Processing incomplete and uncertain data using subspace methods

An approach for processing incomplete or uncertain data based on subspace methods is presented in this paper. The paper addresses the problem of how a subset of a parameter vector describing a signal can be estimated. The term parameter vector refers to the coefficients in the linear combination of basis functions describing a local image neighbourhood. Images are normally described locally using simple basis functions. Low order local momentums such as order 0 (the local DC component), 1 and 2 are commonly used. Low order differentiations are also useful descriptors. In densely regularly sampled images, these descriptors are easily computed using standard convolution. However, when working with irregularly sampled data or incomplete data the signal model has to be of higher order than the signal variations of interest. This is the case where only a part of the parameter vector is to be estimated. If possible, only this part of the parameter should be calculated explicitly as opposed to calculating the whole parameter vector. This paper describes such a method based on partitioning the model subspace into two parts