Magnitude Magnetic Resonance Images Research Articles

Noise estimation in single coil MR images

Magnetic resonance (MR) signal is degraded by acquisition noise. Estimation and removal of noise from MR images is essential for analysis and further pre-processing. The work proposes a new method for noise variance estimation in single coil magnitude MR images. The proposed noise estimator is derived using the Maximum Á Posterior (MAP) estimator. Noise follows a Gaussian distribution at high Signal to Noise (SNR) ratio and Rician distribution at low SNR. In the MAP framework, Gaussian noise model and local statistics of the noisy image are instrumental in estimation of noise at high SNR. The proposed work also exploits the local second order moments in the MAP framework for noise estimation at low SNR. Convergence of the proposed MAP framework further highlights the optimal performance of the noise estimator. Noise estimation experiments conducted on Brainweb database exhibit encouraging performance at high as well as low SNR.

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.

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.

Electrical conductivity-based contrast imaging for characterizing prostatic tissues: in vivo animal feasibility study

BackgroundElectrical conductivity-based magnetic resonance (MR) imaging may provide unique information on tissue condition because its contrast originates from the concentration and mobility of ions in the cellular space. We imaged the conductivity of normal canine prostate in vivo and evaluated tissue contrast in terms of both the conductivity distribution and anatomical significance.MethodsFive healthy laboratory beagles were used. After clipping the pelvis hair, we attached electrodes and placed each dog inside the bore of an MRI scanner. During MR scanning, we injected imaging currents into two mutually orthogonal directions between two pairs of electrodes. A multi spin echo pulse sequence was used to obtain the MR magnitude and magnetic flux density images. The projected current density algorithm was used to reconstruct the conductivity image.ResultsConductivity images showed unique contrast depending on the prostatic tissues. From the conductivity distribution, conductivity was highest in the center area and lower in the order of the middle and outer areas of prostatic tissues. The middle and outer areas were, respectively, 11.2 and 25.5% lower than the center area. Considering anatomical significance, conductivity was highest in the central zone and lower in the order of the transitional and peripheral zones in all prostates. The transitional and peripheral zones were, respectively, 7.5 and 17.8% lower than the central zone.ConclusionsCurrent conductivity-based MR imaging can differentiate prostatic tissues without using any contrast media or additional MR scans. The electrical conductivity images with unique contrast to tissue condition can provide a prior information on tissues in situ to be used for human imaging.

On 1-Laplacian Elliptic Equations Modeling Magnetic Resonance Image Rician Denoising

Modeling magnitude Magnetic Resonance Images (MRI) rician denoising in a Bayesian or generalized Tikhonov framework using Total Variation (TV) leads naturally to the consideration of nonlinear elliptic equations. These involve the so called $1$-Laplacian operator and special care is needed to properly formulate the problem. The rician statistics of the data are introduced through a singular equation with a reaction term defined in terms of modified first order Bessel functions. An existence theory is provided here together with other qualitative properties of the solutions. Remarkably, each positive global minimum of the associated functional is one of such solutions. Moreover, we directly solve this non--smooth non--convex minimization problem using a convergent Proximal Point Algorithm. Numerical results based on synthetic and real MRI demonstrate a better performance of the proposed method when compared to previous TV based models for rician denoising which regularize or convexify the problem. Finally, an application on real Diffusion Tensor Images, a strongly affected by rician noise MRI modality, is presented and discussed.

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.

