Randomly Perturbed Radial Trajectories for Compressed Sensing MRI

Introduction: The recently introduced Compressed Sensing (CS) theory illustrates that a small number of random linear measurements can be sufficient to reconstruct sparse or compressible signals [1,2,3]. Since the number of measurements necessary for perfect reconstruction using the CS theory can be drastically smaller than the number of measurements required by the Nyquist sampling theory, CS has the potential to significantly accelerate data acquisition in MRI [4-10]. Although the initial CS theory was based on completely random sampling, it was later suggested that such random sampling may not always be necessary [11]. More specifically, recent results indicate that CS methods can yield exact recovery if the sparsity basis and the measurement basis obey the uniform uncertainty principle and are incoherent [11]. This pertains to MRI since complete random sampling is difficult to achieve with existing hardware. Earlier work in CS for MRI explored strategies for randomizing measurements for spirals [4] and 3DFT trajectories [5]. Recently, reconstructions from CS MRI data acquired on regular radial trajectories were demonstrated [7-10]. While the CS reconstruction of undersampled regular radial data resulted in significant reduction of streaking artifacts, compared to filtered backprojection or regridding, we demonstrate here that further improvements are possible by randomly perturbing the radial trajectories.