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Irregular sampling theorems for wavelet subspaces

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3 Author(s)
Wen Chen ; Dept. of Inf. Network Sci., Univ. of Electro-Commun., Tokyo, Japan ; Itoh, S. ; Shiki, J.

From the Paley-Wiener 1/4-theorem, the finite energy signal f(t) can be reconstructed from its irregularly sampled values f(k+δκ) if f(t) is band-limited and supκκ|<1/4. We consider the signals in wavelet subspaces and wish to recover the signals from its irregular samples by using scaling functions. Then the method of estimating the upper bound of supκκ | such that the irregularly sampled signals can be recovered is very important. Following the work done by Liu and Walter (see J. Fourier Anal. Appl., vol.2, no.2, p.181-9, 1995), we present an algorithm which can estimate a proper upper bound of supκ κ|. Compared to Paley-Wiener 1/4-theorem, this theorem can relax the upper bound for sampling in some wavelet subspaces

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Information Theory, IEEE Transactions on  (Volume:44 ,  Issue: 3 )