Adaptive wavelet-based image characterizations have been proposed in previous works for Content-based Image Retrieval (CBIR) applications. In these applications, the same wavelet basis was used to characterize each query image: this wavelet basis was tuned to maximize the retrieval performance in a training dataset. We take it one step further in this paper: a different wavelet basis is used to characterize each query image. A regression function, tuned to maximize the retrieval performance in the training dataset, is used to estimate the best wavelet filter, in terms of expected retrieval performance, for each query image. A simple image characterization, based on the standardized moments of the wavelet coefficient distributions, is presented. An algorithm is proposed to compute this image characterization almost instantly for every possible separable or non-separable wavelet filter. Therefore, using a different wavelet basis for each query image does not considerably increase computation times. On the other hand, significant retrieval performance increases were obtained in a medical image dataset, a texture dataset, a face recognition dataset and an object picture dataset. This additional flexibility in wavelet adaptation paves the way to relevance feedback on image characterization itself, not simply on the way image characterizations are combined.