A robust electrical conductivity imaging method with total variation and wavelet regularization

PurposeThis study aims to develop and evaluate a robust conductivity imaging method that combines total variation and wavelet regularization to enhance the accuracy of conductivity maps.Theory and methodsThe proposed approach is based on a gradient-based method. The central equation is derived from Maxwell's equation and describes the relationship between conductivity and the transceive phase. A linear system equation is obtained via a finite-difference method and solved using a least-squares method. Total variation and wavelet transform regularization terms are added to the minimization problem and solved using the Split Bregman method to improve reconstruction stability. The proposed approach is compared with conventional and gradient-based methods. Numerical simulations are performed to validate the accuracy of the developed method, and the effects of noise are determined. Phantom and in vivo experiments are conducted at 3 T to verify the clinical applicability of the proposed method.ResultsNumerical simulations show that the proposed method is more robust than other methods and can suppress the effects of noise. The quantitative conductivity value of the phantom experiment agrees with the measured value. The in vivo experiment results present a clear structure, and the conductivity value of the tumor region is significantly higher than that around healthy tissues.ConclusionThe proposed electrical conductivity imaging method can improve the quality of conductivity reconstruction, and thus, has future clinical applications.     

Robust tensor estimation in diffusion tensor imaging

The signal response measured in diffusion tensor imaging is subject to detrimental influences caused by noise. Noise fields arise due to various contributions such as thermal and physiological noise and sources related to the hardware imperfection. As a result, diffusion tensors estimated by different linear and non-linear least squares methods in absence of a proper noise correction tend to be substantially corrupted. In this work, we propose an advanced tensor estimation approach based on the least median squares method of the robust statistics. Both constrained and non-constrained versions of the method are considered. The performance of the developed algorithm is compared to that of the conventional least squares method and of the alternative robust methods proposed in the literature. Two examples of simulated diffusion attenuations and experimental in vivo diffusion data sets were used as a basis for comparison. The robust algorithms were shown to be advantageous compared to the least squares method in the cases where elimination of the outliers is desirable. Additionally, the constraints were applied in order to prevent generation of the non-positive definite tensors and reduce related artefacts in the maps of fractional anisotropy. The developed method can potentially be exploited also by other MR techniques where a robust regression or outlier localisation is required.     

基于高斯核主成分分析的多通道拉曼光谱重建

针对多通道拉曼成像系统常会受荧光背景、噪声等非线性因素的影响而导致拉曼光谱重建结果一般的问题,提出了一种基于高斯核主成分分析的拉曼光谱重建算法.首先利用相似度因子对标定样本数据集进行预处理,其次通过高斯核函数将标定样本以非线性形式映射至高维特征空间,接着在特征空间中对映射后的数据集提取基函数并通过伪逆法求得与之对应的基函数系数.使用聚甲基丙烯酸甲酯作为测试样本,并引入均方根误差来评估拉曼光谱重建结果的准确性.实验结果表明,相比传统的伪逆法与维纳估计法,该算法具有更高的重建精度及抗噪能力,且能有效降低标定样本中不良数据和成像系统中非线性因素对拉曼光谱重建的影响.因此,该算法可以为多通道拉曼快速成像提供一种有效的拉曼光谱重建算法.     

Fast multi-contrast MRI reconstruction

Multi-contrast magnetic resonance imaging (MRI) is a useful technique to aid clinical diagnosis. This paper proposes an efficient algorithm to jointly reconstruct multiple T1/T2-weighted images of the same anatomical cross section from partially sampled k-space data. The joint reconstruction problem is formulated as minimizing a linear combination of three terms, corresponding to a least squares data fitting, joint total variation (TV) and group wavelet-sparsity regularization. It is rooted in two observations: 1) the variance of image gradients should be similar for the same spatial position across multiple contrasts; 2) the wavelet coefficients of all images from the same anatomical cross section should have similar sparse modes. To efficiently solve this problem, we decompose it into joint TV regularization and group sparsity subproblems, respectively. Finally, the reconstructed image is obtained from the weighted average of solutions from the two subproblems, in an iterative framework. Experiments demonstrate the efficiency and effectiveness of the proposed method compared to existing multi-contrast MRI methods.     

