Nonlinear blind sensor fusion and identification

When several uncharacterized sensors measure the same unknown signal or image, we would like to simultaneously combine the measurements into an estimate of true source (fusion) and learn the properties of the individual sensors (identification). This paper presents a model in which sensors perform (time-invariant) linear filtering followed by pointwise nonlinear squashing with additive noise and shows how, given several such noisy nonlinear observations, it is possible to recover the true signal and also estimate the sensor parameters. The setup assumes that both the linear filtering and the nonlinear squashing are spatially (temporally) invariant, but does not make any prior assumptions (such as smoothness, sparsity or heavily tailed marginals) about the signal being recovered and thus is appropriate for a variety of source distributions, such as astronomical images, speech signals and hyperspectral satellite data which may violate one or more standard prior assumptions. An efficient estimation algorithm minimizes the sum of squared errors between the predicted sensor outputs and the sensor readings actually observed, using an efficient procedure, isomorphic to the backpropagation algorithm. The setup can be thought of as learning the weights and unknown common input for several one-layer neural networks given their outputs.