Information-theoretic approach to optimal quantization

The authors offer transinformation maximization as the criterion for optimal signal quantization for most applications in lieu of the more conventional criteria, such as mean- square-error minimization first proposed by Max. Optimal quantization for signal transinformation (which reduces to entropy in the noise-free case) using a uniform digitizer and a companding gain function is considered, and specifically applied to the image acquisition problem for ATR (Automatic Target Recognizer) processing. Both pre- and post-gain noisy channels are examined under linear sensor gain (with extension to non-linear gains); maximum achievable entropy, transinformation, SNR, and minimum mean square error are computed for several typical input distributions. The authors establish the following arguments supporting Maximum Transinformation Acquisition--MTA (noise)--and Maximum Entropy Acquisition-- MEA (no-noise): (1) MTA 'matches' the sensor/digitizer channel to the input signal in an information-theoretic sense, preserving as much analog information as possible. (2) MTA can be closely approximated with a less computationally intensive algorithm than actual transinformation. (3) Net information content is the crucial quantity governing a priori detection and recognition in cluttered environments. (4) MEA provides the best overall pixel intensity spread throughout the image, maximizing the probability of pixel differences where analog intensities differ; MTA provides very near optimal SNR and noise-free pixel contrasts. (5) MTA provides a standard, repeatable, and globally optimal acquisition method for extracting information for ATRs in the absence of a priori scene knowledge; MTA can also be applied locally to maximize information content within a region of interest.