Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging

International audienceIn diffusion MRI (dMRI) domain, many High Angular Resolution Diffusion Imaging (HARDI) methods were proposed to estimate Ensemble Average Propagator (EAP) and Orientation Distribution Function (ODF). They normally need many samples, which limits their applications. Some Compressive Sensing (CS) based methods were proposed to estimate ODF in Q-Ball Imaging (QBI) from limited samples. However EAP estimation is much more difficult than ODF in QBI. Recently Spherical Polar Fourier Imaging (SPFI) was proposed to represent diffusion signal using Spherical Polar Fourier (SPF) basis without specific assumption on diffusion signals and analytically obtain EAP and ODF via the Fourier dual SPF (dSPF) basis from arbitrarily sampled signal. Normally the coefficients of SPF basis are estimated via Least Square with weighted L2 norm regularization (L2-SPFI). However, L2-SPFI needs a truncated basis to avoid overfitting, which brings some estimation errors. By considering the Fourier relationship between EAP and signal and the Fourier basis pair provided in SPFI, we propose a novel EAP estimation method, named L1-SPFI, to estimate EAP from limited samples using CS technique, and favorably compare it to the classical L2-SPFI method. L1-SPFI estimates the coefficients in SPFI using least square with weighted L1 norm regularization. The weights are designed to enhance the sparsity. L1-SPFI significantly accelerates the ordinary CS based Fourier reconstruction method. This is performed by using SPF basis pair in CS estimation process which avoids the numerical Fourier transform in each iteration step. By considering high order basis in L1 optimization, L1-SPFI improves EAP reconstruction especially for the angular resolution. The proposed L1-SPFI was validated by synthetic, phantom and real data. The CS EAP and ODF estimations are discussed in detail and we show that recovering the angular information from CS EAP requires much less samples than exact CS EAP reconstruction. Various experiments on synthetic, phantom and real data validate the fact that SPF basis can sparsely represent DW-MRI signals and L1-SPFI largely improves the CS EAP reconstruction especially the angular resolution

Learning-based Ensemble Average Propagator Estimation

By capturing the anisotropic water diffusion in tissue, diffusion magnetic resonance imaging (dMRI) provides a unique tool for noninvasively probing the tissue microstructure and orientation in the human brain. The diffusion profile can be described by the ensemble average propagator (EAP), which is inferred from observed diffusion signals. However, accurate EAP estimation using the number of diffusion gradients that is clinically practical can be challenging. In this work, we propose a deep learning algorithm for EAP estimation, which is named learning-based ensemble average propagator estimation (LEAPE). The EAP is commonly represented by a basis and its associated coefficients, and here we choose the SHORE basis and design a deep network to estimate the coefficients. The network comprises two cascaded components. The first component is a multiple layer perceptron (MLP) that simultaneously predicts the unknown coefficients. However, typical training loss functions, such as mean squared errors, may not properly represent the geometry of the possibly non-Euclidean space of the coefficients, which in particular causes problems for the extraction of directional information from the EAP. Therefore, to regularize the training, in the second component we compute an auxiliary output of approximated fiber orientation (FO) errors with the aid of a second MLP that is trained separately. We performed experiments using dMRI data that resemble clinically achievable $q$-space sampling, and observed promising results compared with the conventional EAP estimation method.Comment: Accepted by MICCAI 201

Compressive sensing based Q-space resampling for handling fast bulk motion in hardi acquisitions

Diffusion-weighted (DW) MRI has become a widely adopted imaging modality to reveal the underlying brain connectivity. Long acquisition times and/or non-cooperative patients increase the chances of motion-related artifacts. Whereas slow bulk motion results in inter-gradient misalignment which can be handled via retrospective motion correction algorithms, fast bulk motion usually affects data during the application of a single diffusion gradient causing signal dropout artifacts. Common practices opt to discard gradients bearing signal attenuation due to the difficulty of their retrospective correction, with the disadvantage to lose full gradients for further processing. Nonetheless, such attenuation might only affect limited number of slices within a gradient volume. Q-space resampling has recently been proposed to recover corrupted slices while saving gradients for subsequent reconstruction. However, few corrupted gradients are implicitly assumed which might not hold in case of scanning unsedated infants or patients in pain. In this paper, we propose to adopt recent advances in compressive sensing based reconstruction of the diffusion orientation distribution functions (ODF) with under sampled measurements to resample corrupted slices. We make use of Simple Harmonic Oscillator based Reconstruction and Estimation (SHORE) basis functions which can analytically model ODF from arbitrary sampled signals. We demonstrate the impact of the proposed resampling strategy compared to state-of-art resampling and gradient exclusion on simulated intra-gradient motion as well as samples from real DWI data

Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging

International audienceIn diffusion MRI (dMRI) domain, many High Angular Resolution Diffusion Imaging (HARDI) methods were proposed to estimate Ensemble Average Propagator (EAP) and Orientation Distribution Function (ODF). They normally need many samples, which limits their applications. Some Compressive Sensing (CS) based methods were proposed to estimate ODF in Q-Ball Imaging (QBI) from limited samples. However EAP estimation is much more difficult than ODF in QBI. Recently Spherical Polar Fourier Imaging (SPFI) was proposed to represent diffusion signal using Spherical Polar Fourier (SPF) basis without specific assumption on diffusion signals and analytically obtain EAP and ODF via the Fourier dual SPF (dSPF) basis from arbitrarily sampled signal. Normally the coefficients of SPF basis are estimated via Least Square with weighted L2 norm regularization (L2-SPFI). However, L2-SPFI needs a truncated basis to avoid overfitting, which brings some estimation errors. By considering the Fourier relationship between EAP and signal and the Fourier basis pair provided in SPFI, we propose a novel EAP estimation method, named L1-SPFI, to estimate EAP from limited samples using CS technique, and favorably compare it to the classical L2-SPFI method. L1-SPFI estimates the coefficients in SPFI using least square with weighted L1 norm regularization. The weights are designed to enhance the sparsity. L1-SPFI significantly accelerates the ordinary CS based Fourier reconstruction method. This is performed by using SPF basis pair in CS estimation process which avoids the numerical Fourier transform in each iteration step. By considering high order basis in L1 optimization, L1-SPFI improves EAP reconstruction especially for the angular resolution. The proposed L1-SPFI was validated by synthetic, phantom and real data. The CS EAP and ODF estimations are discussed in detail and we show that recovering the angular information from CS EAP requires much less samples than exact CS EAP reconstruction. Various experiments on synthetic, phantom and real data validate the fact that SPF basis can sparsely represent DW-MRI signals and L1-SPFI largely improves the CS EAP reconstruction especially the angular resolution

Modélisation locale en imagerie par résonance magnétique de diffusion : de l'acquisition comprimée au connectome

L’imagerie par résonance magnétique pondérée en diffusion est une modalité d’imagerie médicale non invasive qui permet de mesurer les déplacements microscopiques des molécules d’eau dans les tissus biologiques. Il est possible d’utiliser cette information pour inférer la structure du cerveau. Les techniques de modélisation locale de la diffusion permettent de calculer l’orientation et la géométrie des tissus de la matière blanche. Cette thèse s’intéresse à l’optimisation des métaparamètres utilisés par les modèles locaux. Nous dérivons des paramètres optimaux qui améliorent la qualité des métriques de diffusion locale, de la tractographie de la matière blanche et de la connectivité globale. L’échantillonnage de l’espace-q est un des paramètres principaux qui limitent les types de modèle et d’inférence applicable sur des données acquises en clinique. Dans cette thèse, nous développons une technique d’échantillonnage de l’espace-q permettant d’utiliser l’acquisition comprimée pour réduire le temps d’acquisition nécessaire

Estimation of Fiber Orientations Using Neighborhood Information

Data from diffusion magnetic resonance imaging (dMRI) can be used to reconstruct fiber tracts, for example, in muscle and white matter. Estimation of fiber orientations (FOs) is a crucial step in the reconstruction process and these estimates can be corrupted by noise. In this paper, a new method called Fiber Orientation Reconstruction using Neighborhood Information (FORNI) is described and shown to reduce the effects of noise and improve FO estimation performance by incorporating spatial consistency. FORNI uses a fixed tensor basis to model the diffusion weighted signals, which has the advantage of providing an explicit relationship between the basis vectors and the FOs. FO spatial coherence is encouraged using weighted l1-norm regularization terms, which contain the interaction of directional information between neighbor voxels. Data fidelity is encouraged using a squared error between the observed and reconstructed diffusion weighted signals. After appropriate weighting of these competing objectives, the resulting objective function is minimized using a block coordinate descent algorithm, and a straightforward parallelization strategy is used to speed up processing. Experiments were performed on a digital crossing phantom, ex vivo tongue dMRI data, and in vivo brain dMRI data for both qualitative and quantitative evaluation. The results demonstrate that FORNI improves the quality of FO estimation over other state of the art algorithms.Comment: Journal paper accepted in Medical Image Analysis. 35 pages and 16 figure

