Noise estimation in single- and multiple-coil magnetic resonance data based on statistical models

Noise estimation is a challenging task in magnetic resonance imaging (MRI), with applications in quality assessment, filtering or diffusion tensor estimation. Main noise estimators based on the Rician model are revisited and classified in this article, and new useful methods are proposed. Additionally, all the surveyed estimators are extended to the noncentral chi model, which applies to multiple-coil MRI and some important parallel imaging algorithms for accelerated acquisitions. The proposed new noise estimation procedures, based on the distribution of local moments, show better performance in terms of smaller variance and unbiased estimation over a wide range of experiments, with the additional advantage of not needing to explicitly segment the background of the image.     

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

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

An MRI denoising method using image data redundancy and local SNR estimation

This paper presents an LMMSE-based method for the three-dimensional (3D) denoising of MR images assuming a Rician noise model. Conventionally, the LMMSE method estimates the noise-less signal values using the observed MR data samples within local neighborhoods. This is not an efficient procedure to deal with this issue while the 3D MR data intrinsically includes many similar samples that can be used to improve the estimation results. To overcome this problem, we model MR data as random fields and establish a principled way which is capable of choosing the samples not only from a local neighborhood but also from a large portion of the given data. To follow the similar samples within the MR data, an effective similarity measure based on the local statistical moments of images is presented. The parameters of the proposed filter are automatically chosen from the estimated local signal-to-noise ratio. To further enhance the denoising performance, a recursive version of the introduced approach is also addressed. The proposed filter is compared with related state-of-the-art filters using both synthetic and real MR datasets. The experimental results demonstrate the superior performance of our proposal in removing the noise and preserving the anatomical structures of MR images.     

Parameter estimation for power-law distributions by maximum likelihood methods

Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the exponent are a mathematically sound alternative to graphical methods.     

Accelerated magnetic resonance imaging using the sparsity of multi-channel coil images

Joint estimation of coil sensitivities and output image (JSENSE) is a promising approach that improves the reconstruction of parallel magnetic resonance imaging (pMRI). However, when acceleration factor increases, the signal to noise ratio (SNR) of JSENSE reconstruction decreases as quickly as that of the conventional pMRI. Although sparse constraints have been used to improve the JSENSE reconstruction in recent years, these constraints only use the sparsity of the output image, which cannot fully exploit the prior information of pMRI. In this paper, we use the sparsity of coil images, instead of the output image, to exploit more prior information for JSENSE. Numerical simulation, phantom and in vivo experiments demonstrate that the proposed method has better performance than the SparseSENSE method and the constrained JSENSE method using the sparsity of the output image only.     

最大似然参数估计水声通信帧同步技术研究

水声通信中传统帧同步方法仅仅依赖于匹配滤波输出的相关系数,在复杂信道条件下,容易出现误触发和漏同步。针对这一问题,分析了水声信道中噪声、多普勒和多径对帧同步的影响,提出了一种基于参数估计的帧同步方法.在同步过程中引入参数估计,将信号参数作为检测判决依据,以降低误触发率和漏检率;同时对最大似然估计算法进行适当简化,以降低实现复杂度。计算机仿真实验验证了新的帧同步方法相对于传统方法在定时精度和相关系数方面的优势。实际水声通信实验结果表明,无论是静止平台还是移动平台之间的通信,新的帧同步方法均能有效提高匹配滤波器输出的相关系数,提升接收机检测能力,从而避免出现误触发和漏同步。     

A novel acquisition-reconstruction algorithm for surface magnetic resonance imaging

In U-shaped, hand-size magnetic resonance surface scanners, imaging is performed along only one spatial direction, with the application of just one gradient (one-dimensional imaging). Lateral spatial resolution can be obtained by magnet displacement, but, in this case, resolution is very poor (on the order of some millimeters) and cannot be useful for high-resolution imaging applications. In this article, an innovative technique for acquisition and reconstruction of images produced by U-shaped, hand-size MRI surface scanners is presented. The proposed method is based on the acquisition of overlapping strips and an analytical reconstruction technique; it is capable of arbitrarily improving spatial lateral resolution without either using a second magnetic field gradient or making any assumptions about the imaged sample extension. Numerical simulations on synthetic images are reported demonstrating the method functionalities. The presented method also makes it possible to use U-shaped, hand-size MRI surface scanners for high-resolution biomedical applications, such as the imaging of skin lesions.     

