Conductivity image reconstruction from defective data in MREIT: numerical simulation and animal experiment

Magnetic resonance electrical impedance tomography (MREIT) is designed to produce high resolution conductivity images of an electrically conducting subject by injecting current and measuring the longitudinal component, Bz, of the induced magnetic flux density B = (Bx, By, Bz). In MREIT, accurate measurements of Bz are essential in producing correct conductivity images. However, the measured Bz data may contain fundamental defects in local regions where MR magnitude image data are small. These defective Bz data result in completely wrong conductivity values there and also affect the overall accuracy of reconstructed conductivity images. Hence, these defects should be appropriately recovered in order to carry out any MREIT image reconstruction algorithm. This paper proposes a new method of recovering Bz data in defective regions based on its physical properties and neighboring information of Bz. The technique will be indispensable for conductivity imaging in MREIT from animal or human subjects including defective regions such as lungs, bones, and any gas-filled internal organs.     

Denoising functional MR images: a comparison of wavelet denoising and Gaussian smoothing

We present a general wavelet-based denoising scheme for functional magnetic resonance imaging (fMRI) data and compare it to Gaussian smoothing, the traditional denoising method used in fMRI analysis. One-dimensional WaveLab thresholding routines were adapted to two-dimensional (2-D) images, and applied to 2-D wavelet coefficients. To test the effect of these methods on the signal-to-noise ratio (SNR), we compared the SNR of 2-D fMRI images before and after denoising, using both Gaussian smoothing and wavelet-based methods. We simulated a fMRI series with a time signal in an active spot, and tested the methods on noisy copies of it. The denoising methods were evaluated in two ways: by the average temporal SNR inside the original activated spot, and by the shape of the spot detected by thresholding the temporal SNR maps. Denoising methods that introduce much smoothness are better suited for low SNRs, but for images of reasonable quality they are not preferable, because they introduce heavy deformations. Wavelet-based denoising methods that introduce less smoothing preserve the sharpness of the images and retain the original shapes of active regions. We also performed statistical parametric mapping on the denoised simulated time series, as well as on a real fMRI data set. False discovery rate control was used to correct for multiple comparisons. The results show that the methods that produce smooth images introduce more false positives. The less smoothing wavelet-based methods, although generating more false negatives, produce a smaller total number of errors than Gaussian smoothing or wavelet-based methods with a large smoothing effect.     

MR image denoising method for brain surface 3D modeling

The goal of Optoelectronics Letters is to rapidly report original, new and important results in the fields of photonics and optoelectronics in English, to advance the international academic exchanges. Optoelectronics Letters pays a particularly attention to the cross topics between photonics and electronics.     

Electrical conductivity imaging using gradient B, decomposition algorithm in magnetic resonance electrical impedance tomography (MREIT)

In magnetic resonance electrical impedance tomography (MREIT), we try to visualize cross-sectional conductivity (or resistivity) images of a subject. We inject electrical currents into the subject through surface electrodes and measure the z component Bz of the induced internal magnetic flux density using an MRI scanner. Here, z is the direction of the main magnetic field of the MRI scanner. We formulate the conductivity image reconstruction problem in MREIT from a careful analysis of the relationship between the injection current and the induced magnetic flux density Bz. Based on the novel mathematical formulation, we propose the gradient Bz decomposition algorithm to reconstruct conductivity images. This new algorithm needs to differentiate Bz only once in contrast to the previously developed harmonic Bz algorithm where the numerical computation of (inverted delta)2Bz is required. The new algorithm, therefore, has the important advantage of much improved noise tolerance. Numerical simulations with added random noise of realistic amounts show the feasibility of the algorithm in practical applications and also its robustness against measurement noise.     

Harmonic decomposition in PDE-based denoising technique for magnetic resonance electrical impedance tomography

Recent progress in magnetic resonance electrical impedance tomography (MREIT) research via simulation and biological tissue phantom studies have shown that conductivity images with higher spatial resolution and accuracy are achievable. In order to apply MREIT to human subjects, one of the important remaining problems to be solved is to reduce the amount of the injection current such that it meets the electrical safety regulations. However, by limiting the amount of the injection current according to the safety regulations, the measured MR data such as the z-component of magnetic flux density Bz in MREIT tend to have low SNR and get usually degraded in their accuracy due to the nonideal data acquisition system of an MR scanner. Furthermore, numerical differentiations of the measured Bz required by the conductivity image reconstruction algorithms tend to further deteriorate the quality and accuracy of the reconstructed conductivity images. In this paper, we propose a denoising technique that incorporates a harmonic decomposition. The harmonic decomposition is especially suitable for MREIT due to the physical characteristics of Bz. It effectively removes systematic and random noises, while preserving important key features in the MR measurements, so that improved conductivity images can be obtained. The simulation and experimental results demonstrate that the proposed denoising technique is effective for MREIT, producing significantly improved quality of conductivity images. The denoising technique will be a valuable tool in MREIT to reduce the amount of the injection current when it is combined with an improved MREIT pulse sequence.     

