O-space imaging: Highly efficient parallel imaging using second-order nonlinear fields as encoding gradients with no phase encoding.

Recent improvements in parallel imaging have been driven by the use of greater numbers of independent surface coils placed so as to minimize aliasing along the phase-encode direction(s). However, gains from increasing the number of coils diminish as coil coupling problems begin to dominate and the ratio of acceleration gain to expense for multiple receiver chains becomes prohibitive. In this work, we redesign the spatial-encoding strategy in order to gain efficiency, achieving a gradient encoding scheme that is complementary to the spatial encoding provided by the receiver coils. This approach leads to "O-space" imaging, wherein the gradient shapes are tailored to an existing surface coil array, making more efficient use of the spatial information contained in the coil profiles. In its simplest form, for each acquired echo the Z2 spherical harmonic is used to project the object onto sets of concentric rings, while the X and Y gradients are used to offset this projection within the imaging plane. The theory is presented, an algorithm is introduced for image reconstruction, and simulations reveal that O-space encoding achieves high encoding efficiency compared to sensitivity encoding (SENSE) radial k-space trajectories, and parallel imaging technique with localized gradients (PatLoc), suggesting that O-space imaging holds great potential for accelerated scanning.