Using the Program

The mock data for the absorbance $ \boldsymbol{A}$ are generated by an Abel transformation of the density function:

$\displaystyle \rho(r) = r^2 (1-r^2) + \frac{1}{5} \exp \left\{ -250\left(r-\frac{1}{4}\right)^2 \right\},$ (15)

which is evaluated at $N_0 = \mbox{\texttt{N\_grid}}$ equally spaced points and multiplied by the model matrix $ \tilde{M}$ defined by (7). Then, Gaussian noise with zero mean and standard deviation Sigma noise is added; seed may be changed to obtain different sequencies of normally distributed random numbers.

Before starting the reconstruction by pressing the button Compute, the standard deviation of the data points corresponding to $ \sigma_i$ in (11), the value of the default model $ \boldsymbol{m}$ which is chosen flat and the initial value of the hyperparameter $ \alpha$ have to be specified. Moreover, the number of data points N_data and the number of control points N_knots for spline interpolation may be set.

Suggested exercises

Danilo Neuber 2003-10-03