Nonlocal linear minimum mean square error methods for denoising MRI

Abstract The presence of noise results in quality deterioration of magnetic resonance (MR) images and thus limits the visual inspection and influence the quantitative measurements from the data. In this work, an efficient two stage linear minimum mean square error (LMMSE) method is proposed for the enhancement of magnitude MR images in which data in the presence of noise follows a Rician distribution. The conventional Rician LMMSE estimator determines a closed-form analytical solution to the aforementioned inverse problem. Even-though computationally efficient, this approach fails to take advantage of data redundancy in the 3D MR data and hence leads to a suboptimal filtering performance. Motivated by this observation, we put forward the concept of nonlocal implementation with LMMSE estimation method. To select appropriate samples for the nonlocal version of the LMMSE estimation, the similarity weights are computed using Euclidean distance between either the gray level values in the spatial domain or the coefficients in the transformed domain. Assuming that the signal dependent component of the noise is optimally suppressed by this filtering and the rest is a white and uncorrelated noise with the image, we adopt a second stage LMMSE filtering in the principal component analysis (PCA) domain to further enhance the image and the noise variance is adaptively adjusted. Experiments on both simulated and real data show that the proposed filters have excellent filtering performance over other state-of-the-art methods.

Denoising MR images using non-local means filter with combined patch and pixel similarity.

Denoising is critical for improving visual quality and reliability of associative quantitative analysis when magnetic resonance (MR) images are acquired with low signal-to-noise ratios. The classical non-local means (NLM) filter, which averages pixels weighted by the similarity of their neighborhoods, is adapted and demonstrated to effectively reduce Rician noise without affecting edge details in MR magnitude images. However, the Rician NLM (RNLM) filter usually blurs small high-contrast particle details which might be clinically relevant information. In this paper, we investigated the reason of this particle blurring problem and proposed a novel particle-preserving RNLM filter with combined patch and pixel (RNLM-CPP) similarity. The results of experiments on both synthetic and real MR data demonstrate that the proposed RNLM-CPP filter can preserve small high-contrast particle details better than the original RNLM filter while denoising MR images.

A modified Rician LMMSE estimator for the restoration of magnitude MR images

In this article two modified versions of a simple and recently proposed method which is known as linear minimum mean square error (LMMSE) estimator for denoising of magnetic resonance (MR) images are presented. In the introduced approaches the self-similarity and natural redundancy of the acquired MR image are considered to achieve the higher performance of unknown signal estimation. Since, the MR data are in a large majority 3D, the proposed methods are developed to deal with 3D volumes. The introduced methods are compared with related state-of-the-art schemes over both clinical and simulated MR data. The quantitative and qualitative results show their superior denoising ability.

Magnetic susceptibility derived from T2 and T‐weighted magnetic resonance magnitude images

AbstractA method of measuring absolute magnetic susceptibility using T2 and T‐weighted magnetic resonance images is described. We used magnitude images derived from spin echo and gradient echo acquisitions, without the use of phase information. The findings are validated analytically and also using experimental phantoms. We show that a combination of magnetic resonance images can provide information needed to deduce the absolute susceptibility of the sample. Careful consideration of sample relaxation times and image acquisition parameters is required to ensure that calculations are accurate. We conducted an investigation of optimal imaging parameters and validated our results. © 2012 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 41B: 28–36, 2012

Maximum likelihood estimation-based denoising of magnetic resonance images using restricted local neighborhoods

In this paper, we propose a method to denoise magnitude magnetic resonance (MR) images, which are Rician distributed. Conventionally, maximum likelihood methods incorporate the Rice distribution to estimate the true, underlying signal from a local neighborhood within which the signal is assumed to be constant. However, if this assumption is not met, such filtering will lead to blurred edges and loss of fine structures. As a solution to this problem, we put forward the concept of restricted local neighborhoods where the true intensity for each noisy pixel is estimated from a set of preselected neighboring pixels. To this end, a reference image is created from the noisy image using a recently proposed nonlocal means algorithm. This reference image is used as a prior for further noise reduction. A scheme is developed to locally select an appropriate subset of pixels from which the underlying signal is estimated. Experimental results based on the peak signal to noise ratio, structural similarity index matrix, Bhattacharyya coefficient and mean absolute difference from synthetic and real MR images demonstrate the superior performance of the proposed method over other state-of-the-art methods.

