High-rate interpolation of random signals from nonideal samples
IEEE Transactions on Signal Processing
Estimation and model selection for an IDE-based spatio-temporal model
IEEE Transactions on Signal Processing
Noninvertible gabor transforms
IEEE Transactions on Signal Processing
Sampling from a system-theoretic viewpoint part I: concepts and tools
IEEE Transactions on Signal Processing
The ill-posedness of the sampling problem and regularized sampling algorithm
Digital Signal Processing
Reconstruction from non-uniform samples: A direct, variational approach in shift-invariant spaces
Digital Signal Processing
Hi-index | 35.70 |
Digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuous-time signal from a sequence of corrupted discrete-time samples. In this paper, a general formulation of this problem is developed that treats the interpolation problem from ideal, noisy samples, and the deconvolution problem in which the signal is filtered prior to sampling, in a unified way. The signal reconstruction is performed in a shift-invariant subspace spanned by the integer shifts of a generating function, where the expansion coefficients are obtained by processing the noisy samples with a digital correction filter. Several alternative approaches to designing the correction filter are suggested, which differ in their assumptions on the signal and noise. The classical deconvolution solutions (least-squares, Tikhonov, and Wiener) are adapted to our particular situation, and new methods that are optimal in a minimax sense are also proposed. The solutions often have a similar structure and can be computed simply and efficiently by digital filtering. Some concrete examples of reconstruction filters are presented, as well as simple guidelines for selecting the free parameters (e.g., regularization) of the various algorithms