Optimal design of simultaneous source encoding

Abstract

A broad range of parameter estimation problems involve the collection of an excessively large number of observations N. Typically, each such observation involves excitation of the domain through injection of energy at some predefined sites and recording of the response of the domain at another set of locations. It has been observed that similar results can often be obtained by considering a far smaller number K of multiple linear superpositions of experiments with (Formula presented.). This allows the construction of the solution to the inverse problem in time (Formula presented.) instead of (Formula presented.). Given these considerations it should not be necessary to perform all the N experiments but only a much smaller number of K experiments with simultaneous sources in superpositions with certain weights. Devising such procedure would results in a drastic reduction in acquisition time. The question we attempt to rigorously investigate in this work is: what are the optimal weights? We formulate the problem as an optimal experimental design problem and show that by leveraging techniques from this field an answer is readily available. Designing optimal experiments requires some statistical framework and therefore the statistical framework that one chooses to work with plays a major role in the selection of the weights.