Abstract. In his original paper on random forests, Breiman proposed two different decision tree ensembles: one generated from "orthogonal" trees with thresholds on individual features in every split, and one from "oblique" trees separating the feature space by randomly oriented hyperplanes. In spite of a rising interest in the random forest framework, however, ensembles built from orthogonal trees (RF) have gained most, if not all, attention so far.In the present work we propose to employ "oblique" random forests (oRF) built from multivariate trees which explicitly learn optimal split directions at internal nodes using linear discriminative models, rather than using random coefficients as the original oRF. This oRF outperforms RF, as well as other classifiers, on nearly all data sets but those with discrete factorial features. Learned node models perform distinctively better than random splits. An oRF feature importance score shows to be preferable over standard RF feature importance scores such as Gini or permutation importance. The topology of the oRF decision space appears to be smoother and better adapted to the data, resulting in improved generalization performance. Overall, the oRF propose here may be preferred over standard RF on most learning tasks involving numerical and spectral data.

Purpose We introduce and validate a scalable retrospective motion correction technique for brain imaging that incorporates a machine learning component into a model‐based motion minimization. Methods A convolutional neural network (CNN) trained to remove motion artifacts from 2D T2‐weighted rapid acquisition with refocused echoes (RARE) images is introduced into a model‐based data‐consistency optimization to jointly search for 2D motion parameters and the uncorrupted image. Our separable motion model allows for efficient intrashot (line‐by‐line) motion correction of highly corrupted shots, as opposed to previous methods which do not scale well with this refinement of the motion model. Final image generation incorporates the motion parameters within a model‐based image reconstruction. The method is tested in simulations and in vivo motion experiments of in‐plane motion corruption. Results While the convolutional neural network alone provides some motion mitigation (at the expense of introduced blurring), allowing it to guide the iterative joint‐optimization both improves the search convergence and renders the joint‐optimization separable. This enables rapid mitigation within shots in addition to between shots. For 2D in‐plane motion correction experiments, the result is a significant reduction of both image space root mean square error in simulations, and a reduction of motion artifacts in the in vivo motion tests. Conclusion The separability and convergence improvements afforded by the combined convolutional neural network+model‐based method shows the potential for meaningful postacquisition motion mitigation in clinical MRI.

To demonstrate a navigator/tracking-free retrospective motion estimation technique that facilitates clinically acceptable reconstruction time. Methods: Scout accelerated motion estimation and reduction (SAMER) uses a single 3-5 s, low-resolution scout scan and a novel sequence reordering to independently determine motion states by minimizing the data-consistency error in a SENSE plus motion forward model. This eliminates time-consuming alternating optimization as no updates to the imaging volume are required during the motion estimation. The SAMER approach was assessed quantitatively through extensive simulation and was evaluated in vivo across multiple motion scenarios and clinical imaging contrasts. Finally, SAMER was synergistically combined with advanced encoding (Wave-CAIPI) to facilitate rapid motion-free imaging. Results: The highly accelerated scout provided sufficient information to achieve accurate motion trajectory estimation (accuracy ~0.2 mm or degrees). The novel sequence reordering improved the stability of the motion parameter estimation and image reconstruction while preserving the clinical imaging contrast. Clinically acceptable computation times for the motion estimation (~4 s/shot) are demonstrated through a fully separable (non-alternating) motion search across the shots. Substantial artifact reduction was demonstrated in vivo as well as corresponding improvement in the quantitative error metric. Finally, the extension of SAMER to Wave-encoding enabled rapid high-quality imaging at up to R = 9-fold acceleration. Conclusion: SAMER significantly improved the computational scalability for retrospective motion estimation and correction.

