Signal recovery from the approximation component in the non-downsampled wavelet transform

It is well known that a signal can be perfectly reconstructed from its wavelet-decomposed components: an approximation component and a set of detail components. Can a signal be recovered from its approximation component without detail components? This paper gives an answer to this question using a non-downsampled wavelet transform. Our experiments and analyses show that a signal can be recovered from its approximation coefficients solely by performing the non-downsampled wavelet transform iteratively. The results from the 2-level and 4-level wavelet transforms show that the recovered signal converges to the original signal as the number of iteration increases.