@Article{Kybic-ieeeSP2002a, IS = { zkontrolovano 05 Dec 2003 }, UPDATE = { 2003-10-17 }, author = {Jan Kybic and Thierry Blu and Michael Unser}, title = {Generalized sampling: A variational approach. {P}art {I} --- {T}heory}, year = {2002}, month = {August}, pages = {1965--1976}, journal = {IEEE Transactions on Signal Processing}, publisher = {Institute of Electrical and Electronics Engineers}, address = {445 Hoes Lane, Piscataway, U.S.A. }, issn = { 1053-5888 }, volume = { 50 }, number = { 8 }, authorship = {50-40-10 }, annote = {We consider the problem of reconstructing a~multidimensional vector function from a~finite set of linear measures. These can be irregularly sampled responses of several linear filters. Traditional approaches reconstruct in an~a~priori given space; e.g., the space of bandlimited functions. Instead, we have chosen to specify a~reconstruction that is optimal in the sense of a~quadratic plausibility criterion $J$. First, we present the solution of the generalized interpolation problem. Later, we consider also the approximation problem and we show that both lead to the same class of solutions. }, keywords = { sampling, reconstruction, variational criterion, thin-plate splines }, project = { epfl_kybic_thesis}, psurl = { [Pdf,210kB] }, url = {ftp://cmp.felk.cvut.cz/pub/cmp/articles/kybic/Kybic-ieeeSP2002a.pdf}, }