Estimating intensity variance due to noise in registered images

Image registration refers to the process of finding the spatial correspondence between two or more images. This is usually done by applying a spatial transformation, computed automatic or manually, to a given image using a continuous image model computed either with interpolation or approximation methods. We show that noise induced signal variance in interpolated images differs significantly from the signal variance of the original images in native space. We describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images, the spatial transformations computed by the registration procedure, and the interpolation or approximation kernel chosen. Our approach is applied to diffusion tensor (DT) MRI data. We show that incorrect noise variance estimates in registered diffusion weighted images can affect the estimated DT parameters, their estimated uncertainty, as well as indices of goodness of fit such as chi-square maps. In addition to DT-MRI, we believe that this methodology would be useful any time parameter extraction methods are applied to registered or interpolated data.