Nonuniform Sampling (NUS)

Nonuniform Sampling (NUS)

count first;i last;i

Writes a sequence of integers to the standard output, one per line, counting from first to last. If the output is redirected to a file, it is suitable for use as a trivial sampling schedule.

sampfunc dim1;l [dim2;l dim3;l] schedule-file;l

Sets time-domain data values to 1 for all indices contained in schedule-file. Those not contained in schedule-file are set to zero.

sampsched

Through a series of interactive prompts, this program computes and writes out the values in a sampling schedule. The schedule can be exponential, sine-modulated exponential, or random.

select1d dim;l schedule-file;l

Throws away all data points whose index along the specified dimension is not listed in the one-dimensional schedule-file (one integer entry per line). The resulting data set is compressed.

select2d dim1;l dim2;l schedule-file;l

Throws away all data points whose indices along the specified dimensions are not listed in the two-dimensional schedule-file (two integer entries per line). The resulting data set is compressed.

zsample1d dim;l schedule-file;l

Sets the values of all data entries not listed in the one-dimensional NUS schedule-file to zero. Useful for computing the 1D impulse spectrum, sometimes referred to as the point-spread function (PSF).

zsample2d dim1;l dim2;l schedule-file;l

Sets the values of all data entries not listed in the two-dimensional NUS schedule-file to zero. Useful for computing the 2D impulse spectrum, sometimes referred to as the point-spread function (PSF).

Nonuniform sampling (NUS) is the process of collecting time-domain data at non-fixed intervals. The sampling can be regular, for example corresponding to sampling along radial time vectors (used to obtain spectra of tilted planes, as in back-projection reconstruction), or irregular, for example random sampling. The use of NUS precludes the use of the discrete Fourier transform for computing spectra. Suitable alternatives include multidimensional decomposition, maximum entropy reconstruction, maximum likelihood reconstruction, and minimum l1-norm reconstruction. The advantage of NUS is that it frequently affords high-resolution spectra from much smaller data sets (hence quicker to acquire) than conventional uniform sampling.

The key to using NUS in multidimensional NMR is to design an efficient sampling scheme. While this remains an active area of research, the SBTOOLS website hosts a web-based tool for generating a variety of sampling schemes. RNMRTK includes additional tools for generating sampling schedules and manipulating NUS data (listed below).