Chirp-pulse microwave computerized tomography (CP-MCT) is an imaging modality developed at the Department of Biocybernetics, University of Niigata (Niigata, Japan), which intends to reduce the microwave-tomography problem to an X-ray-like situation. We have recently shown that data acquisition in CP-MCT can be described in terms of a linear model derived from scattering theory. In this paper, we validate this model by showing that the theoretically computed response function is in good agreement with the one obtained from a regularized multiple deconvolution of three data sets measured with the prototype of CP-MCT. Furthermore, the reliability of the model as far as image restoration in concerned, is tested in the case of space-invariant conditions by considering the reconstruction of simple on-axis cylindrical phantoms.

Mathematical results on ill-posed and ill-conditioned problems are reviewed and the formal aspects of regularization theory in the linear case are introduced. Specific topics in early vision and their regularization are then analyzed rigorously, characterizing existence, uniqueness, and stability of solutions. A fundamental difficulty that arises in almost every vision problem is scale, that is, the resolution at which to operate. Methods that have been proposed to deal with the problem include scale-space techniques that consider the behavior of the result across a continuum of scales. From the point of view of regulation theory, the concept of scale is related quite directly to the regularization parameter lambda . It suggested that methods used to obtained the optimal value of lambda may provide, either directly or after suitable modification, the optimal scale associated with the specific instance of certain problems.>