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Generalized sampling: extension to frames and inverse and ill-posed problems
Generalized sampling is new framework for sampling and reconstruction in infinite-dimensional Hilbert spaces. Given measurements (inner products) of an element with respect to one basis, it allows one to reconstruct in another, arbitrary basis, in a way that is both convergent and numerically stable. However, generalized sampling is thus far only valid for sampling and reconstruction in systems that comprise bases. Thus, in the first part of this paper we extend this framework from bases todoi:10.1088/0266-5611/29/1/015008 fatcat:t66s2e5ry5aajgmjauuntagt4y