Noise measurement from magnitude MRI using local estimates of variance and skewness

In this note, we address the estimation of the noise level in magnitude magnetic resonance (MR) images in the absence of background data. Most of the methods proposed earlier exploit the Rayleigh distributed background region in MR images to estimate the noise level. These methods, however, cannot be used for images where no background information is available. In this note, we propose two different approaches for noise level estimation in the absence of the image background. The first method is based on the local estimation of the noise variance using maximum likelihood estimation and the second method is based on the local estimation of the skewness of the magnitude data distribution. Experimental results on synthetic and real MR image datasets show that the proposed estimators accurately estimate the noise level in a magnitude MR image, even without background data.

Evaluation of a Validation Method for MR Imaging-Based Motion Tracking Using Image Simulation

Magnetic Resonance (MR) imaging-based motion and deformation tracking techniques combined with finite element (FE) analysis are a powerful method for soft tissue constitutive model parameter identification. However, deriving deformation data from MR images is complex and generally requires validation. In this paper a validation method is presented based on a silicone gel phantom containing contrasting spherical markers. Tracking of these markers provides a direct measure of deformation. Validation of in vivo medical imaging techniques is often challenging due to the lack of appropriate reference data and the validation method may lack an appropriate reference. This paper evaluates a validation method using simulated MR image data. This provided an appropriate reference and allowed different error sources to be studied independently and allowed evaluation of the method for various signal-to-noise ratios (SNRs). The geometric bias error was between 0– voxels while the noisy magnitude MR image simulations demonstrated errors under 0.1161 voxels (SNR: 5–35).

A Nonlocal Maximum Likelihood Estimation Method for Rician Noise Reduction in MR Images

Postacquisition denoising of magnetic resonance (MR) images is of importance for clinical diagnosis and computerized analysis, such as tissue classification and segmentation. It has been shown that the noise in MR magnitude images follows a Rician distribution, which is signal-dependent when signal-to-noise ratio (SNR) is low. It is particularly difficult to remove the random fluctuations and bias introduced by Rician noise. The objective of this paper is to estimate the noise free signal from MR magnitude images. We model images as random fields and assume that pixels which have similar neighborhoods come from the same distribution. We propose a nonlocal maximum likelihood (NLML) estimation method for Rician noise reduction. Our method yields an optimal estimation result that is more accurate in recovering the true signal from Rician noise than NL means algorithm in the sense of SNR, contrast, and method error. We demonstrate that NLML performs better than the conventional local maximum likelihood (LML) estimation method in preserving and defining sharp tissue boundaries in terms of a well-defined sharpness metric while also having superior performance in method error.

MRI denoising using Non-Local Means

Magnetic Resonance (MR) images are affected by random noise which limits the accuracy of any quantitative measurements from the data. In the present work, a recently proposed filter for random noise removal is analyzed and adapted to reduce this noise in MR magnitude images. This parametric filter, named Non-Local Means (NLM), is highly dependent on the setting of its parameters. The aim of this paper is to find the optimal parameter selection for MR magnitude image denoising. For this purpose, experiments have been conducted to find the optimum parameters for different noise levels. Besides, the filter has been adapted to fit with specific characteristics of the noise in MR image magnitude images (i.e. Rician noise). From the results over synthetic and real images we can conclude that this filter can be successfully used for automatic MR denoising.

Quantitative analysis of focal masses at MR imaging: a plea for standardization.

To assess the effects of changing analytic method variables on the signal intensity (SI) difference-to-noise ratios (SDNRs) for the contrast between lesions and background organs depicted on magnetic resonance (MR) images and to propose a standardized analytic method for the quantitative analysis of focal masses seen at MR imaging. The SIs of 48 liver metastases (originating from colorectal cancer) in 20 patients, the surrounding liver parenchyma, and the background noise were measured on T2-weighted MR images. All 2000 and 2001 issues of the American Journal of Roentgenology, the Journal of Magnetic Resonance Imaging, Magnetic Resonance Imaging, and Radiology were searched for articles describing quantitative analyses. SDNRs were calculated by using formulas from these articles and various region-of-interest (ROI) locations to measure metastasis and background noise SIs. The Wilcoxon signed rank test was used to compare the various SDNR calculations. In 34 articles in which quantitative analyses of focal masses are described, the reported SDNRs were calculated with four different formulas. The SDNRs for our study material calculated with the four formulas reported in the literature differed grossly in both number and unit. The SDNRs for ROIs encompassing the entire metastasis differed significantly (P =.034) from the SDNRs for ROIs in a homogeneous area of the metastasis margin. Differences in SDNRs between various noise ROI locations were significant (P <.022). Slight changes in the variables of quantitative analysis of focal masses had marked effects on reported SDNRs. To overcome these effects, the use of a standardized method involving one formula, a lesion ROI in a homogeneous area at the metastasis margin, and a background noise ROI along the phase-encoding axis in the air (including systematic noise) is proposed for the quantitative analysis of findings on magnitude MR images.

