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Parallel MR Image Reconstruction
Published in Joseph Suresh Paul, Raji Susan Mathew, Regularized Image Reconstruction in Parallel MRI with MATLAB®, 2019
Joseph Suresh Paul, Raji Susan Mathew
The scanning time can be reduced by an appropriate selection of the data acquisition mode and k-space sampling scheme. The k-space sampling trajectory refers to the path used for navigating the sampling locations for data acquisition. This path illustrates the acquisition strategy and has direct influence on the artifacts induced. Therefore, the image reconstruction algorithm should be employed accordingly. Although, the most popular k-space trajectory is Cartesian, other trajectories that include radial, spiral, or rosette type patterns are also employed for data acquisition. The k-space coverage also varies depending on the sampling pattern. If multiple receiver coils and parallel imaging reconstruction techniques are used, the aliasing artifacts could be reduced effectively or even removed, thereby improving the actual scanning time. The imaging speed can be accelerated by acquiring only a portion of the k-space data. Using parallel imaging, k-space data acquisition can be accelerated by means of under-sampling. However, as the Nyquist sampling theorem is violated, aliasing artifacts are introduced in the images. The structure of the artifacts depends on the sampling trajectory used.
Biomedical Imaging Magnetic Resonance Imaging
Published in Lawrence S. Chan, William C. Tang, Engineering-Medicine, 2019
The spatial resolution of an MR image is determined by the extent of k-space coverage (i.e., kmax), while the field-of-view (FOV) is determined by the separation of neighboring k-space points (i.e., Δk). A higher spatial resolution can be achieved by extending k-space coverage farther. To adequately sample k-space without excessively long scan times, various fast imaging techniques have been developed. These techniques are primarily based on two strategies. The first strategy focuses on improving k-space sampling efficiency by traversing k-space rapidly. Examples of this strategy include fast spin echo (FSE; also known as RARE or turbo spin echo) (Hennig et al. 1986), echo planar imaging (EPI) (Mansfield 2007), spiral (Ahn et al. 1986), twisted projection imaging (TPI) (Boada et al. 1997), etc. The second strategy is to acquire less data than what is conventionally required, followed by novel image reconstruction algorithms utilizing other information (such as RF coil sensitivity and data sparsity) and/or advanced mathematical tools. A large number of techniques in this category have been developed, as exemplified by SMASH (Sodickson and Manning 1997), SENSE (Pruessmann et al. 1999), GRAPPA (Griswold et al. 2002), compressive sensing (Lustig et al. 2007), etc.
Magnetic Resonance Elastography
Published in Adil Al-Mayah, Biomechanics of Soft Tissues, 2018
The acquired RF signals are analyzed for frequency and phase, and the resulting data are stored as a spatial Fourier Transform, referred to as k-space, which at the end of data acquisition is converted into MR images through the application of an inverse Fourier Transform. The MR images are signal maps, for which the signal strength at a given location is a function of the local concentration of protons (proton density) and other parameters associated with the chemical environment of the protons (the longitudinal relaxation time, T1) and the interaction of neighboring spins (the transverse relaxation time, T2). The signal contrast between different tissue types in MR images is caused by variations in these properties, and the pulse sequences are varied to emphasize different contrasts.
On image restoration from random sampling noisy frequency data with regularization
Published in Inverse Problems in Science and Engineering, 2019
In many engineering configurations, instead of the spatial noisy data for each pixel , the practical measurement data may be the incomplete frequency data, which are specified at a finite number of discrete frequencies within some band-limited interval. For example, in magnetic resonance imaging (MRI), the data collected by an MR scanner are, roughly speaking, in the frequency domain (called K-space data) rather than in the spatial domain. One of the main stage for MRI is the K-space data acquisition. In this stage, energy from a radio frequency pulse is directed to a small section of the targeted anatomy at a time. As a result, the protons within that area are forced to spin in a certain frequency and get aligned to the direction of the magnet. Upon stopping the radio frequency, the physical system gets back to its normal state and releases energy that is then recorded for analysis. This process is repeated until enough data are collected for reconstructing an image of high quality in the second stage. For more details about how MRI system works, see [5] and the references therein. For this configuration, the data-fitting term in (1) should be replaced by , where is the discrete Fourier transform converting the spatial matrix into frequency matrix , while is a sampling matrix extracting the incomplete frequency data from full relatively noisy frequency data .