We propose a theoretical study of the conditions guaranteeing that a decoder will obtain an optimal signal recovery from an underdetermined set of linear measurements. This special type of performance guarantee is termed instance optimality and is typically related with certain properties of the dimensionality-reducing matrix M. Our work extends traditional results in sparse recovery, where ins...

The literature on sparse recovery often adopts the “norm” ( ) as the penalty to induce sparsity of the signal satisfying an underdetermined linear system. The performance of the corresponding minimization problem can be characterized by its null space constant. In spite of the NP-hardness of computing the constant, its properties can still help in illustrating the performance of minimization. I...

Abstract—In system identification of structured models, the prediction error method provides asymptotically efficient estimates under mild assumptions, but in general it requires solving a non-convex optimization problem. An alternative class of methods uses a non-parametric model as intermediate step to obtain the model of interest. The weighted null-space fitting (WNSF) method belongs to this...

A hierarchical approach to the single-pair shortest path problem subdivides a network with n vertices into r regions with the same number m of vertices (n = rm) and iteratively creates higher levels of a hierarchical network by merging a constant number c of adjacent regions. In a hierarchical approach, shortest paths are computed at higher levels and expanded towards lower levels through intra...

A uniqueness theorem for Minkowski space and de Sitter space associated with the occurrence of null lines (inextendible globally achronal null geodesics) is presented. This result is obtained as a consequence of the null splitting theorem, which is also discussed.