Iterative Optimization in Inverse Problems

198 Iterative Optimization in Inverse Problems

selecting a realization of a random variable governed by f

j

(v). For example,

there could be J bowls of colored marbles, and we randomly select a bowl,

and then randomly select a marble within the selected bowl. For each n

the number v

n

is the numerical code for the color of the nth marble drawn.

In this illustration we are using a mixture of probability functions, but we

could have used probability density functions.

13.8.4 The Acceptable Data

We approach the mixture problem by creating acceptable data. We

imagine that we could have obtained x

n

= j

n

,forn =1, ..., N,wherethe

selection of v

n

is governed by the ...