Accelerating MRI Using GROG Gridding Followed by ESPIRiT for Non-Cartesian Trajectories

Parallel imaging plays an important role to reduce data acquisition time in magnetic resonance imaging (MRI). Under-sampled non-Cartesian trajectories accelerate the MRI scan time, but the resulting images may have aliasing artifacts. To remove these artifacts, a variety of methods have been developed within the scope of parallel imaging in the recent past. In this paper, the use of Eigen-vector-based iterative Self-consistent Parallel Imaging Reconstruction Technique (ESPIRiT) along with self-calibrated GRAPPA operator gridding (self-calibrated GROG) on radial k-space data for accelerated MR image reconstruction is presented. The proposed method reconstructs the solution image from non-Cartesian k-space data in two steps: First, the acquired radial data is gridded using self-calibrated GROG and then ESPIRIT is applied on this gridded data to get the un-aliased image. The proposed method is tested on human head data and the short-axis cardiac radial data. The quality of the reconstructed images is evaluated using artifact power (AP), root-mean-square error (RMSE) and peak signal-to-noise ratio (PSNR) at different acceleration factors (AF). The results of the proposed method (GROG followed by ESPIRiT) are compared with GROG followed by pseudo-Cartesian GRAPPA reconstruction approach (conventionally used). The results show that the proposed method provides considerable improvement in the reconstructed images as compared to conventionally used pseudo-Cartesian GRAPPA with GROG, e.g., 87, 67 and 82% improvement in terms of AP for 1.5T, 3T human head and short-axis cardiac radial data, 63, 45 and 57% improvement in terms of RMSE for 1.5T, 3T human head and short-axis cardiac radial data, 11, 7 and 9% improvement in terms of PSNR for 1.5T, 3T human head and short-axis cardiac radial data, respectively, at AF = 4.     

Retrospective correction of bias in diffusion tensor imaging arising from coil combination mode

PurposeTo quantify and retrospectively correct for systematic differences in diffusion tensor imaging (DTI) measurements due to differences in coil combination mode.BackgroundMulti-channel coils are now standard among MRI systems. There are several options for combining signal from multiple coils during image reconstruction, including sum-of-squares (SOS) and adaptive combine (AC). This contribution examines the bias between SOS- and AC-derived measures of tissue microstructure and a strategy for limiting that bias.MethodsFive healthy subjects were scanned under an institutional review board-approved protocol. Each set of raw image data was reconstructed twice—once with SOS and once with AC. The diffusion tensor was calculated from SOS- and AC-derived data by two algorithms—standard log-linear least squares and an approach that accounts for the impact of coil combination on signal statistics. Systematic differences between SOS and AC in terms of tissue microstructure (axial diffusivity, radial diffusivity, mean diffusivity and fractional anisotropy) were evaluated on a voxel-by-voxel basis.ResultsSOS-based tissue microstructure values are systematically lower than AC-based measures throughout the brain in each subject when using the standard tensor calculation method. The difference between SOS and AC can be virtually eliminated by taking into account the signal statistics associated with coil combination.ConclusionsThe impact of coil combination mode on diffusion tensor-based measures of tissue microstructure is statistically significant but can be corrected retrospectively. The ability to do so is expected to facilitate pooling of data among imaging protocols.     

An efficient method for model refinement in diffuse optical tomography

Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.     

