Sampling in practice: is the best reconstruction space bandlimited?

Shannon's sampling theory and its variants provide effective solutions to the problem of reconstructing a signal from its samples in some "shift-invariant " space, which may or may not be bandlimited. In this paper, we present some further justification for this type of representation, while addressing the issue of the specification of the best reconstruction space. We consider a realistic setting where a multidimensional signal is prefiltered prior to sampling and the samples corrupted by additive noise. We consider two formulations of the reconstruction problem. In the first deterministic approach, we determine the continuous-space function that minimizes a variational, Tikhonov-like criterion that includes a discrete data term and a suitable continuous-space regularization functional. In the second formulation, we seek the minimum mean square error (MMSE) estimation of the signal assuming that the input signal is a realization of a stationary random process. Interest...

• Type: Conference
• Year: 2005
• Where: ICIP
• Authors: Sathish Ramani, Dimitri Van De Ville, Michael Unser
• Keywords: ICIP 2005, Image Processing