High-fidelity, accelerated whole-brain submillimeter in vivo diffusion MRI using gSlider-spherical ridgelets (gSlider-SR).

PURPOSE: To develop an accelerated, robust, and accurate diffusion MRI acquisition and reconstruction technique for submillimeter whole human brain in vivo scan on a clinical scanner. METHODS: We extend the ultra-high resolution diffusion MRI acquisition technique, gSlider, by allowing undersampling in q-space and radiofrequency (RF)-encoding space, thereby dramatically reducing the total acquisition time of conventional gSlider. The novel method, termed gSlider-SR, compensates for the lack of acquired information by exploiting redundancy in the dMRI data using a basis of spherical ridgelets (SR), while simultaneously enhancing the signal-to-noise ratio. Using Monte Carlo simulation with realistic noise levels and several acquisitions of in vivo human brain dMRI data (acquired on a Siemens Prisma 3T scanner), we demonstrate the efficacy of our method using several quantitative metrics. RESULTS: For high-resolution dMRI data with realistic noise levels (synthetically added), we show that gSlider-SR can reconstruct high-quality dMRI data at different acceleration factors preserving both signal and angular information. With in vivo data, we demonstrate that gSlider-SR can accurately reconstruct 860 µm diffusion MRI data (64 diffusion directions at b=2000s/mm2 ), at comparable quality as that obtained with conventional gSlider with four averages, thereby providing an eight-fold reduction in scan time (from 1 hour 20 to 10 minutes). CONCLUSIONS: gSlider-SR enables whole-brain high angular resolution dMRI at a submillimeter spatial resolution with a dramatically reduced acquisition time, making it feasible to use the proposed scheme on existing clinical scanners.

Multi-site harmonization of diffusion MRI data in a registration framework.

Diffusion MRI (dMRI) data acquired on different scanners varies significantly in its content throughout the brain even if the acquisition parameters are nearly identical. Thus, proper harmonization of such data sets is necessary to increase the sample size and thereby the statistical power of neuroimaging studies. In this paper, we present a novel approach to harmonize dMRI data (the raw signal, instead of dMRI derived measures such as fractional anisotropy) using rotation invariant spherical harmonic (RISH) features embedded within a multi-modal image registration framework. All dMRI data sets from all sites are registered to a common template and voxel-wise differences in RISH features between sites at a group level are used to harmonize the signal in a subject-specific manner. We validate our method on diffusion data acquired from seven different sites (two GE, three Philips, and two Siemens scanners) on a group of age-matched healthy subjects. We demonstrate the efficacy of our method by statistically comparing diffusion measures such as fractional anisotropy, mean diffusivity and generalized fractional anisotropy across these sites before and after data harmonization. Validation was also done on a group oftest subjects, which were not used to "learn" the harmonization parameters. We also show results using TBSS before and after harmonization for independent validation of the proposed methodology. Using synthetic data, we show that any abnormality in diffusion measures due to disease is preserved during the harmonization process. Our experimental results demonstrate that, for nearly identical acquisition protocol across sites, scanner-specific differences in the signal can be removed using the proposed method in a model independent manner.

A joint compressed-sensing and super-resolution approach for very high-resolution diffusion imaging.

Diffusion MRI (dMRI) can provide invaluable information about the structure of different tissue types in the brain. Standard dMRI acquisitions facilitate a proper analysis (e.g. tracing) of medium-to-large white matter bundles. However, smaller fiber bundles connecting very small cortical or sub-cortical regions cannot be traced accurately in images with large voxel sizes. Yet, the ability to trace such fiber bundles is critical for several applications such as deep brain stimulation and neurosurgery. In this work, we propose a novel acquisition and reconstruction scheme for obtaining high spatial resolution dMRI images using multiple low resolution (LR) images, which is effective in reducing acquisition time while improving the signal-to-noise ratio (SNR). The proposed method called compressed-sensing super resolution reconstruction (CS-SRR), uses multiple overlapping thick-slice dMRI volumes that are under-sampled in q-space to reconstruct diffusion signal with complex orientations. The proposed method combines the twin concepts of compressed sensing and super-resolution to model the diffusion signal (at a given b-value) in a basis of spherical ridgelets with total-variation (TV) regularization to account for signal correlation in neighboring voxels. A computationally efficient algorithm based on the alternating direction method of multipliers (ADMM) is introduced for solving the CS-SRR problem. The performance of the proposed method is quantitatively evaluated on several in-vivo human data sets including a true SRR scenario. Our experimental results demonstrate that the proposed method can be used for reconstructing sub-millimeter super resolution dMRI data with very good data fidelity in clinically feasible acquisition time.

