Complexity regularized shape estimation from noisy Fourier data

We consider the estimation of an unknown arbitrary 2D object shape from sparse noisy samples of its Fourier transform. The estimate of the closed boundary curve is parametrized by normalized Fourier descriptors (FDs). We use Rissanen´s (1998) MDL criterion. to regularize this ill-posed non-linear inverse problem and determine an optimum tradeoff between approximation and estimation errors by picking an optimum order for the FD parametrization. The performance of the proposed estimator is quantified in terms of the area discrepancy between the true and estimated object. Numerical results demonstrate the effectiveness of the proposed approach.