Statistical self-calibration of SPOT satellite imaging instrument

Abstract

SPOT satellites imaging instruments acquire rows of up to 6000 elements using a CCD linear array. The other dimension is obtained by the column-wise scanning resulting from the motion of the satellite. In practice, the responses of the detectors are not strictly identical along the array, which generates a stripe effect in the direction of columns. Our aim is to perform the calibration of the detectors response from the observed image, without supervision, in the restricted case of perfectly linear responses. In a Bayesian framework, we rely on a first-order Markov model for the image and on a Gaussian model for the gains of the detector. The MAP estimate minimizes a criterion, quadratic, convex, or nonconvex according to the chosen Markov model. In the quadratic case, MAP computation amounts to solving a tridiagonal linear system. In the other cases, we take advantage of introducing an equivalent augmented half-quadratic criterion, which can be minimized by iterately solving tridiagonal linear systems. Minimizing nonconvex criteria provides the best results, although convergence towards the global minimizer is not ensured in this case.