Microwave breast imaging with an under-determined reconstruction parameter mesh

Microwave imaging has been proposed as a method for detecting breast tumors because of the high electrical property contrast between tumors and normal tissue. We are currently developing a tomographic system which can generally be treated as an ill-conditioned inverse problem and utilize a Gauss-Newton iterative algorithm to handle its nonlinear nature. The ill-conditioning is generally related to the number of parameters being reconstructed with respect to the amount of measurement data. Our initial implementation restricted the number of parameters to close to that of the measurement data. However, this sparse discretization of the imaging zone severely limited the resolution and required a high degree of spatial filtering to stabilize the algorithm convergence. We are currently exploring significantly increasing the number of reconstruction parameters to the point of making the problem considerably under-determined. Initial results indicate that the benefit in terms of increased degrees of freedom has resulted in dramatically improved resolution without compromising stability.