Reconstruction algorithm for novel ultrafast magnetic resonance imaging

We introduce a new magnetic field geometry, B-x(x, y) = g(y)y cos(q(x)x), t o spatially encode magnetic resonance imaging (MRI). The field is called th e PERL field since it is PERiodic in x and Linear in y. A technique is prop osed to acquire two-dimensional (2D) data without switching the encoding fi elds. The time-domain PERL signal and image are not related by a two-dimens ional Fourier transform (2DFT). They are related by a 1DFT in the x-dimensi on and a new Bessel function integral transform, called the PERL transform, in the y-dimension. We numerically solve this equation and develop a recon struction algorithm. The algorithm is evaluated by assuming a known spin de nsity which is then used to calculate the PERL signal. This signal is the i nput for the algorithm. We show the reconstructed image matches the convolu tion of the initial assumed spin density and a point spread function (PSF). We identify the PSF and describe the conditions under which it approaches delta. (C) 1999 John Wiley & Sons, Inc.