Robust NL-Means Filter With Optimal Pixel-Wise Smoothing Parameter for Statistical Image Denoising

Most denoising methods require that some smoothing parameters be set manually to optimize their performance. Among these methods, a new filter based on nonlocal weighting (NL-means filter) has been shown to have a very attractive denoising capacity. In this paper, we propose fixing the smoothing parameter of this filter automatically. The smoothing parameter corresponds to the bandwidth h of a local constant regression. We use the C_p statistic embedded in Newton's method to optimize h in a point-wise fashion. This statistic also has the advantage of being a reliable measure of the quality of the denoising process for each pixel. In addition, we introduce a robust regression in the NL-means filter designed to greatly reduce the blur yielded by the weighting. Finally, we show how the automatic denoising model can be extended to images degraded by multiplicative noise. Experiments conducted on images with additive and multiplicative noise demonstrate a high denoising power with a degree of detail preservation...     

磁共振图像阀值去噪方法研究

磁共振成像已成为脑功能病理和解剖研究的主要手段，是医学影像学领域中最活跃的技术。由于在成像过程中复杂的电磁场环境容易受到人体热噪声干扰，使得磁共振图像去噪成为很重要的研究热点。小波分析具有多尺度分辨和去相关性等特点，在去除被白噪声污染的磁共振图像方面得到了广泛应用。但磁共振图像经传统的小波分析去噪后，细节信息部分丢失，图像的边缘变得模糊．针时这些问题，时经典的小波阀值去噪方法进行了改进，将关键参数取值与预估计联系起来，将阀值的选定与图像的局部特征结合起来，提出一种灵活的、自适应的去噪新方法。与经典方法相比，采用本方法处理的噪声图像去噪后图像的细节更丰富，边缘信息完善，视觉效果更好。     

Feature-preserving MRI denoising: a nonparametric empirical Bayes approach

This paper presents a novel method for Bayesian denoising of magnetic resonance (MR) images that bootstraps itself by inferring the prior, i.e., the uncorrupted-image statistics, from the corrupted input data and the knowledge of the Rician noise model. The proposed method relies on principles from empirical Bayes (EB) estimation. It models the prior in a nonparametric Markov random field (MRF) framework and estimates this prior by optimizing an information-theoretic metric using the expectation-maximization algorithm. The generality and power of nonparametric modeling, coupled with the EB approach for prior estimation, avoids imposing ill-fitting prior models for denoising. The results demonstrate that, unlike typical denoising methods, the proposed method preserves most of the important features in brain MR images. Furthermore, this paper presents a novel Bayesian-inference algorithm on MRFs, namely iterated conditional entropy reduction (ICER). This paper also extends the application of the proposed method for denoising diffusion-weighted MR images. Validation results and quantitative comparisons with the state of the art in MR-image denoising clearly depict the advantages of the proposed method.     

An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation

An adaptive spatial fuzzy c-means clustering algorithm is presented in this paper for the segmentation of three-dimensional (3-D) magnetic resonance (MR) images. The input images may be corrupted by noise and intensity nonuniformity (INU) artifact. The proposed algorithm takes into account the spatial continuity constraints by using a dissimilarity index that allows spatial interactions between image voxels. The local spatial continuity constraint reduces the noise effect and the classification ambiguity. The INU artifact is formulated as a multiplicative bias field affecting the true MR imaging signal. By modeling the log bias field as a stack of smoothing B-spline surfaces, with continuity enforced across slices, the computation of the 3-D bias field reduces to that of finding the B-spline coefficients, which can be obtained using a computationally efficient two-stage algorithm. The efficacy of the proposed algorithm is demonstrated by extensive segmentation experiments using both simulated and real MR images and by comparison with other published algorithms.     

Markov random field segmentation of brain MR images

Describes a fully-automatic three-dimensional (3-D)-segmentation technique for brain magnetic resonance (MR) images. By means of Markov random fields (MRF's) the segmentation algorithm captures three features that are of special importance for MR images, i.e., nonparametric distributions of tissue intensities, neighborhood correlations, and signal inhomogeneities. Detailed simulations and real MR images demonstrate the performance of the segmentation algorithm. In particular, the impact of noise, inhomogeneity, smoothing, and structure thickness are analyzed quantitatively. Even single-echo MR images are well classified into gray matter, white matter, cerebrospinal fluid, scalp-bone, and background. A simulated annealing and an iterated conditional modes implementation are presented     

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.     

