The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-286

“On Theory and Regularization of Scale-Limited Extrapolation”

by Li-Chien Lin and C.-C. Jay Kuo

September 1995

We propose a scale-limited signal model based on wavelet representation and study the reconstructability of scale-limited signals via extrapolation in this research. In analogy with the band-limited case, we define a scale-limited time-concentrated operator, and examine various vector spaces associated with such an operator. It is proved that the scale-limited signal space can be decomposed into the direct sum of two subspaces and only the component in one subspace can be exactly reconstructed, where the reconstructable subspace can be interpreted as a space consisting of scale/time-limited signals. Due to the ill-posedness of scale-limited extrapolation, a regularization process is introduced for noisy data extrapolation.

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