A viable method for goodness-of-fit test in maximum likelihood fit

A test statistic is proposed to perform the goodness-of-fit test in the unbinned maximum likelihood fit. Without using a detailed expression of the efficiency function, the test statistic is found to be strongly correlated with the maximum likelihood function if the efficiency function varies smoothly. We point out that the correlation coefficient can be estimated by the Monte Carlo technique. With the established method, two examples are given to illustrate the performance of the test statistic.     

On the use of the maximum likelihood estimation for analysis of vibrato tones

Characteristics of frequency vibrato are usually explained by the frequency center, rate, and extent. For analysis of vibrato tones, we apply the maximum likelihood estimation to the enhanced fundamental frequency track obtained from a short-time Fourier transform. We have also suggested the values of the parameters in the estimation and the averaging process to reduce the estimation error. Experiments show that the proposed method can be used for accurate and reliable analysis of vibrato tones.     

Characterization of water distribution in bread during storage using magnetic resonance imaging

A soy bread of fully acceptable quality and containing 49% soy ingredients (with or without 5% almond powder) has been recently developed in our laboratory.

An investigation on water distribution and mobility, as probed by proton signal intensity and T₂ magnetic resonance images, during storage was designed to examine possible relations between water states and hindered staling rate upon soy or soy–almond addition.

Water proton distribution throughout soy-containing loaves was found to be very homogeneous in fresh breads with and without almond, with minimal water migration occurring during prolonged storage. In contrast, traditional wheat bread displayed an inhomogeneous water proton population that tended to change (with higher moisture migration towards the outer perimeter of the slice) during storage. Similar results were found for water mobility throughout the loaves, as depicted in T₂ images. On intensity images of all considered bread varieties, the outer perimeter corresponding to the crust exhibited lower signal intensity due to decreased water content. Higher T₂ values were found in the crust of soy breads with and without almond, which were attributed to lipids.

The results indicated that the addition of soy to bread improved the homogeneous distribution of water molecules, which may hinder the staling rate of soy-containing breads. However, incorporation of almond had little effect on the water proton distribution or mobility of soy breads.     

Proton magnetic resonance spectroscopic images and MRI volumetric studies for lateralization of temporal lobe epilepsy

We obtained 2D magnetic resonance (MR) spectroscopic images (MRSI) and MRI volumetric measurements (MRIV) of amygdala and hippocampus in 30 consecutive patients with temporal lobe epilepsy (TLE) being evaluated for surgical treatment. Both MRSI and MRIV lateralization showed good agreement with the current gold standard of clinical-EEG lateralization. Each exam separately correctly lateralized 25 out of 30 patients with no false lateralization. Combining both exams, lateralization could be achieved in 28 out of 30 patients. The two patients with no significant asymmetry had bitemporal EEG abnormalities, and bilateral damage on both MRIV and MRSI. There was a good correlation between the magnitude of the MRSI and MRIV asymmetry (Pearson COEFFICIENT = 0.83; p < .0001). Both MRSI and MRIV were normal in our patients with seizures originating outside the temporal lobes. Both MRIV and MRSI can lateralize TLE in 83% of patients. Combination of the two modalities allows lateralization in 93% of patients. Patients who cannot be lateralized generally have symmetrical bitemporal abnormalities; they are not incorrectly lateralized. The structural and chemical pathologic abnormalities seen in TLE seem to be associated with the seizure focus, and may be as, or even more, reliable than a few recorded seizures in predicting the side from which most seizures originate.     

