th  - 1987 - 51st ENC Conference

MK25
OPTIMIZATION OF QUANTITATIVE PERFORMANCE OF
SPECTRAL ANALYSIS BY MINIMAL SAMPLING
Jerome L. Ackerman* and Vikram Janakiraman-
Department of Radiology, NNR Facility,
Massachusetts General Hospital, Boston, MA 02114
Minimal sampling is a non-Fourier method of spectral
analysis in vhich the complex amplitudes of prespecified basis
signals are extracted by an algebraic solution. The basis
signals may be simple sine and cosine raves as in the discrete
Fourier transform. Alternatively, they may be oscillations with
finite decay rate, or they may be the FID's corresponding to
arbitrary lineshapes or subspectra. The utility of this form of
spectral analysis lies in the principle that for each unknown
amplitude, only one sample of the signal need be obtained. This
can greatly reduce the time of the data acquisition process and
size of the data set in multidimensional acquisitions.
For example, in the collection of a COSY tvo-dimensional
data set from a compound vith tventy spectral lines in the normal
one-dimensional spectrum, there are exactly tventy possible
frequencies in each of the dimensions of the two-dimensional
spectrum (ignoring the possible appearance of multi-quantum
artifacts). It is therefore possible, using minimal sampling, to
collect the two-dlmensional data set vlth only twenty samples in
the first time dimension. (One could also collect only twenty
samples of each FID, rather than the usual 512 or so, but that
would not offer any significant savings in total acquisition
time.)
The drastic reduction in the total number of data values
acquired would suggest that the algorithm would suffer from very
poor signal-to-noise performance. Sovever, the actual
performance is significantly better than one might at first
suspect. Most importantly, we have found a specific procedure
for optimizing the data collection process by maximizing the
noise immunity of the matrix transformation which actually
accomplishes the spectral analysis.
We will present an algorithm for optimizing the
quantitative performance of minimal sampling, and illustrate the
results of this process for simulated and actual data.
"Permanent address: University of Pennsylvania,
Philadelphia, PA 19104