Exact reconstruction of an evolving signal from incomplete information of its current and future states

lunch will be served

Let f ¿ 2(I) be a signal at time t = 0 of an evolution process controlled by a bounded linear operator A that produces the signals Af, A2f, · · · at times t = 1, 2, · · ·. Let Y = {f(i), Af(i), · · · , Ali f(i) : i ¿ ¿ ¿ I} be the spatio-temporal samples taken at various time levels. The problem under consideration is to ¿nd necessary and su¿cient conditions on A, ¿, li in order to recover any f ¿ 2(I) from the measurements Y . This is the so called Dynamical Sampling Problem in which we seek to recover a signal f by combining coarse samples of f and its futures states Alf. Various versions of dynamical sampling problems exhibit features that are similar to many fundamental problems: deconvolution, ¿lter banks, super-resolution, compressed sensing etc. In this talk, we will discuss the problem and show some recent results.