Meir Shinnar

A new approach to automatic shimming

Abstract A fast, algebraic technique for automatic magnet shimming is presented. It is based on field maps computed by phase measurement within Carr-Purcell echo sequences. The correction computation itself is carried out by an algorithm which compensates field inhomogeneities within the sample by a linear combination of all shim control functions. The procedure is noniterative, thus avoiding instability problems and improving speed performance. Two algorithms are discussed: (a) a Chebychev approach which minimizes the maximum field deviation (minimax) and (b) a least-squares algorithm.

The synthesis of pulse sequences yielding arbitrary symmetric magnetization vectors

Abstract A new procedure and computer algorithm is presented to allow the synthesis of a pulse sequence which will generate an arbitrary frequency-dependent spin excitation, subject only to the restriction that it is symmetric about 0 Hz. The resultant magnetization vector after any N + 1 pulse sequence about a fixed axis is exactly expressible as an N -term Fourier cosine series. We develop a technique in which the required final z -magnetization vector ( M z ) as a function of frequency is expressed as an N-term Fourier series. We then form a consistent Fourier series for ( M xy ). As many as 2 2 N +1 different pulse sequences may be directly generated, all of which produce a different M xy ( f ), but the same M z ( f ). We then generate a pulse sequence which will give us the desired M z ( f ) and M xy ( f ). A complete description of the computer algorithm with numerical examples for certain pulse sequences is included.

A generalized pisarenko technique for analyzing the NMR FID

Abstract Recently, several different methods for directly analyzing the time-domain NMR signal have been proposed. We have derived a new technique to determine the components of the true free induction decay in the presence of noise. The algorithm has its origins in the Pisarenko method of harmonic retrieval and therefore has very high discrimination between closely spaced frequencies. This algorithm incorporates knowledge of the noise power to analyze the FID. As in other techniques, calculating the decay time of an exponentially damped signal in the presence of noise continues to be the most difficult component of the problem. We apply the technique both to simulated data and to one example of physiologic NMR data to show its power.