Choice of an appropriate starting point. Estimated upstream aberration maps with one spectral channel for three different starting points. [i] Without turbulent aberrations in the simulated images. [ii] With turbulent aberrations in the simulated images. From left to right, with a dynamic range adapted to the visualization: “true” simulated aberration map, (a) and (a’) estimated aberrations with a random aberration map (rms value of the simulated aberrations) as starting point, (b) and (b’) estimated aberrations with a zero aberration map as starting point, and (c) and (c’) estimated aberrations with a random aberration map (rms value 10⁸ times lower than the “true” one) as starting point. The estimation is performed with a regularization on the star flux.