ABSTRACT
A fundamental inverse problem is the reconstruction of a function from finitely many measurements pertaining to that function. This problem is central to radar, sonar, optical imaging, transmission and emission tomography, magnetic resonance imaging, and many other applications. Because the measured data is limited, it cannot serve to determine one single correct answer. In each of these applications some sort of prior information is incorporated in the reconstruction process in order to produce a usable solution. Minimizing a cost function is a standard technique used to single out one solution from the many possibilities. The reconstruction algorithms often employ projection techniques to guarantee that the reconstructed function is consistent with the known constraints. Typical image reconstruction problems involve thousands of data values and iterative algorithms are required to perform the desired optimization.
