  We provide the construction of a set of square matrices whose translates and
rotates provide a Parseval frame that is optimal for approximating a given
dataset of images. Our approach is based on abstract harmonic analysis
techniques. Optimality is considered with respect to the quadratic error of
approximation of the images in the dataset with their projection onto a linear
subspace that is invariant under translations and rotations. In addition, we
provide an elementary and fully self-contained proof of optimality, and the
numerical results from datasets of natural images.
