We consider network coding for a noiseless broadcast channel where each receiver demands a subset of messages available at the transmitter and is equipped with noisy side information in the form an erroneous version of the message symbols it demands. We view the message symbols as elements from a finite field and assume that the number of symbol errors in the noisy side information is upper bou...

In this article we tackle the problem of inverse non linear ill-posed problems from a statistical point of view. We discuss the problem of estimating an indirectly observed function, without prior knowledge of its regularity, based on noisy observations. For this we consider two approaches: one based on the Tikhonov regularization procedure, and another one based on model selection methods for ...

Metric Labeling problems have been introduced as a model for understanding noisy data with pair-wise relations between the data points. One application of labeling problems with pair-wise relations is image understanding, where the underlying assumption is that physically close pixels are likely to belong to the same object. In this paper we consider a variant of this problem, we will call Para...

Abstract Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown function PDE is be determined from partial knowledge of its solutions. This usually a highly non-linear ill-posed problem, for which unique reconstructability results, stability estimates global convergence numerical methods are very hard achieve....

Estimating a vector from noisy quadratic observations is a task that arises naturally in many contexts, from dimensionality reduction, to synchronization and phase retrieval problems. It is often the case that additional information is available about the unknown vector (for instance, sparsity, sign or magnitude of its entries). Many authors propose non-convex quadratic optimization problems th...