From near, examine their glasses. This cost analysis is oversimplified in that most applications do not require dense operators. With sparse operators, the cost advantage of adjoints is even more pronounced since for adjoints, the cost savings of operator sparseness translate directly to real cost savings. The situation is less favorable and much more muddy for inversion. The reason that Chapter 2 covers iterative methods and neglects exact methods is that in practice iterative methods are not run to their theoretical completion but they run until we run out of patience.
Cost is a big part of the story, but the story has many other parts.
Inversion, while being the only logical path to the best answer, is a path littered with pitfalls. The first pitfall is that the data is rarely able to determine a complete solution reliably. Generally there are aspects of the image that are not learnable from the data. In this chapter we study the simplest, most transparant example of data insufficiency. Data exists at irregularly spaced positions in a plane.