Under the general regression setup, $y_i = f_i + \epsilon_i$, we are interested in estimating a possibly multivariate regression function $f$. The wavelet thresholding is a simple operation in the wavelet domain that selects the subset of wavelet coefficients corresponding to an estimator of $f$ when back-transformed. We propose selection of the subset in a semisupervised fashion. A neighbor concept and distance function appropriate for wavelet domains is proposed. The \textit{unlabeled} coefficients are not independent and fall on a low dimensional manifold in the space of all wavelet coefficients. The decision to include a coefficient in the model depends not only on its magnitude but also on the distances from the \textit{labeled} and unlabeled coefficients. The method's theoretical properties are discussed and its performance is demonstrated on simulated examples.