Real-time dynamic vocal tract imaging using an accelerated spiral GRE sequence and low rank plus sparse reconstruction

PurposeTo develop a real-time dynamic vocal tract imaging method using an accelerated spiral GRE sequence and low rank plus sparse reconstruction.MethodsSpiral k-space sampling has high data acquisition efficiency and thus is suited for real-time dynamic imaging; further acceleration can be achieved by undersampling k-space and using a model-based reconstruction. Low rank plus sparse reconstruction is a promising method with fast computation and increased robustness to global signal changes and bulk motion, as the images are decomposed into low rank and sparse terms representing different dynamic components. However, the combination with spiral scanning has not been well studied. In this study an accelerated spiral GRE sequence was developed with an optimized low rank plus sparse reconstruction and compared with L1-SPIRiT and XD-GRASP methods. The off-resonance was also corrected using a Chebyshev approximation method to reduce blurring on a frame-by-frame basis.ResultsThe low rank plus sparse reconstruction method is sensitive to the weights of the low rank and sparse terms. The optimized reconstruction showed advantages over other methods with reduced aliasing and improved SNR. With the proposed method, spatial resolution of 1.3*1.3 mm² with 150 mm field-of-view (FOV) and temporal resolution of 30 frames-per-second (fps) was achieved with good image quality. Blurring was reduced using the Chebyshev approximation method.ConclusionThis work studies low rank plus sparse reconstruction using the spiral trajectory and demonstrates a new method for dynamic vocal tract imaging which can benefit studies of speech disorders.     

Motion predicted online dynamic MRI reconstruction from partially sampled k-space data

In this work we address the problem of reconstructing dynamic MRI sequences in an online fashion, i.e. reconstructing the current frame given that the previous frames have been already reconstructed. The reconstruction consists of a prediction and a correction step. The prediction step is based on an Auto-Regressive AR(1) model. Assuming that the prediction is good, the difference between the predicted frame and the actual frame (to be reconstructed) will be sparse. In the correction step, the difference between the predicted frame and the actual frame is estimated from partially sampled K-space data via a sparsity promoting least squares minimization problem. We have compared the proposed method with state-of-the-art methods in online dynamic MRI reconstruction. The experiments have been carried out on 2D and 3D Dynamic Contrast Enhanced (DCE) MRI datasets. Results show that our method yields the least reconstruction error.     

Characterization of a wavelength selection method using near-infrared spectroscopy and partial least squares with false nearest neighbors and its application in the detection of the chemical oxygen demand of waste liquid

Abstract

The spectral wavelength selection method is important in near-infrared spectroscopy. Eliminating redundant information and extracting useful information can improve the prediction accuracy and modeling efficiency of the quantitative analysis model for spectral analysis to obtain a near-infrared calibration model with strong predictability and good robustness. This paper proposes a wavelength selection method for near-infrared spectroscopy by combining the partial least squares and false nearest neighbor methods. In this method, the correlation between the characteristic wavelength variables and the measured index is assessed by means of a similarity-based distance measure of the characteristic wavelength variable, and the characteristic wavelength is selected according to the order of the correlation. The method was used to select characteristic wavelengths from the near-infrared spectrum of waste liquid to establish a prediction model for the chemical oxygen demand. Compared with the full-spectrum partial least squares and interval partial least squares based models, the number of characteristic wavelength variables is reduced from 1557 to 176, and the prediction accuracy of the model is improved. This method both simplifies the model and achieves higher prediction accuracy. Therefore, this study provides a novel solution for wavelength selection for multivariate calibration in near-infrared spectroscopy.     

Cardiac magnetic resonance imaging using radial k-space sampling and self-calibrated partial parallel reconstruction

Radial sampling has been demonstrated to be potentially useful in cardiac magnetic resonance imaging because it is less susceptible to motion than Cartesian sampling. Nevertheless, its capability of imaging acceleration remains limited by undersampling-induced streaking artifacts. In this study, a self-calibrated reconstruction method was developed to suppress streaking artifacts for highly accelerated parallel radial acquisitions in cardiac magnetic resonance imaging. Two- (2D) and three-dimensional (3D) radial k-space data were collected from a phantom and healthy volunteers. Images reconstructed using the proposed method and the conventional regridding method were compared based on statistical analysis on a four-point scale imaging scoring. It was demonstrated that the proposed method can effectively remove undersampling streaking artifacts and significantly improve image quality (P<.05). With the use of the proposed method, image score (1–4, 1=poor, 2=good, 3=very good, 4=excellent) was improved from 2.14 to 3.34 with the use of an undersampling factor of 4 and from 1.09 to 2.5 with the use of an undersampling factor of 8. Our study demonstrates that the proposed reconstruction method is effective for highly accelerated cardiac imaging applications using parallel radial acquisitions without calibration data.     

