Handling Motion in Sparse Reconstruction with Whiskers

INTRODUCTION In dynamic imaging it is often beneficial to enforce both temporal and spatial sparsity to minimize the number of sparse coefficients required to represent the object (1,2). In general, the minimum number of K-Space samples required to produce good results in sparse reconstruction is approximately four times the number of sparse coefficients (3). Patient motion that is periodic or smooth can be sparsely represented in a Wavelet-Fourier domain. Patient motion that is neither periodic nor smooth will reduce sparsity in the temporal direction and degrade the success of the sparse reconstruction. It is therefore beneficial to detect and correct as much patient motion as possible to maximize temporal sparsity and thus reduce the total number of K-Space samples required. This is accomplished using a hybrid Radial-Cartesian sampling technique called Whiskers (4). This sequence has an inherent ability to correct bulk patient motion and is well suited to non-linear sparse reconstruction. THEORY This work utilizes a pulse sequence named Whiskers (for the whiskers looking pattern in K-Space and lack of a clever acronym) that combines the resolution and undersampling characteristics of radial imaging with the motion correction techniques of Cartesian trajectories. The sequence acquires data near the edge of K-Space in a radial fashion (Fig. 1a) and rectilinearly near the center of K-Space (Fig. 1b). Each segment of the Whiskers sequence acquires different radial arms of K-Space but always acquires the same set of Cartesian lines at the center of K-Space. As a result, for each segment we have a low resolution image of the object which can be used to detect rigid body motion and rotation. The segmented data set is then corrected for this motion prior to reconstruction. In addition to motion, low order phase variations can be problematic in sparse reconstruction (1). This type of phase error can also be easily quantified with the Whiskers sequence and consequently corrected prior to reconstruction. The Whiskers sequence also produces nearly incoherent artifacts similar to that of a radial trajectory, making it a suitable candidate for sparse reconstruction. METHOD In these simulations we adopt a reconstruction method often used with KT-Sparse (2):