ABSTRACT
In Chapter 13 we considered the problem of estimating a nonnegative function of a continuous variable from finitely many of its Fourier coefficients. The estimate was again a function of a continuous variable. In such cases, we would convert the estimate to a finite vector just prior to graphing the estimate. In this chapter we discuss an alternative approach, in which the nonnegative function to be estimated is discretized at the outset. Discrete entropy maximization and related procedures are then used to reconstruct the nonnegative vector from finitely many linear-functional values. Unlike the MEM and the IPDFT methods, the algorithms we focus on here, primarily the multiplicative algebraic reconstruction technique (MART) and its simultaneous version, the SMART, are iterative.
