Estimation of binary images by minimizing convex criteria

Reconstructing binary images is a problem which arises in various application fields. In this paper, this problem is considered in a regularization framework: the sought solution minimizes an objective function (a criterion). Criteria defined over the set of the binary images are nonconvex and there are no general methods permitting one to calculate the global minimum, while approximate solutions are very often of limited interest. On the other hand, general-purpose reconstruction techniques, based on convex criteria, yield continuous-valued smooth estimates which are far from binarity. We propose two methods which are based on convex criteria and introduce binarity only partially. More precisely, we construct objective functions whose minimizers are continuous-valued but have a quasi-binary shape. In other words, these estimates are composed essentially of binary-valued pixels while nonbinary pixels are rare. According to our approach, the construction of these objective functions is based on analytical considerations. The resultant methods are stable and numerically attractive