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Much of what we understand about the world is learned by making indirect measurements. For instance, we measure two-dimensional images of the world and from these infer 3-D structure, or we measure gravitational fields and from these infer the density of rock below earth's surface. The field of Inverse Problems is concerned with learning about causes of phenomena by measuring the related effects, and inverting the models relating the two. It is often of interest, particularly in imaging problems, to know the limits to how well a certain object or quantity can be detected or estimated. While a multitude of imaging algorithms have been developed for varied tasks, relatively few studies are available that put the performance of these many algorithms into proper perspective by comparing them to limits or bounds on such performance, as derived from first principles. In this spirit, it is particularly instructive to study the relationship between imaging and the mathematical theory of information and communication. I will describe in this talk some of our work in this direction and illustrate with some examples from motion estimation, and resolution enhancement.