Chemograms Data Processing Through Wavelet Transform

The chemograms data processing include filtering, baseline correction, peaks detection and discrimination, resolving of overlapping peaks, data compressing, and the interpretation of chemograms. Various conventional methods had been developed in these respects, however they are not fully satisfactory regarding precision and efficiency. The main characteristic of wavelet transform (WT) is that it decomposes a signal into localized contributions, and each of the contributions represents the information of different frequency components contained in the original signal. WT is generally called multi-resolution analysis and therefore yields a lot of applications in signal and image processing. The works developed in this field by former researchers were summarized in the first part of our work. The excellent properties of WT were then explored in processing chemograms data associated with many other mathematical tools such as numerical analysis, logic induction, model recognition, neural network and multivariate analysis. Some novel methods and algorithms were proposed for the noise identification, signal detection, peak recognition, decomposing of overlapping peaks of chromatogram and quantitative information extraction from near infrared spectroscopy (NIRS). The contents of this thesis were organized as follows:Chapter one gives an introduction of chemograms data processing. Based on the characteristic of the scientific discipline of analytical chemistry and chemometrics, the inclusion and main purposes of chemograms data processing were defined. It was then determined to focus our work on using WT. The works developed in the field of chromatogram and NIRS data processing based on WT were emphatically was reviewed, and the scheme and goal of this work were determined.Chapter two reviews the basic theory about WT. In comparing with the Fourier transform, the properties of localization and adaptive time-frequency window of WT were interpreted in detail. Due to the redundancy of continue wavelet transform, the preference of using discrete wavelet transform was also explained. The principle of multi-resolution analysis was discussed, and the decomposition of signal frequency in space-scale was described. Both multi-resolution analysis and two channel filters wereused as objects to explain the principle of discrete wavelet transform and Mallat's pyramid algorithm. The concepts regarding bi-orthogonal wavelet which will be frequently used in our research was introduced concisely. Finally, some examples were given for showing the application of WT to the signal processing.In chapter three, the various noises and noise removing methods including the method based on WT was extensively discussed. Particular attention was paid upon the noise pulse with its width close to that of signal peaks. It is important but difficult to identify this kind of noise pulse from signal peaks in chromatographic data automatically. The spike of a normal chemograms peak is usually smoother than that of a noise pulse caused by imperfection of experimental running, so the singularity analysis through WT was proposed to identify whether the spikes corresponding to the chemogram peaks or the noise pulses. The situation of Lipschitz exponent varying with the width of spike caused by signal and noise pulses was carefully studied. The results showed that it provides us with an effective measure to discriminate the noise pulse from signal peaks in chromatogram.In chapter four, a systematic method based on WT was developed to detect complex chemogram with overlapped peak groups. The conventional methods of peak detection was firstly reviewed and the shortcomings were discussed. Taking advantage of multi-resolution analysis and the different characteristics of WT modulus maximum between chemical signals and noises, a new algorithm was proposed to detect the complex overlapping peaks based on the theory of singularity detection with WT and logic induction. Satisfactory results were obtained from both the simulated and practical spectrogr...