Fine-granularity and spatially-adaptive regularization for projection-based image deblurring

Spatially Adaptive Regularization in Total Field Inversion for Quantitative Susceptibility Mapping

Adaptive Total Field Inversion is described for quantitative susceptibility mapping (QSM) reconstruction from total field data through a spatially adaptive suppression of shadow artifacts through spatially adaptive regularization. The regularization for shadow suppression consists of penalizing low-frequency components of susceptibility in regions of small susceptibility contrasts as estimated by R2∗ derived signal intensity. Compared with a conventional local field method and two previously proposed regularized total field inversion methods, improvements were demonstrated in phantoms and subjects without and with hemorrhages. This algorithm, named TFIR, demonstrates the lowest error in numerical and gadolinium phantom datasets. In COSMOS data, TFIR performs well in matching ground truth in high-susceptibility regions. For patient data, TFIR comes close to meeting the quality of the reference local field method and outperforms other total field techniques in both clinical scores and shadow reduction.

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TFIR's adaptive regularization obtains magnetic susceptibility from magnetic field

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TFIR has low artifact incidence on both quantitative and clinical scores

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The error for TFIR is low on various numerical and ground truth tests

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Clinical applications for TFIR include hemorrhages and whole head mapping

A general framework for regularized, similarity-based image restoration

Any image can be represented as a function defined on a weighted graph, in which the underlying structure of the image is encoded in kernel similarity and associated Laplacian matrices. In this paper, we develop an iterative graph-based framework for image restoration based on a new definition of the normalized graph Laplacian. We propose a cost function, which consists of a new data fidelity term and regularization term derived from the specific definition of the normalized graph Laplacian. The normalizing coefficients used in the definition of the Laplacian and associated regularization term are obtained using fast symmetry preserving matrix balancing. This results in some desired spectral properties for the normalized Laplacian such as being symmetric, positive semidefinite, and returning zero vector when applied to a constant image. Our algorithm comprises of outer and inner iterations, where in each outer iteration, the similarity weights are recomputed using the previous estimate and the updated objective function is minimized using inner conjugate gradient iterations. This procedure improves the performance of the algorithm for image deblurring, where we do not have access to a good initial estimate of the underlying image. In addition, the specific form of the cost function allows us to render the spectral analysis for the solutions of the corresponding linear equations. In addition, the proposed approach is general in the sense that we have shown its effectiveness for different restoration problems, including deblurring, denoising, and sharpening. Experimental results verify the effectiveness of the proposed algorithm on both synthetic and real examples.

Multi-compartment T2 relaxometry using a spatially constrained multi-Gaussian model

The brain's myelin content can be mapped by T2-relaxometry, which resolves multiple differentially relaxing T2 pools from multi-echo MRI. Unfortunately, the conventional fitting procedure is a hard and numerically ill-posed problem. Consequently, the T2 distributions and myelin maps become very sensitive to noise and are frequently difficult to interpret diagnostically. Although regularization can improve stability, it is generally not adequate, particularly at relatively low signal to noise ratio (SNR) of around 100-200. The purpose of this study was to obtain a fitting algorithm which is able to overcome these difficulties and generate usable myelin maps from noisy acquisitions in a realistic scan time. To this end, we restrict the T2 distribution to only 3 distinct resolvable tissue compartments, modeled as Gaussians: myelin water, intra/extra-cellular water and a slow relaxing cerebrospinal fluid compartment. We also impose spatial smoothness expectation that volume fractions and T2 relaxation times of tissue compartments change smoothly within coherent brain regions. The method greatly improves robustness to noise, reduces spatial variations, improves definition of white matter fibers, and enhances detection of demyelinating lesions. Due to efficient design, the additional spatial aspect does not cause an increase in processing time. The proposed method was applied to fast spiral acquisitions on which conventional fitting gives uninterpretable results. While these fast acquisitions suffer from noise and inhomogeneity artifacts, our preliminary results indicate the potential of spatially constrained 3-pool T2 relaxometry.

Bayesian algorithm using spatial priors for multiexponential T₂ relaxometry from multiecho spin echo MRI

Multiexponential T₂ relaxometry is a powerful research tool for detecting brain structural changes due to demyelinating diseases such as multiple sclerosis. However, because of unusually high signal-to-noise ratio requirement compared with other MR modalities and ill-posedness of the underlying inverse problem, the T₂ distributions obtained with conventional approaches are frequently prone to noise effects. In this article, a novel multivoxel Bayesian algorithm using spatial prior information is proposed. This prior takes into account the expectation that volume fractions and T₂ relaxation times of tissue compartments change smoothly within coherent brain regions. Three-dimensional multiecho spin echo MRI data were collected from five healthy volunteers at 1.5 T and myelin water fraction maps were obtained using the conventional and proposed algorithms. Compared with the conventional method, the proposed method provides myelin water fraction maps with improved depiction of brain structures and significantly lower coefficients of variance in white matter.