The pursuit of ever higher field strengths and faster data acquisitions has led to the construction of coil arrays with high numbers of elements. With the sensitivity encoding (SENSE) technique, it has been shown that the sensitivity of those elements can be used for spatial image encoding. Here, a proofof-principle is presented of a method that can be considered an extreme case of the SENSE approach, completely abstaining from using encoding gradients. The resulting sensitivity encoded free-induction decay (FID) data are then not used for imaging, but for determining B 0 field inhomogeneity distribution. The method has therefore been termed "SENSE shimming" (SSH Although modern MR scanners produce highly homogeneous fields, this is often more than counterbalanced by the increased susceptibility effects at field strengths of 3T and higher. Therefore, today's scanners are equipped with a set of shim coils that can be used for reversing the effects of the subject-induced inhomogeneities. Strategies for finding optimal field correction parameters, called "shimming," can be classified into static and dynamic, depending on whether they are used before or during the acquisition. Among the most popular static shimming solutions are the line-shape characterization of free-induction decays (FIDs), along with stimulated-echo acquisition mode (STEAM)-based methods (1), projections along selected diagonals (2), and 2D and 3D field maps (3). For the dynamic case, methods acquiring a limited number of projections are popular (e.g., Refs. 4 -6) with every method having a tradeoff between acquisition speed and accuracy.For imaging, the concept of reducing acquisition time by using coil arrays was introduced with the well-known simultaneous acquisition of spatial harmonics (SMASH) (7) and SENSE (8) techniques, where the spatially-varying sensitivities of the individual coil elements are used as additional spatial encoding information. This allows the reduction of the amount of needed phase encoding steps while usually keeping the k-space extent unchanged; thus, the acquisition time can be shortened by a reduction factor R, with the number of coil elements being the theoretical maximum. The resulting foldovers are then resolved using previously measured sensitivities.The method presented here uses a special case of this setup: we abstain completely from using traditional frequency and phase encoding, thus yielding a foldover of all pixels into one; i.e., observing a single discrete point on an FID, which we will call the "FID point" throughout this work. We then address the question, as to whether a limited number of FID points seen by the elements of a coil array, along with the respective sensitivities, can be used to assess B 0 field inhomogeneities. The inhomogeneities are described using reasonable model functions, for example a spherical harmonic set, with a number N inhom of coefficients. It is clear that for the described method the number of coil elements, N coil , will be a theoretical upper limit for N inhom ; however,...

BACKGROUND AND PURPOSE: Volumetric brain MR imaging typically has long acquisition times. We sought to evaluate an ultrafast MPRAGE sequence based on Wave-CAIPI (Wave-MPRAGE) compared with standard MPRAGE for evaluation of regional brain tissue volumes. MATERIALS AND METHODS: We performed scan-rescan experiments in 10 healthy volunteers to evaluate the intraindividual variability of the brain volumes measured using the standard and Wave-MPRAGE sequences. We then evaluated 43 consecutive patients undergoing brain MR imaging. Patients underwent 3T brain MR imaging, including a standard MPRAGE sequence (acceleration factor [R] ¼ 2, acquisition time [TA] ¼ 5.2 minutes) and an ultrafast Wave-MPRAGE sequence (R ¼ 9, TA ¼ 1.15 minutes for the 32-channel coil; R ¼ 6, TA ¼ 1.75 minutes for the 20-channel coil). Automated segmentation of regional brain volume was performed. Two radiologists evaluated regional brain atrophy using semiquantitative visual rating scales. RESULTS: The mean absolute symmetrized percent change in the healthy volunteers participating in the scan-rescan experiments was not statistically different in any brain region for both the standard and Wave-MPRAGE sequences. In the patients undergoing evaluation for neurodegenerative disease, the Dice coefficient of similarity between volumetric measurements obtained from standard and Wave-MPRAGE ranged from 0.86 to 0.95. Similarly, for all regions, the absolute symmetrized percent change for brain volume and cortical thickness showed ,6% difference between the 2 sequences. In the semiquantitative visual comparison, the differences between the 2 radiologists' scores were not clinically or statistically significant. CONCLUSIONS: Brain volumes estimated using ultrafast Wave-MPRAGE show low intraindividual variability and are comparable with those estimated using standard MPRAGE in patients undergoing clinical evaluation for suspected neurodegenerative disease. ABBREVIATIONS: ASPC ¼ absolute symmetrized percent change; VBM ¼ voxel-based morphometry V olumetric brain MR imaging is widely used in clinical and research settings for the evaluation of patients with suspected neurodegenerative disease. Regional patterns of tissue loss aid in generating a differential diagnosis and assessing prognosis, and the identification of regional volume loss is increasingly used as an outcome measure in trials of potentially disease-modifying therapies. 1-4 Of particular value, the T1-weighted MPRAGE sequence provides excellent spatial resolution and tissue contrast 5 but has long acquisition times due to the need to encode a large number of k-space lines and the added TI required to achieve the prepared T1-weighted contrast. Unfortunately, long