An algorithm for sparse MRI reconstruction by Schatten p-norm minimization

In recent years, there has been a concerted effort to reduce the MR scan time. Signal processing research aims at reducing the scan time by acquiring less K-space data. The image is reconstructed from the subsampled K-space data by employing compressed sensing (CS)-based reconstruction techniques. In this article, we propose an alternative approach to CS-based reconstruction. The proposed approach exploits the rank deficiency of the MR images to reconstruct the image. This requires minimizing the rank of the image matrix subject to data constraints, which is unfortunately a nondeterministic polynomial time (NP) hard problem. Therefore we propose to replace the NP hard rank minimization problem by its nonconvex surrogate — Schatten p-norm minimization. The same approach can be used for denoising MR images as well.Since there is no algorithm to solve the Schatten p-norm minimization problem, we derive an efficient first-order algorithm. Experiments on MR brain scans show that the reconstruction and denoising accuracy from our method is at par with that of CS-based methods. Our proposed method is considerably faster than CS-based methods.     

High-performance rapid MR parameter mapping using model-based deep adversarial learning

PurposeTo develop and evaluate a deep adversarial learning-based image reconstruction approach for rapid and efficient MR parameter mapping.MethodsThe proposed method provides an image reconstruction framework by combining the end-to-end convolutional neural network (CNN) mapping, adversarial learning, and MR physical models. The CNN performs direct image-to-parameter mapping by transforming a series of undersampled images directly into MR parameter maps. Adversarial learning is used to improve image sharpness and enable better texture restoration during the image-to-parameter conversion. An additional pathway concerning the MR signal model is added between the estimated parameter maps and undersampled k-space data to ensure the data consistency during network training. The proposed framework was evaluated on T₂ mapping of the brain and the knee at an acceleration rate R = 8 and was compared with other state-of-the-art reconstruction methods. Global and regional quantitative assessments were performed to demonstrate the reconstruction performance of the proposed method.ResultsThe proposed adversarial learning approach achieved accurate T₂ mapping up to R = 8 in brain and knee joint image datasets. Compared to conventional reconstruction approaches that exploit image sparsity and low-rankness, the proposed method yielded lower errors and higher similarity to the reference and better image sharpness in the T₂ estimation. The quantitative metrics were normalized root mean square error of 3.6% for brain and 7.3% for knee, structural similarity index of 85.1% for brain and 83.2% for knee, and tenengrad measures of 9.2% for brain and 10.1% for the knee. The adversarial approach also achieved better performance for maintaining greater image texture and sharpness in comparison to the CNN approach without adversarial learning.ConclusionThe proposed framework by incorporating the efficient end-to-end CNN mapping, adversarial learning, and physical model enforced data consistency is a promising approach for rapid and efficient reconstruction of quantitative MR parameters.     

High resolution optical coherence tomography by ?1-optimization

An algebraic optical coherence tomography (OCT) method is presented in this paper for high resolution tomography imaging. The method achieves high resolution by formulating the frequency domain OCT (FD-OCT) into a ?₁-optimization based algebraic reconstruction problem. The performance of the proposed algebraic method is evaluated by simulation and experiment, and compared to the FD-OCT method. It is shown that the proposed method can deliver high resolution beyond the coherence length and imaging depth bigger than the ones of the FD-OCT method. The computational load is greatly reduced compared to the traditional algebraic reconstruction methods.     

