Extended forms of Geman & Yang algorithm: application to MRI reconstruction

The main contribution of this communication is the derivation of a generalized form of the Geman & Yang construction for minimization of convex, non-quadratic criteria. The generalization provides a means of obtaining a normal matrix with predefined structure. We show that this property can be used to improve the numerical efficiency of edge preserving MRI reconstruction. The improvement is assessed experimentally using synthetic data. In order to illustrate the practicality of the method, an example of processing large size, 3D real data (the MRI image of a knee) is also provided.