1. Introduction

Data reconstruction methods work by fitting a theoretical model to the experimental data and this ability makes them remarkably versatile. Most applications fall into one of two types. In the first, the data need processing in order to facilitate interpretation by enhancing the signal-to-noise ratio (S/N) and/or the resolution. In the second, the required result has to be calculated from the experimental measurements using a theoretical understanding of the experiment - for example, to generate a zero-charge mass spectrum from electrospray data, or calculate time constants from NMR relaxation measurements. In analytical chemistry, many applications involve the deconvolution of spectroscopic or chromatographic data.

PPL has successfully applied theReSpect data construction algorithm to both these types of problem, particularly in analytical chemistry, where common applications are the deconvolution of spectroscopic and chromatographic data. However, because the method works equally well for more than one dimension, it may be applied to many multi-dimensional techniques.

2. Data Information Content

It is pointless to attempt to extract information that is not present in the data to begin with. For example, if the instrument noise level is such that signals of interest are completely swamped, then the signals cannot be distinguished from the noise and there is insufficient information for them to be revealed. One must therefore consider what makes up the trace that requires interpretation.

 The desired signals in the data rarely conform to what the investigator wishes to see. Ideally, spectroscopic or chromatographic data signals would be sharp peaks that do not overlap so that interpretation and quantification are straightforward. However, the instrument and the experimental conditions almost always broaden the signals to some extent, giving rise to peak overlaps which may inhibit the interpretation and quantification of the data. These problems are exacerbated by noise from the experiment itself and possibly also from the instrument electronics, which tends to obscure the signals.

3. The Data Reconstruction Method

Traditional data processing techniques involving filters, inverse filters and Fourier transforms are linear methods and mathematically simple. They are therefore generally fast to compute and are commonplace in manufacturers' software. Data reconstruction methods involve iterative, non-linear techniques that are computationally intensive and may therefore be relatively time-consuming to perform. Even so, the additional information that may be recovered can be dramatic and will often outweigh the computational time penalty.

What is required is a method that does not broaden peaks when the S/N is enhanced and does not introduce noise when the resolution is enhanced. In addition, it should be possible to quantify the results and provide realistic assessments of position and intensity errors. The analytical chemist is normally able to determine peak shapes from the data, and it is only necessary to devise a fitting method that provides peak positions and intensities. Data reconstruction methods are well suited to large-scale problems of this type. To this end, the ReSpect data reconstruction technique is designed to mathematically reconstruct the data to within the overall noise level of any feature. Naturally, the method is not magic and can recover only the information that remains in the data. In the method described here there is never any attempt to operate directly on the data. Instead, the method always works forwards, mathematically reconstructing the information in the data. The only input is a peak profile - the Model - which must adequately match the profile of the peaks in the data.

 Four results are then available to the user. These are:

  1. The deconvolved result – the Deconvolution - including fully quantified estimates of the peak position and intensity errors. This result represents a resolution enhanced version of the data and shows the underlying detail contained in them.
  2. The Reconstruction of the data. This is obtained by convolving the Deconvolution with the Model, and represents a S/N enhancement of the data.
  3. The Misfit, which is the difference between the data and the Reconstruction.
  4. The Spike Result. Each feature in the Deconvolution is converted to a spike so that the spike heights are directly proportional to the peak intensities with optional graphical display of errors.

In addition, the user may post-process the Reconstruction and the Spike Result so that only those peaks and features above a specified significance level are reported. This enables insignificant or unwanted detail to be eliminated from the results.

Unlike other methods, the ReSpect-based methodology takes into account any variation in the noise level and any variation in data peak width.

4. Quantified results

Peak positions and intensities are determined directly from the Deconvolution and Missfit. Errors are determined from the total noise for any feature and any mismatch between the Model and the actual peak profile of the peaks in the data. The effect of nearby peaks is also taken into account to compute robust errors.