基于双域滤波与引导滤波的快速医学MR图像去噪

针对医学磁共振(Magnetic Resonance,MR)图像 中存在Rician噪声较大以及双域滤波算法对Rician噪声处理不彻底、 运行时间较长的缺点,提出一种双域滤波与引导滤波相结合的快速医学MR 图像去噪算法。 该算法将引导滤波边缘保持后 的图像作为双域滤波算法的原引导图像,减少双域滤波算法的迭代次数,缩短算法运行时间 ;然后通过改进算法权重,结合 原始权重系数和指数核函数,构造新的权重系数,对噪声进行有效处理。实验结果表明,本 文算法能有效去除医学MR图 像噪声,保护图像细节,相比优秀的医学MR图像去噪算法,具有更高的峰值信噪比和结构 相似度;且相比经典双域滤波 算法,改进后的算法能将运行时间减少1/3,相比非局部均值算法, 可减少1/2。     

Local Harmonic $B_z$ Algorithm With Domain Decomposition in MREIT: Computer Simulation Study

Magnetic resonance electrical impedance tomography (MREIT) attempts to provide conductivity images of an electrically conducting object with a high spatial resolution. When we inject current into the object, it produces internal distributions of current density ${bf J}$ and magnetic flux density ${bf B}=(B_x,B_y,B_z)$. By using a magnetic resonance imaging (MRI) scanner, we can measure $B_z$ data where $z$ is the direction of the main magnetic field of the scanner. Conductivity images are reconstructed based on the relation between the injection current and $B_z$ data. The harmonic $B_z$ algorithm was the first constructive MREIT imaging method and it has been quite successful in previous numerical and experimental studies. Its performance is, however, degraded when the imaging object contains low-conductivity regions such as bones and lungs. To overcome this difficulty, we carefully analyzed the structure of a current density distribution near such problematic regions and proposed a new technique, called the local harmonic $B_z$ algorithm. We first reconstruct conductivity values in local regions with a low conductivity contrast, separated from those problematic regions. Then, the method of characteristics is employed to find conductivity values in the problematic regions. One of the most interesting observations of the new algorithm is that it can provide a scaled conductivity image in a local region without knowing conductivity values outside the region. We present the performance of the new algorithm by using computer simulation methods.      

Wavelet-Domain Medical Image Denoising Using Bivariate Laplacian Mixture Model

In this paper, we proposed novel noise reduction algorithms that can be used to enhance image quality in various medical imaging modalities such as magnetic resonance and multidetector computed tomography. The noisy captured 3-D data are first transformed by discrete complex wavelet transform. Using a nonlinear function, we model the data as the sum of the clean data plus additive Gaussian or Rayleigh noise. We use a mixture of bivariate Laplacian probability density functions for the clean data in the transformed domain. The MAP and minimum mean-squared error (MMSE) estimators allow us to efficiently reduce the noise. The employed prior distribution is mixture and bivariate, and thus accurately characterizes the heavy-tail distribution of clean images and exploits the interscale properties of wavelets coefficients. In addition, we estimate the parameters of the model using local information; as a result, the proposed denoising algorithms are spatially adaptive, i.e., the intrascale dependency of wavelets is also well exploited in the enhancement process. The proposed approach results in significant noise reduction while the introduced distortions are not noticeable as a result of accurate statistical modeling. The obtained shrinkage functions have closed form, are simple in implementation, and efficiently enhances data. Our experiments on CT images show that among our derived shrinkage functions usually BiLapGausMAP produces images with higher peak SNR. However, BiLapGausMMSE is preferred especially for CT images, which have high SNRs. Furthermore, BiLapRayMAP yields better noise reduction performance for low SNR MR datasets such as high-resolution whole heart imaging while BiLapGauMAP results in better performance in MR data with higher intrinsic SNR such as functional cine data.      

Application of autoregressive moving average parametric modeling in magnetic resonance image reconstruction

The modeling of data is an alternative to conventional use of the fast Fourier transform (FFT) algorithm in the reconstruction of magnetic resonance (MR) images. The application of the FFT leads to artifacts and resolution loss in the image associated with the effective window on the experimentally-truncated phase encoded MR data. The transient error modeling method treats the MR data as a subset of the transient response of an infinite impulse filter (H(z) = B(z)IA(z)). Thus, the data are approximated by a deterministic autoregressive moving average (ARMA) model. The algorithm for calculating the filter coefficients is described. It is demonstrated that using the filter coefficients to reconstruct the image removes the truncation artifacts and improves the resolution. However, determining the autoregressive (AR) portion of the ARMA filter by algorithms that minimize the forward and backward prediction errors (e.g., Burg) leads to significant image degradation. The moving average (MA) portion is determined by a computationally efficient method of solving a finite difference equation with initial values. Special features of the MR data are incorporated into the transient error model. The sensitivity to noise and the choice of the best model order are discussed. MR images formed using versions of the transient error reconstruction (TERE) method and the conventional FFT algorithm are compared using data from a phantom and a human subject. Finally, the computational requirements of the algorithm are addressed.     