A Compressed-Sensing Approach for Super-Resolution Reconstruction of Diffusion MRI.

We present an innovative framework for reconstructing high-spatial-resolution diffusion magnetic resonance imaging (dMRI) from multiple low-resolution (LR) images. Our approach combines the twin concepts of compressed sensing (CS) and classical super-resolution to reduce acquisition time while increasing spatial resolution. We use subpixel-shifted LR images with down-sampled and non-overlapping diffusion directions to reduce acquisition time. The diffusion signal in the high resolution (HR) image is represented in a sparsifying basis of spherical ridgelets to model complex fiber orientations with reduced number of measurements. The HR image is obtained as the solution of a convex optimization problem which can be solved using the proposed algorithm based on the alternating direction method of multipliers (ADMM). We qualitatively and quantitatively evaluate the performance of our method on two sets of in-vivo human brain data and show its effectiveness in accurately recovering very high resolution diffusion images.

Surface reconstruction in gradient-field domain using compressed sensing.

Surface reconstruction from measurements of spatial gradient is an important computer vision problem with applications in photometric stereo and shape-from-shading. In the case of morphologically complex surfaces observed in the presence of shadowing and transparency artifacts, a relatively large dense gradient measurements may be required for accurate surface reconstruction. Consequently, due to hardware limitations of image acquisition devices, situations are possible in which the available sampling density might not be sufficiently high to allow for recovery of essential surface details. In this paper, the above problem is resolved by means of derivative compressed sensing (DCS). DCS can be viewed as a modification of the classical CS, which is particularly suited for reconstructions involving image/surface gradients. In DCS, a standard CS setting is augmented through incorporation of additional constraints arising from some intrinsic properties of potential vector fields. We demonstrate that using DCS results in reduction in the number of measurements as compared with the standard (dense) sampling, while producing estimates of higher accuracy and smaller variability as compared with CS-based estimates. The results of this study are further supported by a series of numerical experiments.

Functional consequences of neurite orientation dispersion and density in humans across the adult lifespan.

As humans age, a characteristic pattern of widespread neocortical dendritic disruption coupled with compensatory effects in hippocampus and other subcortical structures is shown in postmortem investigations. It is now possible to address age-related effects on gray matter (GM) neuritic organization and density in humans using multishell diffusion-weighted MRI and the neurite-orientation dispersion and density imaging (NODDI) model. In 45 healthy individuals across the adult lifespan (21-84 years), we used a multishell diffusion imaging and the NODDI model to assess the intraneurite volume fraction and neurite orientation-dispersion index (ODI) in GM tissues. We also determined the functional correlates of variations in GM microstructure by obtaining resting-state fMRI and behavioral data. We found a significant age-related deficit in neocortical ODI (most prominently in frontoparietal regions), whereas increased ODI was observed in hippocampus and cerebellum with advancing age. Neocortical ODI outperformed cortical thickness and white matter fractional anisotropy for the prediction of chronological age in the same individuals. Higher GM ODI sampled from resting-state networks with known age-related susceptibility (default mode and visual association networks) was associated with increased functional connectivity of these networks, whereas the task-positive networks tended to show no association or even decreased connectivity. Frontal pole ODI mediated the negative relationship of age with executive function, whereas hippocampal ODI mediated the positive relationship of age with executive function. Our in vivo findings align very closely with the postmortem data and provide evidence for vulnerability and compensatory neural mechanisms of aging in GM microstructure that have functional and cognitive impact in vivo.

Maximum entropy estimation of glutamate and glutamine in MR spectroscopic imaging.

Magnetic resonance spectroscopic imaging (MRSI) is often used to estimate the concentration of several brain metabolites. Abnormalities in these concentrations can indicate specific pathology, which can be quite useful in understanding the disease mechanism underlying those changes. Due to higher concentration, metabolites such as N-acetylaspartate (NAA), Creatine (Cr) and Choline (Cho) can be readily estimated using standard Fourier transform techniques. However, metabolites such as Glutamate (Glu) and Glutamine (Gln) occur in significantly lower concentrations and their resonance peaks are very close to each other making it difficult to accurately estimate their concentrations (separately). In this work, we propose to use the theory of 'Spectral Zooming' or high-resolution spectral analysis to separate the Glutamate and Glutamine peaks and accurately estimate their concentrations. The method works by estimating a unique power spectral density, which corresponds to the maximum entropy solution of a zero-mean stationary Gaussian process. We demonstrate our estimation technique on several physical phantom data sets as well as on in-vivo brain spectroscopic imaging data. The proposed technique is quite general and can be used to estimate the concentration of any other metabolite of interest.

