Figure 4

Iterative model fitting using the L2 _<> norm. In this example, the model is a linear function which is fitted to a set of paired values (x, y_meas). For two of the x values (x = 3 and x = 5), the measured values are thresholds (Greater 3). Fitting a linear function to paired values according to the L2 norm corresponds to the standard linear regression. A depicts the model fit (straight line) to the measured values (black boxes), ignoring any thresholds. For x = 5, the model value y_pred taken from the regression curve is 3.4, above the measured threshold value 3. Therefore, in the next iteration the y_meas* value is set to the model value 3.4. B shows the new linear regression with the adjusted y_meas* values. This procedure is repeated until the y_meas* values no longer change (8 iterations, panel C).