Wavelet-based Rayleigh background removal in MRI

Rayleigh distribution governs noise in ‘no signal’ regions of magnetic resonance magnitude images. Large areas of background noise in MRI images will seriously affect their effective utilisation. A new wavelet-based algorithm is presented that can work efficiently either as a standalone procedure or couple with existing denoising algorithms to significantly improve their effectiveness.

A wavelet-based method for improving signal-to-noise ratio and contrast in MR images

Magnetic resonance (MR) images acquired with fast measurement often display poor signal-to-noise ratio (SNR) and contrast. With the advent of high temporal resolution imaging, there is a growing need to remove these noise artifacts. The noise in magnitude MR images is signal-dependent (Rician), whereas most de-noising algorithms assume additive Gaussian (white) noise. However, the Rician distribution only looks Gaussian at high SNR. Some recent work by Nowak employs a wavelet-based method for de-noising the square magnitude images, and explicitly takes into account the Rician nature of the noise distribution. In this article, we apply a wavelet de-noising algorithm directly to the complex image obtained as the Fourier transform of the raw k-space two-channel (real and imaginary) data. By retaining the complex image, we are able to de-noise not only magnitude images but also phase images. A multiscale (complex) wavelet-domain Wiener-type filter is derived. The algorithm preserves edges better when the Haar wavelet rather than smoother wavelets, such as those of Daubechies, are used. The algorithm was tested on a simulated image to which various levels of noise were added, on several EPI image sequences, each of different SNR, and on a pair of low SNR MR micro-images acquired using gradient echo and spin echo sequences. For the simulated data, the original image could be well recovered even for high values of noise (SNR ≈ 0 dB), suggesting that the present algorithm may provide better recovery of the contrast than Nowak’s method. The mean-square error, bias, and variance are computed for the simulated images. Over a range of amounts of added noise, the present method is shown to give smaller bias than when using a soft threshold, and smaller variance than a hard threshold; in general, it provides a better bias-variance balance than either hard or soft threshold methods. For the EPI (MR) images, contrast improvements of up to 8% (for SNR = 33 dB) were found. In general, the improvement in contrast was greater the lower the original SNR, for example, up to 50% contrast improvement for SNR of about 20 dB in micro-imaging. Applications of the algorithm to the segmentation of medical images, to micro-imaging and angiography (where the correct preservation of phase is important for flow encoding to be possible), as well as to de-noising time series of functional MR images, are discussed.

Parameter estimation from magnitude MR images

This article deals with the estimation of model-based parameters, such as the noise variance and signal components, from magnitude magnetic resonance (MR) images. Special attention has been paid to the estimation of T1- and T2-relaxation parameters. It is shown that most of the conventional estimation methods, when applied to magnitude MR images, yield biased results. Also, it is shown how the knowledge of the proper probability density function of magnitude MR data (i.e., the Rice distribution) can be exploited so as to avoid (or at least reduce) such systematic errors. The proposed method is based on maximum likelihood (ML) estimation. © 1999 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 10, 109–114, 1999

The Rician distribution of noisy MRI data.

The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution. Low signal intensities (SNR < 2) are therefore biased due to the noise. It is shown how the underlying noise can be estimated from the images and a simple correction scheme is provided to reduce the bias. The noise characteristics in phase images are also studied and shown to be very different from those of the magnitude images. Common to both,however, is that the noise distributions are nearly Gaussian for SNR larger than two.