Diffusion propagator estimation from sparse measurements in a tractography framework.

Estimation of the diffusion propagator from a sparse set of diffusion MRI (dMRI) measurements is a field of active research. Sparse reconstruction methods propose to reduce scan time and are particularly suitable for scanning un-coperative patients. Recent work on reconstructing the diffusion signal from very few measurements using compressed sensing based techniques has focussed on propagator (or signal) estimation at each voxel independently. However, the goal of many neuroscience studies is to use tractography to study the pathology in white matter fiber tracts. Thus, in this work, we propose a joint framework for robust estimation of the diffusion propagator from sparse measurements while simultaneously tracing the white matter tracts. We propose to use a novel multi-tensor model of diffusion which incorporates the biexponential radial decay of the signal. Our preliminary results on in-vivo data show that the proposed method produces consistent and reliable fiber tracts from very few gradient directions while simultaneously estimating the bi-exponential decay of the diffusion propagator.

Image deblurring using derivative compressed sensing for optical imaging application.

The problem of reconstruction of digital images from their blurred and noisy measurements is unarguably one of the central problems in imaging sciences. Despite its ill-posed nature, this problem can often be solved in a unique and stable manner, provided appropriate assumptions on the nature of the images to be recovered. In this paper, however, a more challenging setting is considered, in which accurate knowledge of the blurring operator is lacking, thereby transforming the reconstruction problem at hand into a problem of blind deconvolution. As a specific application, the current presentation focuses on reconstruction of short-exposure optical images measured through atmospheric turbulence. The latter is known to give rise to random aberrations in the optical wavefront, which are in turn translated into random variations of the point spread function of the optical system in use. A standard way to track such variations involves using adaptive optics. Thus, for example, the Shack-Hartmann interferometer provides measurements of the optical wavefront through sensing its partial derivatives. In such a case, the accuracy of wavefront reconstruction is proportional to the number of lenslets used by the interferometer and, hence, to its complexity. Accordingly, in this paper, we show how to minimize the above complexity through reducing the number of the lenslets while compensating for undersampling artifacts by means of derivative compressed sensing. Additionally, we provide empirical proof that the above simplification and its associated solution scheme result in image reconstructions, whose quality is comparable to the reconstructions obtained using conventional (dense) measurements of the optical wavefront.

Spatially regularized compressed sensing for high angular resolution diffusion imaging.

Despite the relative recency of its inception, the theory of compressive sampling (aka compressed sensing) (CS) has already revolutionized multiple areas of applied sciences, a particularly important instance of which is medical imaging. Specifically, the theory has provided a different perspective on the important problem of optimal sampling in magnetic resonance imaging (MRI), with an ever-increasing body of works reporting stable and accurate reconstruction of MRI scans from the number of spectral measurements which would have been deemed unacceptably small as recently as five years ago. In this paper, the theory of CS is employed to palliate the problem of long acquisition times, which is known to be a major impediment to the clinical application of high angular resolution diffusion imaging (HARDI). Specifically, we demonstrate that a substantial reduction in data acquisition times is possible through minimization of the number of diffusion encoding gradients required for reliable reconstruction of HARDI scans. The success of such a minimization is primarily due to the availability of spherical ridgelet transformation, which excels in sparsifying HARDI signals. What makes the resulting reconstruction procedure even more accurate is a combination of the sparsity constraints in the diffusion domain with additional constraints imposed on the estimated diffusion field in the spatial domain. Accordingly, the present paper describes an original way to combine the diffusion- and spatial-domain constraints to achieve a maximal reduction in the number of diffusion measurements, while sacrificing little in terms of reconstruction accuracy. Finally, details are provided on an efficient numerical scheme which can be used to solve the aforementioned reconstruction problem by means of standard and readily available estimation tools. The paper is concluded with experimental results which support the practical value of the proposed reconstruction methodology.

Iterative shrinkage approach to restoration of optical imagery.

The problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences. In such cases, the degradation is typically caused by the resolution limitations of an imaging device in use and/or by the destructive influence of measurement noise. Specifically, when the noise obeys a Poisson probability law, standard approaches to the problem of image reconstruction are based upon using fixed-point algorithms which follow the methodology first proposed by Richardson and Lucy. The practice of using these methods, however, shows that their convergence properties tend to deteriorate at relatively high noise levels. Accordingly, in the present paper, a novel method for denoising and/or deblurring of digital images corrupted by Poisson noise is introduced. The proposed method is derived under the assumption that the image of interest can be sparsely represented in the domain of a linear transform. Consequently, a shrinkage-based iterative procedure is proposed, which guarantees the solution to converge to the global maximizer of an associated maximum a posteriori criterion. It is shown in a series of computer-simulated experiments that the proposed method outperforms a number of existing alternatives in terms of stability, precision, and computational efficiency.

