Noise in bilinear problems

Despite the wide application of bilinear problems to problems both in computer vision and in other fields, their behaviour under the effects of noise is still poorly understood. In this paper, we show analytically that marginal distributions on the solution components of a bilinear problem can be bimodal, even with Gaussian measurement error. We demonstrate and compare three different methods of estimating the covariance of a solution. We show that the Hessian at the mode substantially underestimates covariance. Many problems in computer vision can be posed as bilinear problems: i.e. one must find a solution to a set of equations of the form