Fiber Orientation Estimation Guided by a Deep Network

Diffusion magnetic resonance imaging (dMRI) is currently the only tool for noninvasively imaging the brain's white matter tracts. The fiber orientation (FO) is a key feature computed from dMRI for fiber tract reconstruction. Because the number of FOs in a voxel is usually small, dictionary-based sparse reconstruction has been used to estimate FOs with a relatively small number of diffusion gradients. However, accurate FO estimation in regions with complex FO configurations in the presence of noise can still be challenging. In this work we explore the use of a deep network for FO estimation in a dictionary-based framework and propose an algorithm named Fiber Orientation Reconstruction guided by a Deep Network (FORDN). FORDN consists of two steps. First, we use a smaller dictionary encoding coarse basis FOs to represent the diffusion signals. To estimate the mixture fractions of the dictionary atoms (and thus coarse FOs), a deep network is designed specifically for solving the sparse reconstruction problem. Here, the smaller dictionary is used to reduce the computational cost of training. Second, the coarse FOs inform the final FO estimation, where a larger dictionary encoding dense basis FOs is used and a weighted l1-norm regularized least squares problem is solved to encourage FOs that are consistent with the network output. FORDN was evaluated and compared with state-of-the-art algorithms that estimate FOs using sparse reconstruction on simulated and real dMRI data, and the results demonstrate the benefit of using a deep network for FO estimation.Comment: A shorter version is accepted by MICCAI 201

Fast diffusion MRI based on sparse acquisition and reconstruction for long-term population imaging

