An automatic phase correction method in nuclear magnetic resonance imaging

Phase Correction of Fourier Transform Ion Cyclotron Resonance Mass Spectra Using MatLab

“…3 (below), so that for NMR, A=0 in Eq. 3 [28,29]. Furthermore, the phase variation in FT-NMR is usually less than one cycle (G2π) across the spectrum [30,31], so phasing becomes relatively simple for NMR: choose a peak at one end of the spectrum, vary C until the absorption-mode spectrum is equal in height to the magnitude-mode spectrum, and then vary B using the same equation for a peak at the other end of the spectrum.…”

Automated phase correction via maximization of the real signal

“…The computing times were determined with the dedicated stopwatch timer of the program (recommended to be used exclusively in the MatLab documentation instead of the CPU time) and averaged for repeated runs. The results for second and third order can be described as quadratic functions of the number of points (4,8,16, 40 and 121 s for second order and 39, 78, 157, 377 and 1005 s for third order). All first-order computing times are below 2 s. The results for third order are an order of magnitude higher than for second order, so inclusion of all terms of the next-higher fourth order would probably lead to unacceptable computing times.…”

“…Although a number of phase-correction algorithms exist [1][2][3][4][5][6][7][8][9], according to Bernstein et al [10], no completely satisfactory solution has been found. In particular, existing methods are not well suited for multiple unconnected regions of very low SNR.…”

Automatic phasing of MR images. Part I: Linearly varying phase

“…There are many papers that address phasing one-dimensional NMR spectra [7][8][9][10][11][12][13][14] and several papers that address phasing multidimensional NMR spectra [15,16]. However, only four papers were found that directly address the problem of generating absorption-mode images, [17][18][19][20]. Of the four papers, two [17,18] used a zero-order and a single firstorder phase parameter to generate the absorption-mode image.…”

“…The techniques described in these papers are not adequate to phase MR images in which the phase is a linear function in both the readout and phase-encode directions. Liu et al [19] recognized this problem and updated their algorithm to include all of the necessary phase parameters. However, they estimated the first-order phase parameters from the derivative of the image phase, which requires simultaneous estimation of derivatives and solving the phase unwrapping problem.…”