Discrete approximation by variational vector splines for noisy data

We deal with the problem of constructing and/or approximating some curves and surfaces from a noisy data set. The main objective here is to adapt the theory of the discrete smoothing variational splines [A. Kouibia, M. Pasadas, Approximation by discrete variational splines, J. Comput. Appl. Math. 116 (2000) 145-156] to the noisy data case. The problem is formulated and a result of almost sure convergence is established.