Magnetic resonance imaging (MRI) based T1 mapping allows spatially resolved quantification of the tissue-dependent spin-lattice relaxation time constant T1, which is a potential biomarker of various neurodegenerative diseases, including Multiple Sclerosis, Alzheimer disease, and Parkinson’s disease . In conventional T1 MR relaxometry, a quantitative T1 map is obtained from a series of T1-weighted MR images. Acquiring such a series, however, is time consuming. This has sparked the development of more efficient T1 mapping methods, one of which is a super-resolution reconstruction (SRR) framework in which a set of low resolution (LR) T1-weighted images is acquired and from which a high resolution (HR) T1 map is directly estimated. In this paper, the SRR T1 mapping framework is augmented with motion estimation. That is, motion between the acquisition of the LR T1-weighted images is modeled and the motion parameters are estimated simultaneously with the T1 parameters. Based on Monte Carlo simulation experiments, we show that such an integrated motion/relaxometry estimation approach yields more accurate T1 maps compared to a previously reported SRR based T1 mapping approach.

In quantitative magnetic resonance mapping, the variable flip angle (VFA) steady state spoiled gradient recalled echo (SPGR) imaging technique is popular as it provides a series of high resolution weighted images in a clinically feasible time. Fast, linear methods that estimate maps from these weighted images have been proposed, such as DESPOT1 and iterative re-weighted linear least squares. More accurate, non-linear least squares (NLLS) estimators are in play, but these are generally much slower and require careful initialization. In this paper, we present NOVIFAST, a novel NLLS-based algorithm specifically tailored to VFA SPGR mapping. By exploiting the particular structure of the SPGR model, a computationally efficient, yet accurate and precise map estimator is derived. Simulation and in vivo human brain experiments demonstrate a twenty-fold speed gain of NOVIFAST compared with conventional gradient-based NLLS estimators while maintaining a high precision and accuracy. Moreover, NOVIFAST is eight times faster than the efficient implementations of the variable projection (VARPRO) method. Furthermore, NOVIFAST is shown to be robust against initialization.

In quantitative MR T1mapping, the spin-lattice relaxation time T1of tissues is estimated from a series of T1-weighted images. As the T1estimation is a voxel-wise estimation procedure, correct spatial alignment of the T1-weighted images is crucial. Conventionally, the T1-weighted images are first registered based on a general-purpose registration metric, after which the T1map is estimated. However, as demonstrated in this paper, such a two-step approach leads to a bias in the final T1map. In our work, instead of considering motion correction as a preprocessing step, we recover the motion-free T1map using a unified estimation approach. In particular, we propose a unified framework where the motion parameters and the T1map are simultaneously estimated with a Maximum Likelihood (ML) estimator. With our framework, the relaxation model, the motion model as well as the data statistics are jointly incorporated to provide substantially more accurate motion and T1parameter estimates. Experiments with realistic Monte Carlo simulations show that the proposed unified ML framework outperforms the conventional two-step approach as well as state-of-the-art model-based approaches, in terms of both motion and T1map accuracy and mean-square error. Furthermore, the proposed method was additionally validated in a controlled experiment with real T1-weighted data and with two in vivo human brain T1-weighted data sets, showing its applicability in real-life scenarios.

An important factor influencing the quality of magnetic resonance (MR) images is the reconstruction method that is employed, and specifically, the type of prior knowledge that is exploited during reconstruction. In this work, we introduce a new type of prior knowledge, partial discreteness (PD), where a small number of regions in the image are assumed to be homogeneous and can be well represented by a constant magnitude. In particular, we mathematically formalize the partial discreteness property based on a Gaussian Mixture Model (GMM) and derive a partial discreteness image representation that characterizes the salient features of partially discrete images: a constant intensity in homogeneous areas and texture in heterogeneous areas. The partial discreteness representation is then used to construct a novel prior dedicated to the reconstruction of partially discrete MR images. The strength of the proposed prior is demonstrated on various simulated and real k-space data-based experiments with partially discrete images. Results demonstrate that the PD algorithm performs competitively with state-of-the-art reconstruction methods, being flexible and easy to implement.

In magnetic resonance imaging the spin-lattice relaxation time (T1) of tissues is estimated from a set of T1-weighted images. As the T1estimation is a voxel-wise estimation, correct alignment of the T1-weighted images is crucial for T1mapping. Therefore, to correct for motion, the T1-weighted images are often registered prior to the T1estimation. This two-step approach, however, does not provide an accurate motion detection due to the high dynamic contrast changes in the series of images. Moreover, interpolation effects during registration, propagate to the T1estimation. In this work, we propose a unified approach, where the motion estimation is integrated into the T1estimation procedure. The motion model parameters and T1parameters are jointly estimated using a Maximum Likelihood (ML) approach. Results on simulation and real data experiments show a substantial improvement in the precision and accuracy of the estimated T1map compared to the conventional two-step approach.

In Magnetic Resonance (MR) image reconstruction, under-sampled data sets lead to ill-posed reconstruction problems. To regularize these problems, prior knowledge is commonly exploited. In this work, we introduce a new type of prior knowledge, partial discreteness, where part of the image is assumed to be homogeneous and can be well represented by a constant magnitude. We propose a novel reconstruction algorithm that incorporates this prior knowledge by iteratively enforcing discreteness through Bayesian segmentation regularization. Results on simulated MR images of breast implants and MR angiography images evidence the benefits of the partial discreteness prior when compared to state-of-the-art reconstruction methods.

Ultrasound (US) imaging exhibits considerable difficulties for medical visual inspection and for development of automatic analysis methods due to speckle, which negatively affects the perception of tissue boundaries and the performance of automatic segmentation methods. With the aim of alleviating the effect of speckle, many filtering techniques are usually considered as a preprocessing step prior to automatic analysis methods or visual inspection. Most of the state-of-the-art filters try to reduce the speckle effect without considering its relevance for the characterization of tissue nature. However, the speckle phenomenon is the inherent response of echo signals in tissues and can provide important features for clinical purposes. This loss of information is even magnified due to the iterative process of some speckle filters, e.g., diffusion filters, which tend to produce over-filtering because of the progressive loss of relevant information for diagnostic purposes during the diffusion process. In this paper, we propose an anisotropic diffusion filter with a probabilistic-driven memory mechanism to overcome the over-filtering problem by following a tissue selective philosophy. In particular, we formulate the memory mechanism as a delay differential equation for the diffusion tensor whose behavior depends on the statistics of the tissues, by accelerating the diffusion process in meaningless regions and including the memory effect in regions where relevant details should be preserved. Results both in synthetic and real US images support the inclusion of the probabilistic memory mechanism for maintaining clinical relevant structures, which are removed by the state-of-the-art filters.