UBC Theses and Dissertations
New signal enhancement algorithms for one-dimensional and two-dimensional spectroscopic data Foist, Rod Blaine
In research, the usefulness of the analytical results is crucially dependent upon the quality of the measurements. However, data measured by instruments is always corrupted. The desired information—-the "signal"-—may be distorted by a variety of effects, especially noise. In spectroscopy, there are two additional significant causes of signal corruption—-instrumental blurring and baseline distortion. Consequently, signal processing is required to extract the desired signal from the undesired components. Thus, there is an on-going need for signal enhancement algorithms which collectively can 1) perform high quality signal-to-noise-ratio (SNR) enhancement, especially in very noisy environments, 2) remove instrumental blurring, and 3) correct baseline distortions. Also, there is a growing need for automated versions of these algorithms. Furthermore, the spectral analysis technique, Two-Dimensional Correlation Spectroscopy (2DCoS), needs similar solutions to these same problems. This dissertation presents the design of four new signal enhancement algorithms, plus the application of two others, to address these measurement problems and issues. Firstly, methods for one-dimensional (1D) data are introduced—-beginning with an existing algorithm, the Two-Point Maximum Entropy Method (TPMEM). This regularization-based method is very effective in low-SNR signal enhancement and deconvolution. TPMEM is re-examined to clarify its strengths and weaknesses, and to provide ways to compensate for its limitations. Next, a new regularization method, based on the chi-squared statistic, is introduced and demonstrated in its ability for noise reduction and deconvolution. Then, two new 1D automated algorithms are introduced and demonstrated: a noise filter and a baseline correction scheme. Secondly, a new two-dimensional (2D) regularization method (Matrix-MEM or MxMEM), derived from TPMEM, is introduced and applied to SNR enhancement of images. Lastly, MxMEM and 2D wavelets are applied to 2DCoS noise reduction. The main research contributions of this work are 1) the design of three new high performance signal enhancement algorithms for 1D data which collectively address noise, instrumental blurring, baseline correction, and automation, 2) the design of a new high performance SNR enhancement method for 2D data, and 3) the novel application of 2D methods to 2DCoS.
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