An iterative shrinkage approach to total-variation image restoration.

The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the degradation phenomenon is modeled by an ill-conditioned operator. In such a situation, the presence of noise makes it impossible to recover a valuable approximation of the image of interest without using some a priori information about its properties. Such a priori information--commonly referred to as simply priors--is essential for image restoration, rendering it stable and robust to noise. Moreover, using the priors makes the recovered images exhibit some plausible features of their original counterpart. Particularly, if the original image is known to be a piecewise smooth function, one of the standard priors used in this case is defined by the Rudin-Osher-Fatemi model, which results in total variation (TV) based image restoration. The current arsenal of algorithms for TV-based image restoration is vast. In this present paper, a different approach to the solution of the problem is proposed based upon the method of iterative shrinkage (aka iterated thresholding). In the proposed method, the TV-based image restoration is performed through a recursive application of two simple procedures, viz. linear filtering and soft thresholding. Therefore, the method can be identified as belonging to the group of first-order algorithms which are efficient in dealing with images of relatively large sizes. Another valuable feature of the proposed method consists in its working directly with the TV functional, rather then with its smoothed versions. Moreover, the method provides a single solution for both isotropic and anisotropic definitions of the TV functional, thereby establishing a useful connection between the two formulae. Finally, a number of standard examples of image deblurring are demonstrated, in which the proposed method can provide restoration results of superior quality as compared to the case of sparse-wavelet deconvolution.

Fast and accurate reconstruction of HARDI data using compressed sensing.

A spectrum of brain-related disorders are nowadays known to manifest themselves in degradation of the integrity and connectivity of neural tracts in the white matter of the brain. Such damage tends to affect the pattern of water diffusion in the white matter--the information which can be quantified by diffusion MRI (dMRI). Unfortunately, practical implementation of dMRI still poses a number of challenges which hamper its wide-spread integration into regular clinical practice. Chief among these is the problem of long scanning times. In particular, in the case of High Angular Resolution Diffusion Imaging (HARDI), the scanning times are known to increase linearly with the number of diffusion-encoding gradients. In this research, we use the theory of compressive sampling (aka compressed sensing) to substantially reduce the number of diffusion gradients without compromising the informational content of HARDI signals. The experimental part of our study compares the proposed method with a number of alternative approaches, and shows that the former results in more accurate estimation of HARDI data in terms of the mean squared error.

Biomarkers for identifying first-episode schizophrenia patients using diffusion weighted imaging.

Recent advances in diffusion weighted MR imaging (dMRI) has made it a tool of choice for investigating white matter abnormalities of the brain and central nervous system. In this work, we design a system that detects abnormal features (biomarkers) of first-episode schizophrenia patients and then classifies them using these features. We use two different models of the dMRI data, namely, spherical harmonics and the two-tensor model. The algorithm works by first computing several diffusion measures from each model. An affine-invariant representation of each subject is then computed, thus avoiding the need for registration. This representation is used within a kernel based feature selection algorithm to determine the biomarkers that are statistically different between the two populations. Confirmation of how well these biomarkers identify each population is obtained by using several classifiers such as, k-nearest neighbors, Parzen window classifier, and support vector machines to separate 21 first-episode patients from 20 age-matched normal controls. Classification results using leave-many-out cross-validation scheme are given for each representation. This algorithm is a first step towards early detection of schizophrenia.

Information tracking approach to segmentation of ultrasound imagery of the prostate.

The volume of the prostate is known to be a pivotal quantity used by clinicians to assess the condition of the gland during prostate cancer screening. As an alternative to palpation, an increasing number of methods for estimation of the volume of the prostate are based on using imagery data. The necessity to process large volumes of such data creates a need for automatic segmentation tools which would allow the estimation to be carried out with maximum accuracy and efficiency. In particular, the use of transrectal ultrasound (TRUS) imaging in prostate cancer screening seems to be becoming a standard clinical practice because of the high benefit-to-cost ratio of this imaging modality. Unfortunately, the segmentation of TRUS images is still hampered by relatively low contrast and reduced SNR of the images, thereby requiring the segmentation algorithms to incorporate prior knowledge about the geometry of the gland. In this paper, a novel approach to the problem of segmenting the TRUS images is described. The proposed approach is based on the concept of distribution tracking, which provides a unified framework for modeling and fusing image-related and morphological features of the prostate. Moreover, the same framework allows the segmentation to be regularized by using a new type of weak shape priors, which minimally bias the estimation procedure, while rendering the procedure stable and robust. The value of the proposed methodology is demonstrated in a series of in silico and in vivo experiments.

