Generalized SMASH imaging

Abstract

A generalized parallel imaging method has been developed that uses coil profiles to generate missing k-space lines. The proposed method is an extension of SMASH, which uses linear combinations of coil sensitivity profiles to synthesize spatial harmonics. In the generalized SMASH approach described here, coil sensitivity profiles are represented directly in the Fourier domain to provide a general description of the spatial properties of the coils. This removes restrictions imposed by conventional SMASH, so that the choice and position of the receiver coils can be made on the basis of sensitivity to the volume of interest rather than suitability for constructing spatial harmonics. Generalized SMASH also intrinsically allows the freedom to accommodate acquisitions with uniform or nonuniform k-space sampling. Parallel imaging makes use of spatial sensitivity differences between individual coils in an array to partially replace gradient encoding during image acquisition. This reduces acquisition times by decreasing the number of phase encoded lines of k-space that must be acquired. There are three implementations of parallel imaging reported in the literature, known as SENSE (1-4), SMASH (5-7), and SPACE-RIP (8). All these methods require information about the coil sensitivity profiles (reference data), which is used to regenerate a full image dataset from a subsampled k-space acquisition (target data). The reference data is usually obtained as a separate acquisition, often with the subject in situ, although some implementations integrate the reference data acquisition with the target data acquisition (7,9). SENSE (1-4) operates in the image domain for both the target image data and the coil reference data. We use the name SENSE to refer to the Cartesian sampled form. The method used with other k-space trajectories will be referred to explicitly as non-Cartesian SENSE. In SENSE, the target data is acquired with a reduced field of view (FOV), which results in aliasing, and is then unfolded to the full FOV on a pixel-by-pixel basis using the reference data. Reduced FOV imaging imposes a requirement of uniformly spaced samples in the phase encode direction in k-space. Since all processing is done in the image domain, individual pixels in the reduced FOV data get unfolded by integer numbers of final pixels (i.e., 131, 132, 133, etc). This requires the solution of a set of linear simultaneous equations in which pixel intensities are weighted by the coil sensitivity at the final pixel locations. The numerical condition of these equations determines the local noise properties of the unfolded image (3,10), so that the signal-to-noise ratio (SNR) varies from pixel to pixel (3). The resulting patterns of noise variation generally reflect the coil geometry and can have a strong perceptual effect. The SENSE method is very flexible and can be used with any coil geometry, provided satisfactory numerical conditioning is achieved at the pixel locations of interest.SMASH (5,6) operates in k-space for the target image data but uses a...

Coil‐based artifact reduction

“…Solving S ϭ CR for R is the "generalized SMASH" technique (4). The size of S is [n coil ⅐ n pe ϫ 1], where n coil is the number of coils in the current reconstruction and n pe is the number of phase-encode lines acquired.…”

“…In previous work (7), we computed S ␥ using Eqs. [3] and [4] with the object treated as an optimization unknown and the coil profiles assumed known from a previous reference scan (as is typical in parallel imaging). At each iteration the object was modified by motion parameters, which were also optimization-unknowns.…”

“…The remaining data was then reconstructed using a generalized SMASH (4) approach. An alternative method, termed "SMASH Navigators" (5) was developed to both detect and correct for motion.…”

3Parallel magnetic resonance imaging with adaptive radius in k‐space (PARS): Constrained image reconstruction using k‐space locality in radiofrequency coil encoded data

“…Images are reconstructed from undersampled MR signal data sets by combining the spatial encoding capabilities of RF coil arrays with those of magnetic field gradients. Generalized parallel imaging strategies reformulate the MR signal equation in terms of a large encoding matrix (1)(2)(3)(4), and parallel image reconstructions generally involve an inversion of this matrix.…”

SMASH navigators

“…This has been widely exploited to reduce acquisition times by acquiring datasets with fewer phase encode steps (1)(2)(3)(4). A different approach has been to use the redundancy to deal with coherent ghost artifacts (5,6) and to detect and replace corrupted data such as caused by motion (7).…”