Conference Paper

# K-SVD for HARDI denoising

Lab. of Neuro Imaging, Univ. of California, Los Angeles, CA, USA

DOI: 10.1109/ISBI.2011.5872757 Conference: Biomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium on Source: IEEE Xplore

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**ABSTRACT:**Real-world experiments are becoming increasingly more complex, needing techniques capable of tracking this complexity. Signal based measurements are often used to capture this complexity, where a signal is a record of a sample’s response to a parameter (e.g. time, displacement, voltage, wavelength) that is varied over a range of values. In signals the responses at each value of the varied parameter are related to each other, depending on the composition or state sample being measured. Since a signal contains multiple information points, they have rich information content but generally complex to apprehend. Multivariate analysis (MA) has profoundly transformed their analysis by allowing gross simplification of the tangled web of variation. In addition MA has also provided the advantage of being much more robust to the influence of noise than univariate methods of analysis. In recent years there has been a growing awareness that the nature of the multivariate methods allows exploitation of its benefits for purposes other than data analysis, such as pre-processing of signals with the aim of eliminating irrelevant variations prior to analysis of the signal of interest. It has been shown that exploiting multivariate data reduction in an appropriate way can allow high fidelity denoising (removal of irreproducible non-signal), consistent and reproducible noise-insensitive correction of baseline distortions (removal of reproducible non-signals), accurate elimination of interfering signals (removal of reproducible but unwanted signals) and the standardisation of signal amplitude fluctuations. At present the field is relatively small but the possibilities for much wider application are considerable. Where signal properties are suitable for MA (such as the signal being stationary along the x-axis), these signal based corrections have the potential to be highly reproducible, and highly adaptable and are applicable in situations where the data is noisy or where the variations in the signals can be complex. As science seeks to probe datasets in less and less tightly controlled situations the ability to provide high-fidelity corrections in a very flexible manner is becoming more critical and multivariate based signal processing has the potential to provide many solutions. L'analyse multivariée, dont l'analyse en composantes principales (ACP), a transformé, dans des contextes concrets, l'étude de mesures complexes, formées de signaux chargés d'informations. Si la réduction de dimension permet de simplifier grossièrement un enchevêtrement de variations multidimensionnelles, elle est également plus robuste aux perturbations que les méthodes d'analyse univariées. Plus récemment, il est apparu que les propriétés des méthodes multivariées les rendaient propices à d'autres usages que statistiques, comme le traitement des signaux pour l'élimination des variations/fluctuations non pertinentes pour une analyse ultérieure. Il a été montré que l'exploitation spécifique de la réduction de dimension permet un débruitage précis (suppression de "non-signaux/perturbation" non reproductibles), la soustraction fiable et consistante de la ligne de base (suppression de "non-signaux/perturbation" reproductibles), l'éminination d'interférences (suppression de "signaux" reproductibles et inutiles), ainsi que la standardisation des fluctuations d'amplitude des signaux. Si ce champ d'investigation est encore restreint, les possibilités de diffusion de ses applications sont considérables. En effet, ces améliorations, intrinsèquement liées aux signaux eux-mêmes, sont hautement reproductibles entre les répétitions, possèdent une grande capacité d'adaptation et d'application à des situations de bruit, ou de variations complexes dans les signaux. Alors que les disciplines scientifiques sondent des volumes de données toujours plus volumineux, dans des situations de moins en moins étroitement contrôlées, la capacité à apporter des corrections/améliorations précises/haute résolutions, de manière flexible, devient de plus en plus critique. Aussi les traitements de signaux multivariés offrent un éventail de solutions potentiellement très large.Oil & Gas Sciences and Technology. 01/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**We present a novel multi-shell position orientation adaptive smoothing (msPOAS) method for diffusion-weighted magnetic resonance data. Smoothing in voxel and diffusion gradient space is embedded in an iterative adaptive multiscale approach. The adaptive character avoids blurring of the inherent structures and preserves discontinuities. The simultaneous treatment of all q-shells improves the stability compared to single shell approaches such as the original POAS method. The msPOAS implementation simplifies and speeds up calculations, compared to POAS, facilitating its practical application. Simulations and heuristics support the face validity of the technique and its rigorousness. The characteristics of msPOAS were evaluated on single and multi-shell diffusion data of the human brain. Significant reduction in noise while preserving the fine structure was demonstrated for diffusion weighted images, standard DTI analysis and advanced diffusion models such as NODDI. MsPOAS effectively improves the poor signal-to-noise ratio in highly diffusion weighted multi-shell diffusion data, which is required by recent advanced diffusion micro-structure models. We demonstrate the superiority of the new method compared to other advanced denoising methods.NeuroImage 07/2014; 95:90-105. · 6.25 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Diffusion Spectrum Imaging (DSI) reveals detailed local diffusion properties at the expense of substantially long imaging times. It is possible to accelerate acquisition by undersampling in q-space, followed by image reconstruction that exploits prior knowledge on the diffusion probability density functions (pdfs). Previously proposed methods impose this prior in the form of sparsity under wavelet and total variation (TV) transforms, or under adaptive dictionaries that are trained on example datasets to maximize the sparsity of the representation. These compressed sensing (CS) methods require full-brain processing times on the order of hours using Matlab running on a workstation. This work presents two dictionary-based reconstruction techniques that use analytical solutions, and are two orders of magnitude faster than the previously proposed dictionary-based CS approach. The first method generates a dictionary from the training data using Principal Component Analysis (PCA), and performs the reconstruction in the PCA space. The second proposed method applies reconstruction using pseudoinverse with Tikhonov regularization with respect to a dictionary. This dictionary can either be obtained using the KSVD algorithm, or it can simply be the training dataset of pdfs without any training. All of the proposed methods achieve reconstruction times on the order of seconds per imaging slice, and have reconstruction quality comparable to that of dictionarybased CS algorithm.IEEE transactions on medical imaging. 07/2013;

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