Example of the tolerances in the original and new settings for the sparse inversion method. Here the channel is assumed to be the AIA 131 Å and duration is one second. (a) The tolerances as a function of intensities I (tol = tolfac × σ_I, where σ_I is the uncertainty on I, and tolfac is a user-defined factor). The dotted and dashed curves show the tolerances with tolfac of 1.4 and 5 in the original setting, respectively. The new tolfac varies with I, and are increased for the two additional runs (blue and orange lines), in case no solution is found in the first run (red lines). (b) Same as the plot in (a) but for the tolerances in units of intensities I. It shows that the tolerance could be much larger than I itself in the original setting when the intensity is low, but is limited within a certain fraction of I in the new setting.