We have developed a method for blindly removing lens distortions in the absence of any calibration information or explicit knowledge of the imaging device. Shown on the right are images of Einstein with (top and bottom) and without (middle) lens distortion.

This technique works by first noticing that when an image is distorted, specific higher-order correlations are introduced in the frequency domain. The amount of correlation is proportional to the amount of distortion. In order to estimate these correlations we used tools from polyspectral analysis, namely the bispectrum (or its normalized counterpart, the bicoherence) which measures third-order correlations. The lens distortions are blindly removed by simply minimizing these correlations.

(Collaborative work with Alin Popescu)