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Register a new userLow-Rank and Framelet Based Sparsity Decomposition for Interventional MRI Reconstruction
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Objective: Interventional MRI (i-MRI) is crucial for MR image-guided therapy. Current image reconstruction methods for dynamic MR imaging are mostly retrospective that may not be suitable for i-MRI in real-time. Therefore, an algorithm to reconstruct images without a temporal pattern as in dynamic imaging is needed for i-MRI. Methods: We proposed a low-rank and sparsity (LS) decomposition algorithm with framelet transform to reconstruct the interventional feature with a high temporal resolution. Different from the existing LS based algorithm, we utilized the spatial sparsity of both the low-rank and sparsity components. We also used a primal dual fixed point (PDFP) method for optimization of the objective function to avoid solving sub-problems. Intervention experiments with gelatin and brain phantoms were carried out for validation. Results: The LS decomposition with framelet transform and PDFP could provide the best reconstruction performance compared with those without. Satisfying reconstruction results were obtained with only 10 radial spokes for a temporal resolution of 60 ms. Conclusion and Significance: The proposed method has the potential for i-MRI in many different application scenarios.
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In radial fast spin-echo MRI, a set of overlapping spokes with an inconsistent T2 weighting is acquired, which results in an averaged image contrast when employing conventional image reconstruction techniques. This work demonstrates that the problem may be overcome with the use of a dedicated reconstruction method that further allows for T2 quantification by extracting the embedded relaxation information. Thus, the proposed reconstruction method directly yields a spin-density and relaxivity map from only a single radial data set. The method is based on an inverse formulation of the problem and involves a modeling of the received MRI signal. Because the solution is found by numerical optimization, the approach exploits all data acquired. Further, it handles multi-coil data and optionally allows for the incorporation of additional prior knowledge. Simulations and experimental results for a phantom and human brain in vivo demonstrate that the method yields spin-density and relaxivity maps that are neither affected by the typical artifacts from TE mixing, nor by streaking artifacts from the incomplete k-space coverage at individual echo times.
The combination of the sparse sampling and the low-rank structured matrix reconstruction has shown promising performance, enabling a significant reduction of the magnetic resonance imaging data acquisition time. However, the low-rank structured approaches demand considerable memory consumption and are time-consuming due to a noticeable number of matrix operations performed on the huge-size block Hankel-like matrix. In this work, we proposed a novel framework to utilize the low-rank property but meanwhile to achieve faster reconstructions and promising results. The framework allows us to enforce the low-rankness of Hankel matrices constructing from 1D vectors instead of 2D matrices from 1D vectors and thus avoid the construction of huge block Hankel matrix for 2D k-space matrices. Moreover, under this framework, we can easily incorporate other information, such as the smooth phase of the image and the low-rankness in the parameter dimension, to further improve the image quality. We built and validated two models for parallel and parameter magnetic resonance imaging experiments, respectively. Our retrospective in-vivo results indicate that the proposed approaches enable faster reconstructions than the state-of-the-art approaches, e.g., about 8x faster than STDLRSPIRiT, and faithful removal of undersampling artifacts.
Purpose: To introduce, develop, and evaluate a novel denoising technique for diffusion MRI that leverages non-linear redundancy in the data to boost the SNR while preserving signal information. Methods: We exploit non-linear redundancy of the dMRI data by means of Kernel Principal Component Analysis (KPCA), a non-linear generalization of PCAto reproducing kernel Hilbert spaces. By mapping the signal to a high-dimensional space, better redundancy is achieved despite nonlinearities in the data thereby enabling better denoising than linear PCA. We implement KPCA with a Gaussian kernel, with parameters automatically selected from knowledge of the noise statistics, and validate it on realistic Monte-Carlo simulations as well as with in-vivo human brain submillimeter resolution dMRI data. We demonstrate KPCA denoising using multi-coil dMRI data also. Results: SNR improvements up to 2.7 X were obtained in real in-vivo datasets denoised with KPCA, in comparison to SNR gains of up to 1.8 X when using state-of-the-art PCA denoising, e.g., Marchenko- Pastur PCA (MPPCA). Compared to gold-standard dataset references created from averaged data, we showed that lower normalized root mean squared error (NRMSE) was achieved with KPCA compared to MPPCA. Statistical analysis of residuals shows that only noise is removed. Improvements in the estimation of diffusion model parameters such as fractional anisotropy, mean diffusivity, and fiber orientation distribution functions (fODFs)were demonstrated. Conclusion:Non-linear redundancy of the dMRI signal can be exploited with KPCA, which allows superior noise reduction/ SNR improvements than state-of-the-art PCA methods, without loss of signal information.
We propose LSDAT, an image-agnostic decision-based black-box attack that exploits low-rank and sparse decomposition (LSD) to dramatically reduce the number of queries and achieve superior fooling rates compared to the state-of-the-art decision-based methods under given imperceptibility constraints. LSDAT crafts perturbations in the low-dimensional subspace formed by the sparse component of the input sample and that of an adversarial sample to obtain query-efficiency. The specific perturbation of interest is obtained by traversing the path between the input and adversarial sparse components. It is set forth that the proposed sparse perturbation is the most aligned sparse perturbation with the shortest path from the input sample to the decision boundary for some initial adversarial sample (the best sparse approximation of shortest path, likely to fool the model). Theoretical analyses are provided to justify the functionality of LSDAT. Unlike other dimensionality reduction based techniques aimed at improving query efficiency (e.g, ones based on FFT), LSD works directly in the image pixel domain to guarantee that non-$ell_2$ constraints, such as sparsity, are satisfied. LSD offers better control over the number of queries and provides computational efficiency as it performs sparse decomposition of the input and adversarial images only once to generate all queries. We demonstrate $ell_0$, $ell_2$ and $ell_infty$ bounded attacks with LSDAT to evince its efficiency compared to baseline decision-based attacks in diverse low-query budget scenarios as outlined in the experiments.
A novel approach is presented for group statistical analysis of diffusion weighted MRI datasets through voxelwise Orientation Distribution Functions (ODF). Recent advances in MRI acquisition make it possible to use high quality diffusion weighted protocols (multi-shell, large number of gradient directions) for routine in vivo study of white matter architecture. The dimensionality of these data sets is however often reduced to simplify statistical analysis. While these approaches may detect large group differences, they do not fully capitalize on all acquired image volumes. Incorporation of all available diffusion information in the analysis however risks biasing the outcome by outliers. Here we propose a statistical analysis method operating on the ODF, either the diffusion ODF or fiber ODF. To avoid outlier bias and reliably detect voxelwise group differences and correlations with demographic or behavioral variables, we apply the Low-Rank plus Sparse (L + S) matrix decomposition on the voxelwise ODFs which separates the sparse individual variability in the sparse matrix S whilst recovering the essential ODF features in the low-rank matrix L. We demonstrate the performance of this ODF L + S approach by replicating the established negative association between global white matter integrity and physical obesity in the Human Connectome dataset. The volume of positive findings agrees with and expands on the volume found by TBSS, Connectivity based fixel enhancement and Connectometry. In the same dataset we further localize the correlations of brain structure with neurocognitive measures such as fluid intelligence and episodic memory. The presented ODF L + S approach will aid in the full utilization of all acquired diffusion weightings leading to the detection of smaller group differences in clinically relevant settings as well as in neuroscience applications.
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