Optimal input design for NMR system identification

In a wide variety of settings, the measurement of nuclear magnetic resonance (NMR) effects has proven to be a remarkably effective for investigating unknown structures on both large and small scales. Over the years a large body of technique has been developed for improving the sensitivity and resolution of NMR measurements and many recent advances in biochemistry and medicine are dependent on the sophisticated signal processing techniques now used routinely. From a system theoretic perspective, problems in this area can be thought of as identification problems involving bilinear systems. Many ingenious techniques, such as the "two dimensional" Fourier transform procedure have been developed based on particular types of input patterns. Because of the low signal to noise ratios inherent in NMR, the optimization of such methods requires the use of stochastic models for the dynamics and measurement processes. We take a fresh look at problems in this area with the view of finding computational procedures that will determine the inputs which will optimize specific performance measures. In particular, we explore performance measures related to conditional entropy, and in this way develop a formalism for establishing the mathematical limits on what can be accomplished with better input design