Inverse Problems

In addition to model building, as we did in the earlier chapters, we care very much about fitting observations, i.e., indirect measurements, to models. This is at the core of remote sensing, temperature retrieval, prospecting for oil, medical diagnosis, and other inverse problems. In this chapter we present several methods for the systematic formulation of inverse problems, and we give explicit computational procedures for carrying them out. We study their effectiveness and their robustness with respect to errors in observations, in models, in initial estimates. We present results of numerous computational experiments. Studies such as these serve in the planning of experiments. The benefits of analysis in the planning stages of a project can help to avoid unfruitful experiments and inferior designs.