An efficient algorithm for MR image reconstruction without low spatial frequencies

It is demonstrated that if the image to be reconstructed is known to have some zero-valued pixels, the dynamic ranges can be better used by disregarding the largest signals and using signal restoration methods. Low-frequency and high-frequency signals are related, using the knowledge that some pixels are zero, by a set of linear equations in which the number of equations is equal to the number of zero pixels, and the number of unknowns is equal to the number of low-frequency signal samples rejected. An improved Fourier transform (FT), magnetic resonance (MR) imaging method based on a least-square-error (LSE) technique, and an efficient algorithm for signal restoration when the low-frequency components are discarded are presented. In this method, the regions of support in both the image domain and the frequency domain can have arbitrary shapes, and all zero pixels in the image domain can be taken into account. The algorithm has been tested on simulated and experimental data with acceptable results.