Tensor kernels for simultaneous fiber model estimation and tractography.

This paper proposes a novel framework for joint orientation distribution function estimation and tractography based on a new class of tensor kernels. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. In this work, fiber tracking is formulated as recursive estimation: at each step of tracing the fiber, the current estimate of the orientation distribution function is guided by the previous. To do this, second-and higher-order tensor-based kernels are employed. A weighted mixture of these tensor kernels is used for representing crossing and branching fiber structures. While tracing a fiber, the parameters of the mixture model are estimated based on the orientation distribution function at that location and a smoothness term that penalizes deviation from the previous estimate along the fiber direction. This ensures smooth estimation along the direction of propagation of the fiber. In synthetic experiments, using a mixture of two and three components it is shown that this approach improves the angular resolution at crossings. In vivo experiments using two and three components examine the corpus callosum and corticospinal tract and confirm the ability to trace through regions known to contain such crossing and branching.

A filtered approach to neural tractography using the Watson directional function.

We propose a technique to simultaneously estimate the local fiber orientations and perform multi-fiber tractography. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. Further, to overcome noise, many algorithms use a filter as a post-processing step to obtain a smooth trajectory. We formulate fiber tracking as causal estimation: at each step of tracing the fiber, the current estimate of the signal is guided by the previous. To do this, we model the signal as a discrete mixture of Watson directional functions and perform tractography within a filtering framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides an accurate estimate of the local structure at each point along the fiber. We choose the Watson function since it provides a compact representation of the signal parameterized by the principal diffusion direction and a scaling parameter describing anisotropy, and also allows analytic reconstruction of the oriented diffusion function from those parameters. Using a mixture of two and three components (corresponding to two-fiber and three-fiber models) we demonstrate in synthetic experiments that this approach reduces signal reconstruction error and significantly improves the angular resolution at crossings and branchings. In vivo experiments examine the corpus callosum and internal capsule and confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization.

On approximation of orientation distributions by means of spherical ridgelets.

Visualization and analysis of the micro-architecture of brain parenchyma by means of magnetic resonance imaging is nowadays believed to be one of the most powerful tools used for the assessment of various cerebral conditions as well as for understanding the intracerebral connectivity. Unfortunately, the conventional diffusion tensor imaging (DTI) used for estimating the local orientations of neural fibers is incapable of performing reliably in the situations when a voxel of interest accommodates multiple fiber tracts. In this case, a much more accurate analysis is possible using the high angular resolution diffusion imaging (HARDI) that represents local diffusion by its apparent coefficients measured as a discrete function of spatial orientations. In this note, a novel approach to enhancing and modeling the HARDI signals using multiresolution bases of spherical ridgelets is presented. In addition to its desirable properties of being adaptive, sparsifying, and efficiently computable, the proposed modeling leads to analytical computation of the orientation distribution functions associated with the measured diffusion, thereby providing a fast and robust analytical solution for q-ball imaging.

Directional functions for orientation distribution estimation.

Computing the orientation distribution function (ODF) from high angular resolution diffusion imaging (HARDI) signals makes it possible to determine the orientation of fiber bundles of the brain. The HARDI signals are samples measured from a spherical shell and thus require processing on the sphere. Past work on ODF estimation involved using the spherical harmonics or spherical radial basis functions. In this work, we propose three novel directional functions able to represent the measured signals in a very compact manner, i.e., they require very few parameters to completely describe the measured signal. Analytical expressions are derived for computing the corresponding ODF. The directional functions can represent diffusion in a particular direction and mixture models can be used to represent multi-fiber orientations. We show how to estimate the parameters of this mixture model and elaborate on the differences between these functions. We also compare this general framework with estimation of ODF using spherical harmonics on some real and synthetic data. The proposed method could be particularly useful in applications such as tractography and segmentation. Details are also given on different ways in which interpolation can be performed using directional functions. In particular, we discuss a complete Euclidean as well as a "hybrid" framework, comprising of the Riemannian as well as Euclidean spaces, to perform interpolation and compute geodesic distances between two ODF's.