Street categorization for the estimation of day levels using short-term measurements

Day time noise level computation by traffic noise model requires realistic traffic data that is hardly ever available for every single street, therefore direct noise levels measurements may be the alternative. However, direct, continuous measurement of the day time noise level (equivalent level from 7 am to 7 pm) is an expensive strategy if a whole city must be assessed. To overcome this situation, short-term measurements of variable duration are often taken in order to estimate the day time noise level (L_d) because they are less expensive and resource demanding than continuous measurements over a whole day or more. From a set of continuous measurements over more than 48 h in 137 streets of nine different cities, the present work quantifies the error committed when using short-term noise measurements as a function of interval length measurement. To enhance estimation accuracy, both a street categorization and a temporal categorization have been attempted: in first place, it is found that the difference between the short-term noise level and L_d follows a different distribution for main roads than for ordinary streets, therefore the error committed depends on the street category. To be specific, when estimating L_d from a 15 min short time measurement the error committed would be ±2 dB with a percent population coverage of 90%, in the case of main streets and in the case of ordinary streets the same error range covers 72.5% of the population. In second place, if the measurement range time is restricted (temporal categorization) from 9 am to 1 pm and from 2 pm to 5 pm in the case of ordinary streets, the percent population coverage increases to 90% when the error range is ±3 dB. When referring to main streets, the measurement range of time is limited from 10 am to 5 pm to obtain an increase of 2% of the percent population coverage when the error is ±1 and ±2 dB.     

Spatially encoded NMR and the acquisition of 2D magnetic resonance images within a single scan

An approach that enables the acquisition of multidimensional NMR spectra within a single scan has been recently proposed and demonstrated. The present paper explores the applicability of such ultrafast acquisition schemes toward the collection of two-dimensional magnetic resonance imaging (2D MRI) data. It is shown that ideas enabling the application of these spatially encoded schemes within a spectroscopic setting, can be extended in a straightforward manner to pure imaging. Furthermore, the reliance of the original scheme on a spatial encoding and subsequent decoding of the evolution frequencies endows imaging applications with a greater simplicity and flexibility than their spectroscopic counterparts. The new methodology also offers the possibility of implementing the single-scan acquisition of 2D MRI images using sinusoidal gradients, without having to resort to subsequent interpolation procedures or non-linear sampling of the data. Theoretical derivations on the operational principles and imaging characteristics of a number of sequences based on these ideas are derived, and experimentally validated with a series of 2D MRI results collected on a variety of model phantom samples.     

Adaptive segmentation of magnetic resonance images with intensity inhomogeneity using level set method

It is a big challenge to segment magnetic resonance (MR) images with intensity inhomogeneity. The widely used segmentation algorithms are region based, which mostly rely on the intensity homogeneity, and could bring inaccurate results. In this paper, we propose a novel region-based active contour model in a variational level set formulation. Based on the fact that intensities in a relatively small local region are separable, a local intensity clustering criterion function is defined. Then, the local function is integrated around the neighborhood center to formulate a global intensity criterion function, which defines the energy term to drive the evolution of the active contour locally. Simultaneously, an intensity fitting term that drives the motion of the active contour globally is added to the energy. In order to segment the image fast and accurately, we utilize a coefficient to make the segmentation adaptive. Finally, the energy is incorporated into a level set formulation with a level set regularization term, and the energy minimization is conducted by a level set evolution process. Experiments on synthetic and real MR images show the effectiveness of our method.     

A hybrid spatial-spectral denoising method for infrared hyperspectral images using 2DPCA

The traditional noise reduction methods for 3-D infrared hyperspectral images typically operate independently in either the spatial or spectral domain, and such methods overlook the relationship between the two domains. To address this issue, we propose a hybrid spatial-spectral method in this paper to link both domains. First, principal component analysis and bivariate wavelet shrinkage are performed in the 2-D spatial domain. Second, 2-D principal component analysis transformation is conducted in the 1-D spectral domain to separate the basic components from detail ones. The energy distribution of noise is unaffected by orthogonal transformation; therefore, the signal-to-noise ratio of each component is used as a criterion to determine whether a component should be protected from over-denoising or denoised with certain 1-D denoising methods. This study implements the 1-D wavelet shrinking threshold method based on Stein’s unbiased risk estimator, and the quantitative results on publicly available datasets demonstrate that our method can improve denoising performance more effectively than other state-of-the-art methods can.     

