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Implementation of SENSE with Arbitrary k-space Trajectories

A critical issue in MRI is the scan time. Several methods have been proposed to utilize parallel signal acquisition with multiple receiver coils for the purpose of reducing scan time. Spatial coil sensitivity is exploited to reduce the number of gradient-encoding steps, without compromising spatial resolution or the field of view (FOV). Practical implementations of parallel MR were presented by Sodickson and Manning [4] and Pruessmann, et al. [3]. Sodickson, et al. [4, 1] proposed a method known as SiMultaneous Acquisition of Spatial Harmonics (SMASH) which is a k-space implementation of parallel MR imaging. Pruessmann et al. presented a general formulation and performance analysis of the image domain sensitivity encoding method (SENSE). It is reported that the SENSE reconstruction in [3] is a computationally intensive process. For an image of size N × N being reconstructed, the complexity of a general reconstruction is O(N ). A large amounts of memory and processing time are required. Calculating a 128× 128 image, e.g., would require more than 1012 operations and about 1 GB of memory. In [2], Pruessmann et al. propose an efficient implementation. It is based on the idea of performing reconstruction iteratively. By combining fast Fourier transform (FFT) with forward and reverse gridding operations, the complexity of a single iteration is reduced drastically from O(N ) to O(N log N). The number of iterations necessary to achieve a given accuracy can also be reduced by using several measures of numerical optimization. Therefore, the computation time for non-Cartesian SENSE reconstruction is considerably reduced, making sensitivity-encoded imaging practical with arbitrary acquisition patterns. The purpose of my project was to implement the SENSE image reconstruction algorithm proposed by Pruessmann in [2], evaluate its performance using MRI phantom studies, and identify computational issues that need to be addressed for improving its speed performance.