Overview

The general problem considered in the omnt+ project is to best solve a system of integral equations

with a lattice constraint of the form where and are potentially infinite, but measurable, functions. Examples abound, including spectral estimation, spectroscopy, and of particular interest to the omnt+ project, tomography.

Since the unknown is a function, residing in a known function space , the integral equations (1) are not sufficient to uniquely determine . If the equations are consistent, they are underdetermined: there are an infinity of solutions. To overcome this difficulty, we select the ``best'' function by minimizing some measure of the function. Mathematically, we seek solutions to Writing for the system in (1), and incorporating the lattice constraints in the objective function by adding infinities as needed, we have the exactly constrained problem If the data vector , or the measurement process , is known to be inexact, we may relax the constraints to the form