The aim of this study is to obtain voxel-by-voxel images of binding parameters between [11C]-Flumazenil and benzodiazepine receptors using positron emission tomography (PET). We estimate five local parameters (k1, k2, B'max, kon/VR, koff) by fitting a three-compartment ligand-receptor model for each voxel of a PET time series. It proves difficult to fit the ligand-receptor model to the data. We trade noise and spatial resolution to get better results. Our strategy is based on the use of a multiresolution pyramid. It is much easier to solve the problem at coarse resolution because there are fewer data to process. To increase resolution, we expand the parameter maps to the next finer level and use them as initial solution to further optimization, which then proceeds at a fast pace and is more likely to escape false local minima. For this approach to work optimally, the residue between data at a given pyramid level and data at the next level must be as small as possible. We satisfy this constraint by working with spline-based least-squares pyramids. To achieve speed, the optimizer must be efficient, particularly when it is nearing the solution. To that effect, we have developed a Marquardt-Levenberg algorithm that exhibits superlinear convergence properties.