Diffusion weighted magnetic resonance imaging (dMRI) is a unique MRI modality to probe the diffusive molecular transport in biological tissue. Due to its noninvasiveness and its ability to investigate the living human brain at submillimeter scale, dMRI is frequently performed in clinical and biomedical research to study the brain’s complex microstructural architecture. Over the last decades large prospective cohort studies have been set up with the aim to gain new insights into the development and progression of brain diseases across the life span and to discover biomarkers for disease prediction and potentially prevention. To allow for diverse brain imaging using different MRI modalities, stringent scan time limits are typically imposed in population imaging. Nevertheless, population studies aim to apply advanced and thereby time consuming dMRI protocols that deliver high quality data with great potential for future analysis. To allow for time-efficient but also versatile diffusion imaging, this thesis contributes to the investigation of accelerating diffusion spectrum imaging (DSI), an advanced dMRI technique that acquires imaging data with high intra-voxel resolution of tissue microstructure. Combining state-of-the-art parallel imaging and the theory of compressed sensing (CS) enables the acceleration of spatial encoding and diffusion encoding in dMRI. In this way, the otherwise long acquisition times in DSI can be reduced significantly. In this thesis, first, suitable q-space sampling strategies and basis functions are explored that fulfill the requirements of CS theory for accurate sparse DSI reconstruction. Novel 3D q-space sample distributions are investigated for CS-DSI. Moreover, conventional CS-DSI based on the discrete Fourier transform is compared for the first time to CS-DSI based on the continuous SHORE (simple harmonic oscillator based reconstruction and estimation) basis functions. Based on these findings, a CS-DSI protocol is proposed for application in a prospective cohort study, the Rhineland Study. A pilot study was designed and conducted to evaluate the CS-DSI protocol in comparison with state-of-the-art 3-shell dMRI and dedicated protocols for diffusion tensor imaging (DTI) and for the combined hindered and restricted model of diffusion (CHARMED). Population imaging requires processing techniques preferably with low computational cost to process and analyze the acquired big data within a reasonable time frame. Therefore, a pipeline for automated processing of CS-DSI acquisitions was implemented including both in-house developed and existing state-of-the-art processing tools. The last contribution of this thesis is a novel method for automatic detection and imputation of signal dropout due to fast bulk motion during the diffusion encoding in dMRI. Subject motion is a common source of artifacts, especially when conducting clinical or population studies with children, the elderly or patients. Related artifacts degrade image quality and adversely affect data analysis. It is, thus, highly desired to detect and then exclude or potentially impute defective measurements prior to dMRI analysis. Our proposed method applies dMRI signal modeling in the SHORE basis and determines outliers based on the weighted model residuals. Signal imputation reconstructs corrupted and therefore discarded measurements from the sparse set of inliers. This approach allows for fast and robust correction of imaging artifacts in dMRI which is essential to estimate accurate and precise model parameters that reflect the diffusive transport of water molecules and the underlying microstructural environment in brain tissue.Die diffusionsgewichtete Magnetresonanztomographie (dMRT) ist ein einzigartiges MRTBildgebungsverfahren, um die Diffusionsbewegung von Wassermolekülen in biologischem Gewebe zu messen. Aufgrund der Möglichkeit Schichtbilder nicht invasiv aufzunehmen und das lebende menschliche Gehirn im Submillimeter-Bereich zu untersuchen, ist die dMRT ein häufig verwendetes Bildgebungsverfahren in klinischen und biomedizinischen Studien zur Erforschung der komplexen mikrostrukturellen Architektur des Gehirns. In den letzten Jahrzehnten wurden große prospektive Kohortenstudien angelegt, um neue Einblicke in die Entwicklung und den Verlauf von Gehirnkrankheiten über die Lebenspanne zu erhalten und um Biomarker zur Krankheitserkennung und -vorbeugung zu bestimmen. Um durch die Verwendung unterschiedlicher MRT-Verfahren verschiedenartige Schichtbildaufnahmen des Gehirns zu ermöglich, müssen Scanzeiten typischerweise stark begrenzt werden. Dennoch streben Populationsstudien die Anwendung von fortschrittlichen und daher zeitintensiven dMRT-Protokollen an, um Bilddaten in hoher Qualität und mit großem Potential für zukünftige Analysen zu akquirieren. Um eine zeiteffizente und gleichzeitig vielseitige Diffusionsbildgebung zu ermöglichen, leistet diese Dissertation Beiträge zur Untersuchung von Beschleunigungsverfahren für die Bildgebung mittels diffusion spectrum imaging (DSI). DSI ist ein fortschrittliches dMRT-Verfahren, das Bilddaten mit hoher intra-voxel Auflösung der Gewebestruktur erhebt. Werden modernste Verfahren zur parallelen MRT-Bildgebung mit der compressed sensing (CS) Theorie kombiniert, ermöglicht dies eine Beschleunigung der räumliche Kodierung und der Diffusionskodierung in der dMRT. Dadurch können die ansonsten langen Aufnahmezeiten für DSI erheblich reduziert werden. In dieser Arbeit werden zuerst geeigenete Strategien zur Abtastung des q-space sowie Basisfunktionen untersucht, welche die Anforderungen der CS-Theorie für eine korrekte Signalrekonstruktion der dünnbesetzten DSI-Daten erfüllen. Neue 3D-Verteilungen von Messpunkten im q-space werden für die Verwendung in CS-DSI untersucht. Außerdem wird konventionell auf der diskreten Fourier-Transformation basierendes CS-DSI zum ersten Mal mit einem CS-DSI Verfahren verglichen, welches kontinuierliche SHORE (simple harmonic oscillator based reconstruction and estimation) Basisfunktionen verwendet. Aufbauend auf diesen Ergebnissen wird ein CS-DSI-Protokoll zur Anwendung in einer prospektiven Kohortenstudie, der Rheinland Studie, vorgestellt. Eine Pilotstudie wurde entworfen und durchgeführt, um das CS-DSI-Protokoll im Vergleich mit modernster 3-shell-dMRT und mit dedizierten Protokollen für diffusion tensor imaging (DTI) und für das combined hindered and restricted model of diffusion (CHARMED) zu evaluieren. Populationsbildgebung erfordert Prozessierungsverfahren mit möglichst geringem Rechenaufwand, um große akquirierte Datenmengen in einem angemessenen Zeitrahmen zu verarbeiten und zu analysieren. Dafür wurde eine Pipeline zur automatisierten Verarbeitung von CS-DSI-Daten implementiert, welche sowohl eigenentwickelte als auch bereits existierende moderene Verarbeitungsprogramme enthält. Der letzte Beitrag dieser Arbeit ist eine neue Methode zur automatischen Detektion und Imputation von Signalabfall, welcher durch schnelle Bewegungen während der Diffusionskodierung in der dMRT entsteht. Bewegungen der Probanden während der dMRT-Aufnahme sind eine häufige Ursache für Bildfehler, vor allem in klinischen oder Populationsstudien mit Kindern, alten Menschen oder Patienten. Diese Artefakte vermindern die Datenqualität und haben einen negativen Einfluss auf die Datenanalyse. Daher ist es das Ziel, fehlerhafte Messungen vor der dMRI-Analyse zu erkennen und dann auszuschließen oder wenn möglich zu ersetzen. Die vorgestellte Methode verwendet die SHORE-Basis zur dMRT-Signalmodellierung und bestimmt Ausreißer mit Hilfe von gewichteten Modellresidualen. Die Datenimputation rekonstruiert die unbrauchbaren und daher verworfenen Messungen mit Hilfe der verbleibenden, dünnbesetzten Menge an Messungen. Dieser Ansatz ermöglicht eine schnelle und robuste Korrektur von Bildartefakten in der dMRT, welche erforderlich ist, um korrekte und präzise Modellparameter zu schätzen, die die Diffusionsbewegung von Wassermolekülen und die zugrundeliegende Mikrostruktur des Gehirngewebes reflektieren