Quantitative estimation of brain white matter abnormalities in elderly subjects using magnetic resonance imaging

Twenty-five elderly subjects were examined with brain magnetic resonance imaging (MRI). The subjects were divided into two groups: those with Mini-Mental State Examination (MMSE) scores above 25, and those subjects with MMSE scores between 18 and 24. The degree of white matter abnormalities (WMA) (expressed as relative volumes) as well as the presence of cerebrovascular risk factors were evaluated in the two groups. We found that a) subjects with low MMSE scores had significantly larger relative volumes of WMA than the subjects with higher scores, b) a significant correlation (r_s = 0.53, p < 0.009) between MMSE scores and the relative volume of WMA was also established, and c) a weak significant correlation (r_s = −0.51, p < 0.05) between arterial blood pressure and WMA was found in the subjects with high MMSE scores. Besides these findings no other correlations between the presence of cerebrovascular risk factors and WMA were found in any of the groups.     

Error propagation model for microscopic magnetic resonance elastography shear-wave images

Microscopic magnetic resonance elastography is a high-resolution method for visualizing shear waves and assessing the biomechanical viscoelastic properties of small biological samples. In this work, we used error propagation to develop a simple analytical model that relates the signal-to-noise ratio of MR magnitude images to the variance in shear-wave maps collected using gradient-echo and spin-echo phase-contrast pulse sequences. Our model predicts results for shear-wave images in phantoms, which match the experimentally observed phase variance within 8%. This model can be used to optimize MR pulse sequences for elastography studies, as well as other phase-difference techniques in MRI.     

An improved method and experimental results of noise used as reliability estimation for semiconductor lasers

The low-frequency noise is a sensitive non-destructive indicator of semiconductor devices reliability. In this paper, the noises in InGaAsP/InGaAs/GaAlAs double quantum well semiconductor laser diodes (LDs) are measured, and the correlation between the noise and device reliability is studied. The insults indicate that the noise level in the LDs operating in low bias current is very important for estimating device reliability. So when noise is used as reliability indicator, the noise levels in LDs operating in both low and higher bias current should be considered, which improves the validity of reliability estimation.     

Comparing anisotropic diffusion filters for the enhancement of sodium magnetic resonance images

The anisotropic diffusion (AND) filter, an image processing technique derived from physics, was applied to low-resolution sodium magnetic resonance imaging (MRI) to examine the possibilities of image enhancement by postprocessing. We compared six different variants of AND filters. Besides the qualitative good results on phantom measurements, quantitative analyses on MRI of human kidney yielded major improvements in noise reduction and other quality measures: the noise (i.e., the standard deviation in the image background) could be reduced to 1%-2% of its original value, while linear filters (Gaussian, Fermi, Hamming) achieved a reduction to 42%-64%. Besides that, less than 5% of structures and intensities are lost when using AND filters. Comparing the different variants, the two-dimensional and the three-dimensional AND filter outperformed the histogram-of-gradient and tensor-based AND filter. We envision that by using these AND filters, quantitative analysis of sodium MRI of kidney could be improved.     

An optimized solenoidal head radiofrequency coil for low-field magnetic resonance imaging

Applications of low-field magnetic resonance imaging (MRI) systems (<0.3 T) are limited due to the signal-to-noise ratio (SNR) being lower than that provided by systems based on superconductive magnets (≥1.5 T). Therefore, the design of radiofrequency (RF) coils for low-field MRI requires careful consideration as significant gains in SNR can be achieved with the proper design of the RF coil. This article describes an analytical method for the optimization of solenoidal coils. Coil and sample losses are analyzed to provide maximum SNR and optimum B₁ field homogeneity. The calculations are performed for solenoidal coils optimized for the human head at 0.2 T, but the method could also be applied to any solenoidal coil for imaging other anatomical regions at low field. Several coils were constructed to compare experimental and theoretical results. A head magnetic resonance image obtained at 0.2 T with the optimum design is presented.