Scaled canonical coordinates for compression and transmission of noisy sensor measurements

This paper is motivated by sensing and wireless communication, where data compression or dimension reduction may be used to reduce the required communication bandwidth. High-dimensional measurements are converted into low-dimensional representations through linear compression. Our aim is to compress a noisy sensor measurement, allowing for the fact that the compressed measurement will then be transmitted over a noisy channel. We give the closed-form expression for the optimal compression matrix that minimizes the trace or determinant of the error covariance matrix. We show that the solutions share a common architecture consisting of a canonical coordinate transformation, scaling by coefficients which account for canonical correlations and channel noise variance, followed by a coordinate transformation into the sub-dominant invariant subspace of the channel noise.