APIR4EMC: Autocalibrated parallel imaging reconstruction for extended multi-contrast imaging

PurposeTo improve image quality of multi-contrast imaging with the proposed Autocalibrated Parallel Imaging Reconstruction for Extended Multi-Contrast Imaging (APIR4EMC).MethodsAPIR4EMC reconstructs multi-contrast images in an autocalibrated parallel imaging reconstruction framework by adding contrasts as virtual coils. Compensation of signal evolution along the echo train of different contrasts is performed to improve signal prediction for missing samples. As a proof of concept, we performed prospectively accelerated phantom and in-vivo brain acquisitions with T1, T1-fat saturated (Fatsat), T2, PD, and FLAIR contrasts. The k-space sampling patterns of these acquisitions were jointly optimized. Images were jointly reconstructed with the proposed APIR4EMC method as well as individually with GRAPPA. Root mean square error (RMSE) to fully sampled reference images and g-factor maps were computed for both methods in the phantom experiment. Visual evaluation was performed in the in-vivo experiment.ResultsCompared to GRAPPA, APIR4EMC reduced artifacts and improved SNR of the reconstructed images in the phantom acquisitions. Quantitatively, APIR4EMC substantially reduced noise amplification (g-factor) as well as RMSE compared to GRAPPA. Signal evolution compensation reduced artifacts. In the in-vivo experiments, 1 mm³ isotropic 3D images with contrasts of T1, T1-Fatsat, T2, PD, and FLAIR were acquired in as little as 7.5 min with the acceleration factor of 9. Reconstruction quality was consistent with the phantom results.ConclusionCompared to single contrast reconstruction with GRAPPA, APIR4EMC reduces artifacts and noise amplification in accelerated multi-contrast imaging.     

Calibration and data restoration of light field modulated imaging spectrometer

A light field modulated imaging spectrometer(LFMIS) can acquire the spatial-spectral datacube of targets of interest or a scene in a single shot. The spectral information of a point target is imaged on the pixels covered by a microlens.The pixels receive spectral information from different spectral filters to the diffraction and misalignments of the optical components. In this paper, we present a linear spectral multiplexing model of the acquired target spectrum. A calibration method is proposed for calibrating the center wavelengths and bandwidths of channels of an LFMIS system based on the liner-variable filter(LVF) and for determining the spectral multiplexing matrix. In order to improve the accuracy of the restored spectral data, we introduce a reconstruction algorithm based on the total least square(TLS) approach. Simulation and experimental results confirm the performance of the spectrum reconstruction algorithm and validate the feasibility of the proposed calibrating scheme.     

Sparsity-constrained SENSE reconstruction: An efficient implementation using a fast composite splitting algorithm

Parallel imaging and compressed sensing have been arguably the most successful and widely used techniques for fast magnetic resonance imaging (MRI). Recent studies have shown that the combination of these two techniques is useful for solving the inverse problem of recovering the image from highly under-sampled k-space data. In sparsity-enforced sensitivity encoding (SENSE) reconstruction, the optimization problem involves data fidelity (L2-norm) constraint and a number of L1-norm regularization terms (i.e. total variation or TV, and L1 norm). This makes the optimization problem difficult to solve due to the non-smooth nature of the regularization terms. In this paper, to effectively solve the sparsity-regularized SENSE reconstruction, we utilize a new optimization method, called fast composite splitting algorithm (FCSA), which was developed for compressed sensing MRI. By using a combination of variable splitting and operator splitting techniques, the FCSA algorithm decouples the large optimization problem into TV and L1 sub-problems, which are then, solved efficiently using existing fast methods. The operator splitting separates the smooth terms from the non-smooth terms, so that both terms are treated in an efficient manner. The final solution to the SENSE reconstruction is obtained by weighted solutions to the sub-problems through an iterative optimization procedure. The FCSA-based parallel MRI technique is tested on MR brain image reconstructions at various acceleration rates and with different sampling trajectories. The results indicate that, for sparsity-regularized SENSE reconstruction, the FCSA-based method is capable of achieving significant improvements in reconstruction accuracy when compared with the state-of-the-art reconstruction method.     

