Corrupted Data, Filters and Inverse Filters
Even modern scientific instruments generate data that are damaged or corrupted by noise, instrument imperfections and by the physics of the experiment. Generally, the user of a scientific instrument wishes to obtain the best possible results that the instrument is capable of providing and generally post-processing using some form of filter, inverse filter or deconvolution is applied in an attempt to extract the last residue of information. A frequent requirement is to obtain either a deconvolution so that accurate peak positions and intensities may be determined or a signal-to-noise (S/N) enhancement to reveal information masked by noise.
All traditional deconvolution and S/N enhancement data processing techniques are filters or inverse filters and there is a trade-off between resolution and S/N and it is only for grossly over-sampled data that filters can reduce noise without seriously broadening peaks. These methods are normally subjective and it is impossible to assess the accuracy or reliability of any feature in the result. Their major disadvantage is that they operate directly on the data and attempt to undo the corruption and distortion introduced by noise, the instrument and the experiment. This philosophy is unsound because operating on corrupted data can give rise to results that contain artefacts.
In contrast, PPL's methods do not operate on the data in an attempt to reverse the effects of noise and instrument imperfections. Instead, our approach is to mathematically reconstruct the data, using a Model that represents the way in which the data are damaged or corrupted. Our methods are iterative and always work forwards, progressively reconstructing the underlying detail contained in the data - the Deconvolution. At the end of each iteration cycle, the current result is convolved with the Model to produce a corresponding Reconstruction of the data. The difference between this and the actual data guides the calculation towards its conclusion. The program terminates when all convergence criteria are satisfied.