Design of k-space channel combination kernels and integration with parallel imaging

Imaging using high channel-count coil arrays can benefit a broad range of clinical applications through improved signal-to-noise ratio (SNR), higher parallel imaging acceleration factors and increased anatomical coverage (1–3). However, maintaining clinically acceptable reconstruction times can be challenging when using high channel-count coil arrays. A variety of approaches have been explored to improve the efficiency of reconstruction algorithms for high channel-count imaging (4–14). Many of these techniques, including this work, have focused on combining or reducing the effective number of channels earlier in the reconstruction pipeline. In this way, the computational burden on subsequent steps in the reconstruction process is lessened. Channel combination methods can be categorized based on the domain in which channel combination is performed: image-space, time-domain or k-space. Image-space channel combination methods are widely used due to their ability to optimize final image SNR and their ease of use (15). However, image-space solutions can be computationally and memory intensive for high channel-count coil arrays, since channel combination must take place relatively late in the reconstruction pipeline. At the other end of the spectrum, time-domain channel combination (4) has received significant attention. Time-domain channel combination performs channel combination independently at each acquisition time point—at the beginning of the reconstruction pipeline. Time-domain channel combination is very effective in reducing the computation and memory requirements for the image reconstruction pipeline. The weaknesses of time-domain channel combination are (1) SNR can be degraded, sometimes significantly (16) and (2) phase cancellation artifacts are often unavoidable for some coil geometries (5). As a result, time-domain channel combination is not widely used to combine all receiver channels into a single channel data stream. Instead, the approach is typically used to reduce the channel-count significantly but without appreciably degrading image quality (6–12). Methods that take this approach are often referred to as either “array compression” or “coil selection” depending on whether or not they combine channel data streams during the channel reduction. Because these approaches do not output a single channel data set, they must be paired with another channel combination method later in the reconstruction pipeline. In this way, these approaches are complementary to other channel combination strategies, including image-space and k-space approaches (13,14). In comparison to image-space channel combination and time-domain channel combination, k-space channel combination has received relatively less attention. k-Space channel combination can be performed by convolving the k-space data for each channel with its own k-space convolution kernel and summing across channels to create a single or reduced number of k-space data sets. Unlike time-domain channel combination, it is challenging to implement k-space channel combination in hardware as the convolution coefficients are dependent on the k-space sampling strategy. Unlike image-space channel combination, k-space channel combination is unable to optimize SNR independently at every pixel location. However, k-space channel combination does have important advantages: it has more degrees of freedom compared to time-domain channel combination that allow it to achieve better SNR and it can be performed earlier in the reconstruction pipeline compared to image-space channel combination, potentially improving reconstruction efficiency. Early work in k-space channel combination was carried out as part of parallel imaging reconstruction methods. Methods such as SMASH, AUTO-SMASH and VD-AUTO-SMASH combine the parallel imaging unaliasing operation and the channel combination operation into a single step, both in the generation and application of reconstruction coefficients (17–19). Two challenges for these methods are that the SNR of the final combined images can be sub-optimal and they are prone to phase cancellation artifacts (20). Both of these issues can be attributed to sub-optimal channel combination. The GRAPPA method improved on prior k-space parallel imaging methods by separating the unaliasing operation from the channel combination operation and performing channel combination in image-space (20). While this approach has been very successful, it does lead to an increased computational burden, since the unaliasing operation in GRAPPA scales as the square of the number of channels. There is also a large memory requirement as separate data sets for each channel are formed in image-space. As the number of channels grows, a “channel-by-channel” approach becomes increasingly difficult to perform in clinically acceptable reconstruction times. The problem is exacerbated by the clinical motivations for moving to higher channel-counts: acquiring larger image matrices, and the use of more temporal phases for dynamic contrast enhanced imaging. For example, moving from a single phase eight-channel 256 × 256 × 64 acquisition to a 20 phase 32-channel 320 × 320 × 128 acquisition results in a 1000-fold increase in computation for the unaliasing operation of channel-by-channel parallel imaging with image-space channel combination. This increased computational load can be dealt with using both improvements in computing hardware and algorithmic improvements. Using more powerful reconstruction hardware without algorithmic changes has the advantage that this approach poses no risk to altering the image quality. In contrast, algorithmic changes can modify and potentially degrade image quality. However, hardware solutions can be more costly to roll out to a large installed base compared to software solutions. With such large potential increases in computation, it is likely that improvements in both computing hardware and algorithms will be needed. Because of this, it is important that improved algorithms work well with powerful hardware, which for the foreseeable future means that the algorithms must be amenable to parallel computing architectures. This work is motivated by a desire to reduce the computational demands for high channel-count image reconstruction while retaining image quality and supporting sampling schemes acquiring irregularly spaced k-space points on a Cartesian grid. Irregularly spaced sampling schemes used in the experiments in this work consist of the inclusion of internal calibration lines in the reconstruction and the use of variable sample spacing (e.g., acquire two, skip one or skip one, acquire one, skip two to create sampling reductions, R, of 1.5 and 2.5 respectively). The purpose of this work is to describe and evaluate a new method for designing local k-space channel combination kernels and integrating them with parallel imaging. We refer to the approach as the direct virtual coil (DVC) method (21). This work focuses on describing the technical methodology for DVC and relies on separate works to discuss specific clinical applications (22).