Optimizing the transformation of HYSCORE data using the maximum entropy algorithm.

Abstract

Non-uniform sampling (NUS) in combination with the Maximum Entropy (MaxEnt) algorithm as applied to multi-dimensional NMR data has been thoroughly investigated and the NUS approach shown to provide significant sensitivity improvements as compared to methods using uniformly sampled (US) data and the discrete Fourier transform (DFT). Hyperfine sublevel correlation (HYSCORE) is a standard pulse EPR experiment that can potentially benefit greatly from this approach, but the data present unique challenges as compared to NMR. HYSCORE data typically exhibit a very large range of peak intensities, signals are in the form of irregularly shaped ridges with variable intensities, and time traces are generally truncated to save measurement time. MaxEnt has the advantageous properties that it does not require US data, dampens weak signals (noise) and does not suffer from windowing artifacts due to truncation of the time traces. Critical to the success of the MaxEnt algorithm is the choice of the two input parameters aim and def which describe the data noise and contribution of entropy in the optimization, respectively. In this paper we expand our preliminary study on the application of MaxEnt to the reconstruction of HYSCORE spectra to include a detailed analysis on sensitivity to detect weak peaks, investigate the non-linearity of the transformation and ascertain if it can be characterized by the introduction of synthetic peaks, and define a general range for the choice of aim and def. Furthermore, the ability of the MaxEnt method to remove windowing artefacts in uniformly sampled truncated HYSCORE data is described.