Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

The sparsity which is implicit in MR images is exploited to significantly undersample k -space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressedsensing, images with a sparse representation can be recovered from randomly undersampled k -space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noise-like interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudo-random variable-density undersampling of phase-encodes. The reconstruction is performed by minimizing the 1 norm of a transformed image, subject to data

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Sparse MRI: The application of compressed sensing for rapid MR imaging.

The invention relates to a method of parallel imaging for obtaining images by means of magnetic resonance (MR). The method includes the simultaneous measurement of sets of MR singals by an array of receiver coils, and the reconstruction of individual receiver coil images from the sets of MR signals. In order to reduce the acquisition time, the distance between adjacent phase encoding lines in k-space is increased, compared to standard Fourier imaging, by a non-integer factor smaller than the number of receiver coils. This undersampling gives rise to aliasing artifacts in the individual receiver coil images. An unaliased final image with the same field of view as in standard Fourier imaging is formed from a combination of the individual receiver coil images whereby account is taken of the mutually different spatial sensitivities of the receiver coils at the positions of voxels which in the receiver coil images become superimposed by aliasing. This requires the solution of a linear equation by means of the generalised inverse of a sensitivity matrix. The reduction of the number of phase encoding lines by a non-integer factor compared to standard Fourier imaging provides that different numbers of voxels become superimposed (by aliasing) in different regions of the receiver coil images. This effect can be exploited to shift residual aliasing artifacts outside the area of interest.

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SENSE: Sensitivity Encoding for fast MRI

In this study, a novel partially parallel acquisition (PPA) method is presented which can be used to accelerate image acquisition using an RF coil array for spatial encoding. This technique, GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) is an extension of both the PILS and VD-AUTO-SMASH reconstruction techniques. As in those previous methods, a detailed, highly accurate RF field map is not needed prior to reconstruction in GRAPPA. This information is obtained from several k-space lines which are acquired in addition to the normal image acquisition. As in PILS, the GRAPPA reconstruction algorithm provides unaliased images from each component coil prior to image combination. This results in even higher SNR and better image quality since the steps of image reconstruction and image combination are performed in separate steps. After introducing the GRAPPA technique, primary focus is given to issues related to the practical implementation of GRAPPA, including the reconstruction algorithm as well as analysis of SNR in the resulting images. Finally, in vivo GRAPPA images are shown which demonstrate the utility of the technique.

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Generalized autocalibrating partially parallel acquisitions (GRAPPA).

Functional magnetic resonance imaging (fMRI) is currently the mainstay of neuroimaging in cognitive neuroscience. Advances in scanner technology, image acquisition protocols, experimental design, and analysis methods promise to push forward fMRI from mere cartography to the true study of brain organization. However, fundamental questions concerning the interpretation of fMRI data abound, as the conclusions drawn often ignore the actual limitations of the methodology. Here I give an overview of the current state of fMRI, and draw on neuroimaging and physiological data to present the current understanding of the haemodynamic signals and the constraints they impose on neuroimaging data interpretation.

What we can do and what we cannot do with fMRI

The utilization of parallel imaging permits increased MR acquisition speed and efficiency; however, parallel MRI usually leads to a deterioration in the signal-to-noise ratio when compared with otherwise equivalent unaccelerated acquisitions. At high accelerations, the parallel image reconstruction matrix tends to become dominated by one principal component. This has been utilized to enable substantial reductions in g-factor-related noise. A previously published technique achieved noise reductions via a computationally intensive search for multiples of the dominant singular vector which, when subtracted from the image, minimized joint entropy between the accelerated image and a reference image. We describe a simple algorithm that can accomplish similar results without a time-consuming search. Significant reductions in g-factor-related noise were achieved using this new algorithm with in vivo acquisitions at 1.5 T with an eight-element array.

A simple noniterative principal component technique for rapid noise reduction in parallel MR images

Magnetic Resonance Imaging (MRI) is considered the gold standard of medical imaging because of the excellent soft-tissue contrast exhibited in the images reconstructed by the MRI pipeline, which in-turn enables the human radiologist to discern many pathologies easily. More recently, Deep Learning (DL) models have also achieved state-of-the-art performance in diagnosing multiple diseases using these reconstructed images as input. However, the image reconstruction process within the MRI pipeline, which requires the use of complex hardware and adjustment of a large number of scanner parameters, is highly susceptible to noise of various forms, resulting in arbitrary artifacts within the images. Furthermore, the noise distribution is not stationary and varies within a machine, across machines, and patients, leading to varying artifacts within the images. Unfortunately, DL models are quite sensitive to these varying artifacts as it leads to changes in the input data distribution between the training and testing phases. The lack of robustness of these models against varying artifacts impedes their use in medical applications where safety is critical. In this work, we focus on improving the generalization performance of these models in the presence of multiple varying artifacts that manifest due to the complexity of the MR data acquisition. In our experiments, we observe that Batch Normalization, a widely used technique during the training of DL models for medical image analysis, is a significant cause of performance degradation in these changing environments. As a solution, we propose to use other normalization techniques, such as Group Normalization and Layer Normalization (LN), to inject robustness into model performance against varying image artifacts. Through a systematic set of experiments, we show that GN and LN provide better accuracy for various MR artifacts and distribution shifts.

Daniel K. Sodickson

Papers

A simple noniterative principal component technique for rapid noise reduction in parallel MR images

On Sensitivity and Robustness of Normalization Schemes to Input Distribution Shifts in Automatic MR Image Diagnosis