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We propose a linearized wave-equation inversion formulation for time-lapse seismic data sets. Our method poses time-lapse imaging as a joint least-squares problem that utilizes target-oriented approximations to the Hessian of the objective function. Because our method accounts for illumination mismatches --caused by differences in acquisition geometries-- and for band-limited wave-propagation effects, it provides better estimates of production-related changes in reservoir acoustic properties than conventional time-lapse processing methods. Using data sets from a North Sea field, we demonstrate how our method can be used to image differences between time-lapse data sets. Furthermore, we show that obstruction artifacts may be attenuated by wave-equation inversion.