This issue of Optics Express provides a snapshot of current theoretical research in the area of tomographic image reconstruction. The topics have been chosen to illustrate some important principles that arise not only in medical imaging but also in the broader arena of indirect imaging. All of the papers were invited by the editors, and all underwent independent peer review.
The first paper, by Arridge and Schweiger, deals with optical tomography, where light propagates through a turbid medium such as brain tissue. In spite of the diffusive nature of this propagation, it is possible to reconstruct many features of clinical interest. Arridge and Schweiger have been leaders in bringing sophisticated mathematics to this problem, and in the current paper they employ the powerful technique of adjoint differentiation.
The second paper, by Cunningham, Hanson and Battle, also uses adjoint differentiation, but applied to extremely ill-posed problems in gamma-ray tomography, specifically imaging of the beating heart. This group has been instrumental in emphasizing the role of Bayesian methods in image reconstruction, and here they use the adjoint method to maximize the posterior probability of an object model given some very noisy data. The resulting images yield remarkably accurate estimates of ventricular volume.
The paper by Fessler does not deal with tomography per se, but rather with pinhole imaging, which forms the basis for many tomographic imaging systems. Through careful analysis, characteristic of the author, the tradeoff between spatial resolution and noise is studied and optimized.
Wilson and Barrett consider the effect of null functions, an inevitable feature of imaging systems that measure a discrete set of data from a continuous object. They give a practical algorithm for ascertaining the null component of any object with respect to any imaging system, and they illustrate its use by application to a real pinhole-imaging system.