Distance matrices and modified cyclic projections for molecular conformation

Biological compounds exhibit extraordinary functional specificity as a consequence of their precise spatial structure. Two signal recovery algorithms for computing molecular structure from noisy measurements of interatomic distances are presented. The problem is formulated as the minimization of a quadratic cost over the intersection of constraint sets. In a broader signal recovery context, a technique is utilized for iteratively computing the unique projection onto an intersection of closed convex sets, and the simplification possible with an appropriate choice of norm, despite a nonconvex constraint set, is illustrated