A two-dimensional modeling reconstruction technique for magnetic resonance data

Abstract

In both nuclear magnetic resonance spectroscopy and magnetic resonance imaging, spectra or images are commonly reconstructed by calculating the inverse discrete Fourier transform (IDFT) of an experimental two-dimensional complex number data set. Excellent reconstructions are obtained when the data set is large. In many situations, experimental considerations limit the number of data points that can be gathered, (e.g., 128 X 128 data matrix in “echo planar” imaging (I)) resulting in image artifacts. To illustrate the artifacts, the original data and 2D IDFT reconstruction of a medical phantom are shown for a 256 X 256 data set and a truncated 128 X 128 data set in Figs. 1 and 2, respectively. Comparison of the gray scale false color pictures, Figs. la and 2a, show that the truncation causes significant data loss which appears as severe ringing in both directions of the truncated reconstruction, Fig. 2b, because of windowing effects (2). Even with the “large” 256 X 256 data set, Gibb’s ringing is evident around the phantom’s edges, Fig. 1 b. Several papers have discussed the successful application of one-dimensional modeling techniques to data sets that are truncated in one direction (3-8). For these data sets, reconstruction via the IDFT using a fast Fourier transform (FFT) algorithm suffices in the nontruncated data direction. For data sets truncated in both directions, two-dimensional modeling techniques are necessary. A major problem in modeling is that it must be expected that there will be information components of the data that cannot be modeled, either because the model is not totally appropriate or because the true model order is too high for the limited amount of data available. The transient error reconstruction approach (TERA) algorithm (3) has a stage where data that cannot be modeled are reintroduced before actual reconstruction occurs. It is shown in this Note that high quality reconstructions with removal of artifacts are obtained when the one-dimensional TERA algorithm for modeling data is used in both truncated data directions with the data preconditioned via an initial IDFT. An outline ofthe TERA modeling algorithm applied to data truncated in one direction is given below. A more detailed theory for the TERA algorithm applied to magnetic resonance images, and a reformulation of this theory to allow the use of different data models to account for data characteristics, can be found in Refs. (3, 9) respectively. Reconstruction of the magnetic resonance image or magnetic resonance spectroscopy data proceeds with the inverse discrete Fourier transform in the nontruncated