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), to spatially encode magnetic resonance imaging (MRI). The field is called the PERL field since it is PERiodic in x and Linear in y. A technique is proposed to acquire two-dimensional (2D) data without switching the encoding fields. The time-domain PERL signal and image are not related by a two-dimensional Fourier transform (2DFT). They are related by a 1DFT in the x-dimension and a new Bessel function integral transform, called the PERL transform, in the y-dimension. We numerically solve this equation and develop a reconstruction algorithm. The algorithm is evaluated by assuming a known spin density which is then used to calculate the PERL signal. This signal is the input for the algorithm. We show the reconstructed image matches the convolution 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.