Baseline Fits

Both 295 and 260 nm datasets in Fig. 21.4A have been fit to Eqs. (21.31) and (21.34). A problem with these datasets is that the folding transition takes place at low Mg2+ concentrations, leaving insufficient data to determine a lower baseline. Fitting six variables (four variables in Eq. (21.31) and two variables in Eq. (21.34)) gave unrealistic values for mu that were an order of magnitude larger than mF. However, essentially identical values of [Mg2+]0 and Ar2+ are obtained whether mu is fixed as 0 or made to take on the same value as mF. 

Fig. 24. Results from the fit of a single voxel from a. /-refocused PRESS MRSI data set acquired at 4.1 T with 40 ms TE. (a) The top spectrum is the spectral data (thin line) overlaid with the fit result (heavy line), the middle spectrum is spectral data with only the baseline fit overlaid, and the bottom spectrum is the residual spectrum, (b) An expanded plot of the metabolite signal only (with baseline fit subtracted) in the top spectrum and the summed metabolite fits (without baseline) in the middle spectrum. The bottom spectrum contains the labelled, individual metabolite fits, with the vertical scale increased by 2. Reproduced with permission from B. J. Soher, K. Young, V. Govindaraju and A. A. Maudsley, Magn. Reson. Med., 1998, 40, 822. 1998 John Wiley and Sons.

Figure 5 Use of metabolite basis functions to fit clinical MRS data. (A) Final metabolite + baseline fit (black) overlaid on raw data (grey). (B) Non-parametric baseline signal estimation (based on wavelet filtering). (C) Metabolite basis functions modulated via scaling, B0 shift, lineshape and phase 0 and phase 1 to optimally fit raw data. (D) Residual spectrum of metabolite + baseline minus the raw data.

Exspline is an X-window-based program that uses spline first for pre- and postedge fitting baselines. It has the advantage that the Fourier transform, the EXAFS and the pre- and post- baseline fit can be observed interactively. This is a great improvement on Exback, which used non-interactive baseline correction. 

The use of the BRD in the circuit reduced common mode laser noise in the reference and measurement beams. In addition, the fact that the electrical output of the BRD is directly proportional to absorbance reduces errors that can occur due to baseline fitting to measurement detector data. 

Linear Regression Baseline Fitting. This is a very simple approach to baseline correction in that it requires no effort to set up. In this method, a least squares regression line is fit to the responses in each spectral region selected for calibration. This line is then subtracted from the response values in the region before using the data to perform the calibration model calculations (Ref. 52). 

Many automatic baseline correction routines that may be applied without operator intervention are available. These routines may be applied by default for operations such as spectral searching. Automatic basehne functions typically use linear or polynomial baseline fits in regions of the spectmm where no peaks are detected. 

Artifact removal and/or linearization. A common form of artifact removal is baseline correction of a spectrum or chromatogram. Common linearizations are the conversion of spectral transmittance into spectral absorbance and the multiplicative scatter correction for diffuse reflectance spectra. We must be very careful when attempting to remove artifacts. If we do not remove them correctly, we can actually introduce other artifacts that are worse than the ones we are trying to remove. But, for every artifact that we can correctly remove from the data, we make available additional degrees-of-freedom that the model can use to fit the relationship between the concentrations and the absorbances. This translates into greater precision and robustness of the calibration. Thus, if we can do it properly, it is always better to remove an artifact than to rely on the calibration to fit it. Similar reasoning applies to data linearization. 

The denominator in (3.1) can be simplified because the statistical uncertainty of the baseline, hN o, is negligible in practice when the spectra are simulated with numerical line fit routines. The stochastic emission of y-rays by the source leads to a Poisson distribution of counts with the width AA = and since is small, the denominator of (3.1) can be written as ... 

The underlined values in the sample data fit the definition of baseline. You can see how the last non-missing value should be carried forward. The following SAS code selects those proper baseline values. 

Fig. 8. Dependence of (A) corrected diffusion coefficient (D), (B) steady-state fluorescence intensity, and (C) corrected number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The diffusion coefficient and number of particles data shown here are corrected for the effect of viscosity and refractive indices of the urea solutions as described in text. For steady-state fluorescence data the protein was excited at 488 nm using a PTI Alphascan fluorometer (Photon Technology International, South Brunswick, New Jersey). Emission spectra at different urea concentrations were recorded between 500 and 600 nm. A baseline control containing only buffer was subtracted from each spectrum. The area of the corrected spectrum was then plotted against denaturant concentrations to obtain the unfolding transition of the protein. Urea data monitored by steady-state fluorescence were fitted to a simple two-state model. Other experimental conditions are the same as in Figure 6.

Beyond simple data storage and instrument control, modern data systems provide extensive data analysis capabilities, including fitted baselines, peak start and stop tic marks, named components, retention times, timed events and baseline subtraction. Further, they provide advanced capabilities, such as multiple calibration techniques, user-customizable information and reports and collation of multiple reports. If a Laboratory Information Management System (LIMS) is available, the chromatographic data system should be able to directly transfer data files and reports to the LIMS without user intervention. The chapter by McDowall provides a terse but thorough description of the... 

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