A reconstruction method for gappy and noisy arterial flow data

Proper orthogonal decomposition (POD), Kriging interpolation, and smoothing are applied to reconstruct gappy and noisy data of blood flow in a carotid artery. While we have applied these techniques to clinical data, in this paper in order to rigorously evaluate their effectiveness we rely on data obtained by computational fluid dynamics (CFD). Specifically, gappy data sets are generated by removing nodal values from high-resolution 3-D CFD data (at random or in a fixed area) while noisy data sets are formed by superimposing speckle noise on the CFD results. A combined POD-Kriging procedure is applied to planar data sets mimicking coarse resolution "ultrasound-like" blood flow images. A method for locating the vessel wall boundary and for calculating the wall shear stress (WSS) is also proposed. The results show good agreement with the original CFD data. The combined POD-Kriging method, enhanced by proper smoothing if needed, holds great potential in dealing effectively with gappy and noisy data reconstruction of in vivo velocity measurements based on color Doppler ultrasound (CDUS) imaging or magnetic resonance angiography (MRA).     

Magnetic resonance driven electrical impedance tomography: a simulation study

Magnetic resonance electrical impedance tomography (MREIT) is a method for reconstructing a three-dimensional image of the conductivity distribution in a target volume using magnetic resonance (MR). In MREIT, currents are applied to the volume through surface electrodes and their effects on the MR induced magnetic fields are analyzed to produce the conductance image. However, current injection through surface electrodes poses technical problems such as the limitation on the safely applicable currents. In this paper, we present a new method called magnetic resonance driven electrical impedance tomography (MRDEIT), where the magnetic resonance in each voxel is used as the applied magnetic field source, and the resultant electromagnetic field is measured through surface electrodes or radio-frequency (RF) detectors placed near the surface. Because the applied magnetic field is at the RF frequency and eddy currents are the integral components in the method, a vector wave equation for the electric field is used as the basis of the analysis instead of a quasi-static approximation. Using computer simulations, it is shown that complex permittivity images can be reconstructed using MRDEIT, but that improvements in signal detection are necessary for detecting moderate complex permittivity changes.     

Fuzzy local Gaussian mixture model for brain MR image segmentation

Accurate brain tissue segmentation from magnetic resonance (MR) images is an essential step in quantitative brain image analysis. However, due to the existence of noise and intensity inhomogeneity in brain MR images, many segmentation algorithms suffer from limited accuracy. In this paper, we assume that the local image data within each voxel's neighborhood satisfy the Gaussian mixture model (GMM), and thus propose the fuzzy local GMM (FLGMM) algorithm for automated brain MR image segmentation. This algorithm estimates the segmentation result that maximizes the posterior probability by minimizing an objective energy function, in which a truncated Gaussian kernel function is used to impose the spatial constraint and fuzzy memberships are employed to balance the contribution of each GMM. We compared our algorithm to state-of-the-art segmentation approaches in both synthetic and clinical data. Our results show that the proposed algorithm can largely overcome the difficulties raised by noise, low contrast, and bias field, and substantially improve the accuracy of brain MR image segmentation.     

Patch based image denoising using the finite ridgelet transform for less artifacts

Patch based denoising methods have proved to lead to state-of-the-art results. However, in contrast with intensive pursuing of higher peak signal to noise ratio (PSNR), less attention is paid to visual quality improvement of denoised images. In this paper, we first compare the denoising performance in edge and smooth regions. Results reveal that edge regions are the main source for potential performance improvement. This motivates us to investigate the use of the finite ridgelet transform as a local transform for better preservation of directional singularities. A two stage denoising algorithm is then proposed to improve the representation of detail structures. Experimental results in denoising images which only contain white noise show that the proposed algorithm consistently outperforms other methods in terms of PSNR and Structural SIMilarity index. Denoised images by the proposed method also demonstrate good visual quality with the least artifacts and fake structures in experiments on natural images.     

Using human and model performance to compare MRI reconstructions

Magnetic resonance imaging (MRI) reconstruction techniques are often validated with signal-to-noise ratio (SNR), contrast-to-noise ratio, and mean-to-standard-deviation ratio measured on example images. We present human and model observers as a novel approach to evaluating reconstructions for low-SNR magnetic resonance (MR) images. We measured human and channelized Hotelling observers in a two-alternative forced-choice signal-known-exactly detection task on synthetic MR images. We compared three reconstructions: magnitude, wavelet-based denoising, and phase-corrected real. Human observers performed approximately equally using all three reconstructions. The model observer showed very close agreement with the humans over the range of images. These results contradict previous predictions in the literature based on SNR. Thus, we propose that human observer studies are important for validating MRI reconstructions. The model's performance indicates that it may provide an alternative to human studies.