Identification of wheat grain in different states based on hyperspectral imaging technology

Abstract

Nondestructive identification of wheat grains in different states plays an important role in improving the quality of wheat products. This study investigated the possibility of using hyperspectral imaging techniques to discriminate healthy wheat grain, germinated wheat grain, mildewed wheat grain, and shriveled wheat grain (wheat grain infected with fusarium head blight). Both sides of individual wheat kernels were subjected to hyperspectral imaging (866.4–1701.0?nm) to acquire hyperspectral cube data. Spectral data were preprocessed by using standardization and multiple scattering correction. In addition, the principal component loading method was used to extract the characteristic wavelengths of both sides of wheat grains. The sample is divided into calibration set, test set, and validation set. The data of the calibration set are used to train the partial least squares discriminant analysis model, K-nearest neighbor model, and the support vector machine model, and the test set data are used to test the model. The results show that spectral data of both sides can achieve good classification results, while the reverse spectral data perform better. By comparing with each other, the support vector machine model is selected as the best classification model. Finally, using two hyperspectral images (reverse side) that are not involved in training and testing to verify the accuracy of the established support vector machine model, and the classification effect maps of the four wheat grains were visualized. The results indicate that nondestructive classification of wheat grains in different states is feasible based on hyperspectral imaging technology.     

Calibration-less multi-coil MR image reconstruction

In parallel magnetic resonance imaging (MRI), the problem is to reconstruct an image given the partial K-space scans from all the receiver coils. Depending on its position within the scanner, each coil has a different sensitivity profile. All existing parallel MRI techniques require estimation of certain parameters pertaining to the sensitivity profile, e.g., the sensitivity map needs to be estimated for the SENSE and SMASH and the interpolation weights need to be calibrated for GRAPPA and SPIRiT. The assumption is that the estimated parameters are applicable at the operational stage. This assumption does not always hold, consequently the reconstruction accuracies of existing parallel MRI methods may suffer. We propose a reconstruction method called Calibration-Less Multi-coil (CaLM) MRI. As the name suggests, our method does not require estimation of any parameters related to the sensitivity maps and hence does not require a calibration stage. CaLM MRI is an image domain method that produces a sensitivity encoded image for each coil. These images are finally combined by the sum-of-squares method to yield the final image. It is based on the theory of Compressed Sensing (CS). During reconstruction, the constraint that "all the coil images should appear similar" is introduced within the CS framework. This leads to a CS optimization problem that promotes group-sparsity. The results from our proposed method are comparable (at least for the data used in this work) with the best results that can be obtained from state-of-the-art methods.     

De-aliasing for signal restoration in Propeller MR imaging

PurposeObjects falling outside of the true elliptical field-of-view (FOV) in Propeller imaging show unique aliasing artifacts. This study proposes a de-aliasing approach to restore the signal intensities in Propeller images without extra data acquisition.Materials and methodsComputer simulation was performed on the Shepp-Logan head phantom deliberately placed obliquely to examine the signal aliasing. In addition, phantom and human imaging experiments were performed using Propeller imaging with various readouts on a 3.0 Tesla MR scanner. De-aliasing using the proposed method was then performed, with the first low-resolution single-blade image used to find out the aliasing patterns in all the single-blade images, followed by standard Propeller reconstruction. The Propeller images without and with de-aliasing were compared.ResultsComputer simulations showed signal loss at the image corners along with aliasing artifacts distributed along directions corresponding to the rotational blades, consistent with clinical observations. The proposed de-aliasing operation successfully restored the correct images in both phantom and human experiments.ConclusionThe de-aliasing operation is an effective adjunct to Propeller MR image reconstruction for retrospective restoration of aliased signals.