Registration of two high-dimensional data sets often involves dimensionality reduction to yield a single-band image from each data set followed by pairwise image registration. We develop a new application-specific algorithm for dimensionality reduction of high-dimensional data sets such that the weighted harmonic mean of Cramér-Rao lower bounds for the estimation of the transformation parameters for registration is minimized. The performance of the proposed dimensionality reduction algorithm is evaluated using three remotes sensing data sets. The experimental results using mutual information-based pairwise registration technique demonstrate that our proposed dimensionality reduction algorithm combines the original data sets to obtain the image pair with more texture, resulting in improved image registration.