Single pixel camera imaging is an emerging paradigm that allows high-quality images to be provided by a device only equipped with a single point detector. A single pixel camera is an experimental setup able to measure the inner product of the scene under view-the image-with any user-defined pattern. Post-processing a sequence of point measurements obtained with different patterns permits to recover spatial information, as it has been demonstrated by state-of-theart approaches belonging to the compressed sensing framework. In this paper, a new framework for the choice of the patterns is proposed together with a simple and efficient image recovery scheme. Our goal is to overcome the computationally demanding 1-minimization of compressed sensing. We propose to choose patterns among a wavelet basis in an adaptive fashion, which essentially relies onto the prediction of the significant wavelet coefficients' location. More precisely, we adopt a multiresolution strategy that exploits the set of measurements acquired at coarse scales to predict the set of measurements to be performed at a finer scale. Prediction is based on a fast cubic interpolation in the image domain. A general formalism is given so that any kind of wavelets can be used, which enables one to adjust the wavelet to the type of images related to the desired application. Both simulated and experimental results demonstrate the ability of our technique to reconstruct biomedical images with improved quality compared to CS-based recovery. Application to real-time fluorescence imaging of biological tissues could benefit from the proposed method.