Constrained signal reconstruction from wavelet transform coefficients

A new method is introduced for reconstructing a signal from an incomplete sampling of its discrete wavelet transform (DWT). The algorithm yields a minimum-norm estimate satisfying a priori upper and lower bounds on the signal. The method is based on a finite-dimensional representation theory for minimum-norm estimates of bounded signals developed by Cole (1990). Cole´s work provides a representation for minimum-norm estimates of a class of generalized transforms in terms of general correlation data (not just DFTs of autocorrelation lags, as in spectral estimation). One virtue of this great generality is that it includes the inverse DWT