Wavelet encoded MR image reconstruction with compressed sensing

Traditional MRI scanners acquire samples of the encoded image in a spatial frequency (Fourier) domain, known as k-space. The recently developed theory of Compressed Sensing (CS) has shown that a natural image could be acquired and reconstructed from a reduced number of linear projection measurements at sub-Nyquist sample rates. CS is well suited to fast acquisition of MRI by sparse encoding in k-space. However, the commonly used Fourier-encoding MRI scheme only weakly satisfies the incoherent measurements constraint required for CS. MR images can be reconstructed from a more sparse wavelet-encoded k-space than from Fourier-encoded k-space with the same resolution. Wavelet-encoded MRI is flexible in spatially-selective excitations to yield an encoding scheme similar to the "universal encoding". In this work, a CS-MRI scheme has been investigated to accurately reconstruct MR images from sparsely wavelet-encoded k-space. This sparse encoding is achieved with tailored spatially-selective RF pulses, which are designed with Battle-Lemarie wavelet functions. The Fourier transforms of the Battle-Lemarie wavelet functions used as RF pulse profiles are smooth and decay rapidly to zero. This technique provides short RF pulses with relatively precise spatial excitation profiles. Simulator results show that the proposed encoding scheme has different characteristics than conventional Fourier and wavelet encoding methods, and this scheme could be applied to fast MR image acquisition at relatively high resolution.