Subspace interference in statistical signal detection

Signal detection in certain noise environments fits naturally into a statistical hypothesis testing framework. In order to have moderately tractable models, the noise is often assumed to be additive with a multivariate normal distribution. Additionally, computational complexity requirements may demand the assumption of spatial stationarity, particularly in the case when the data is 2-dimensional. Naturally the success of such models is dependent on the degree to which the assumptions are valid. For example, the assumption of spatial stationarity is thrown into serious doubt in typical images, where actual structure exists which might not be amenable to a simple statistical characterisation. In an attempt to improve the validity, we make use of the notion of subspace interference. This assumes that there is an additional unknown signal component present in the data, which is required to lie in a low-dimensional subspace of the original observation space. Invariant hypothesis tests can then be formulated for this problem, which are optimal in a fairly powerful sense. The work to be presented outlines some of the theory involved in specifying the tests and estimating the model parameters from actual data. Since the emphasis is on image rather than signal processing, special care needs to be taken in developing computational methods for the solutions: simple-minded approaches have massive computation and memory requirements.