Theoretical and experimental comparison of the Lorenz information measure, entropy, and the mean absolute error

Abstract

The Lorenz (1905) information measure (LIM) is a function of the observed probability sequence of digital signals, similar to the signal entropy, and is approximately linearly related to the mean absolute error (MAE) in simulations employing uncorrupted and corrupted 2-dimensional Gaussian and magnetic resonance (MR) images. Unlike the MAE, the LIM does not require an uncorrupted reference signal for a distance computation. However, for the particular difference signal case imposed by the definition of the MAE, the LIM is asymptotically bounded by the MAE/signal quantization number ratio. Therefore, in applications where an uncorrupted signal does not exist, and thus, the MAE is undefined, the LIM provides a comparable signal processing performance measure.<>