizing Approach

Parallel magnetic resonance imaging (pMRI) techniques have gained a great importance both in research and clinical communities recently since they considerably accelerate the image acquisition process. However, the image reconstruction algorithms needed to correct the subsampling artifacts affect the nature of noise, i.e., it becomes non-stationary. Some methods have been proposed in the literature dealing with the non-stationary noise in pMRI. However, their performance depends on information not usually available such as multiple acquisitions, receiver noise matrices, sensitivity coil profiles, reconstruction coefficients, or even biophysical models of the data. Besides, some methods show an undesirable granular pattern on the estimates as a side effect of local estimation. Finally, some methods make strong assumptions that just hold in the case of high signal-to-noise ratio (SNR), which limits their usability in real scenarios. We propose a new automatic noise estimation technique for non-stationary Rician noise that overcomes the aforementioned drawbacks. Its effectiveness is due to the derivation of a variance-stabilizing transformation designed to deal with any SNR. The method was compared to the main state-of-the-art methods in synthetic and real scenarios. Numerical results confirm the robustness of the method and its better performance for the whole range of SNRs.

A portable image-based cytometer for rapid malaria detection and quantification

Increasing resistance by malaria parasites to currently used antimalarials across the developing world warrants timely detection and classification so that appropriate drug combinations can be administered before clinical complications arise. However, this is often challenged by low levels of infection (referred to as parasitemia) and presence of predominantly young parasitic forms in the patients' peripheral blood. Herein, we developed a simple, inexpensive and portable image-based cytometer that detects and numerically counts Plasmodium falciparum infected red blood cells (iRBCs) from Giemsa-stained smears derived from infected blood. Our cytometer is able to classify all parasitic subpopulations by quantifying the area occupied by the parasites within iRBCs, with high specificity, sensitivity and negligible false positives (~ 0.0025%). Moreover, we demonstrate the application of our image-based cytometer in testing anti-malarial efficacy against a commercial flow cytometer and demonstrate comparable results between the two methods. Collectively, these results highlight the possibility to use our image-based cytometer as a cheap, rapid and accurate alternative for antimalarial testing without compromising on efficiency and minimal processing time. With appropriate filters applied into the algorithm, to rule out leukocytes and reticulocytes, our cytometer may also be used for field diagnosis of malaria.

Reconstruction of Undersampled Big Dynamic MRI Data Using Non-Convex Low-Rank and Sparsity Constraints

Dynamic magnetic resonance imaging (MRI) has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t)-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM) is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments.

Effective Alternating Direction Optimization Methods for Sparsity-Constrained Blind Image Deblurring

Single-image blind deblurring for imaging sensors in the Internet of Things (IoT) is a challenging ill-conditioned inverse problem, which requires regularization techniques to stabilize the image restoration process. The purpose is to recover the underlying blur kernel and latent sharp image from only one blurred image. Under many degraded imaging conditions, the blur kernel could be considered not only spatially sparse, but also piecewise smooth with the support of a continuous curve. By taking advantage of the hybrid sparse properties of the blur kernel, a hybrid regularization method is proposed in this paper to robustly and accurately estimate the blur kernel. The effectiveness of the proposed blur kernel estimation method is enhanced by incorporating both the L1-norm of kernel intensity and the squared L2-norm of the intensity derivative. Once the accurate estimation of the blur kernel is obtained, the original blind deblurring can be simplified to the direct deconvolution of blurred images. To guarantee robust non-blind deconvolution, a variational image restoration model is presented based on the L1-norm data-fidelity term and the total generalized variation (TGV) regularizer of second-order. All non-smooth optimization problems related to blur kernel estimation and non-blind deconvolution are effectively handled by using the alternating direction method of multipliers (ADMM)-based numerical methods. Comprehensive experiments on both synthetic and realistic datasets have been implemented to compare the proposed method with several state-of-the-art methods. The experimental comparisons have illustrated the satisfactory imaging performance of the proposed method in terms of quantitative and qualitative evaluations.

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.

Non Local Spatial and Angular Matching: Enabling higher spatial resolution diffusion MRI datasets through adaptive denoising

Diffusion magnetic resonance imaging (MRI) datasets suffer from low Signal-to-Noise Ratio (SNR), especially at high b-values. Acquiring data at high b-values contains relevant information and is now of great interest for microstructural and connectomics studies. High noise levels bias the measurements due to the non-Gaussian nature of the noise, which in turn can lead to a false and biased estimation of the diffusion parameters. Additionally, the usage of in-plane acceleration techniques during the acquisition leads to a spatially varying noise distribution, which depends on the parallel acceleration method implemented on the scanner. This paper proposes a novel diffusion MRI denoising technique that can be used on all existing data, without adding to the scanning time. We first apply a statistical framework to convert both stationary and non stationary Rician and non central Chi distributed noise to Gaussian distributed noise, effectively removing the bias. We then introduce a spatially and angular adaptive denoising technique, the Non Local Spatial and Angular Matching (NLSAM) algorithm. Each volume is first decomposed in small 4D overlapping patches, thus capturing the spatial and angular structure of the diffusion data, and a dictionary of atoms is learned on those patches. A local sparse decomposition is then found by bounding the reconstruction error with the local noise variance. We compare against three other state-of-the-art denoising methods and show quantitative local and connectivity results on a synthetic phantom and on an in-vivo high resolution dataset. Overall, our method restores perceptual information, removes the noise bias in common diffusion metrics, restores the extracted peaks coherence and improves reproducibility of tractography on the synthetic dataset. On the 1.2 mm high resolution in-vivo dataset, our denoising improves the visual quality of the data and reduces the number of spurious tracts when compared to the noisy acquisition. Our work paves the way for higher spatial resolution acquisition of diffusion MRI datasets, which could in turn reveal new anatomical details that are not discernible at the spatial resolution currently used by the diffusion MRI community.

A Dictionary Learning Method with Total Generalized Variation for MRI Reconstruction

Reconstructing images from their noisy and incomplete measurements is always a challenge especially for medical MR image with important details and features. This work proposes a novel dictionary learning model that integrates two sparse regularization methods: the total generalized variation (TGV) approach and adaptive dictionary learning (DL). In the proposed method, the TGV selectively regularizes different image regions at different levels to avoid oil painting artifacts largely. At the same time, the dictionary learning adaptively represents the image features sparsely and effectively recovers details of images. The proposed model is solved by variable splitting technique and the alternating direction method of multiplier. Extensive simulation experimental results demonstrate that the proposed method consistently recovers MR images efficiently and outperforms the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.

Feature-Preserving Noise Removal

Conventional image restoration algorithms use transform-domain filters, which separate the noise from the sparse signal among the transform components or apply spatial smoothing filters in real space whose design relies on prior assumptions about the noise statistics. These filters also reduce the information content of the image by suppressing spatial frequencies or by recognizing only a limited set of shapes. Here we show that denoising can be efficiently done using a nonlinear filter, which operates along patch neighborhoods and multiple copies of the original image. The use of patches enables the algorithm to account for spatial correlations in the random field whereas the multiple copies are used to recognize the noise statistics. The nonlinear filter, which is implemented by a hierarchical multistage system of multilayer perceptrons, outperforms state-of-the-art denoising algorithms such as those based on collaborative filtering and total variation. Compared to conventional denoising algorithms, our filter can restore images without blurring them, making it attractive for use in medical imaging where the preservation of anatomical details is critical.

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.