We demonstrate the utility of a multiresolution approach for target detection in SAR imagery. Man-made objects exhibit characteristic phase and amplitude fluctuations as the image resolution is varied, while natural terrain has a random signature. We construct a number of detection strategies: an optimal invariant multiresolution detector based on a derived multiresolution increments process; and a generalized likelihood ratio detector to differentiate between a first-order autoregressive multiresolution increments process and white noise. We show that these schemes significantly outperform a standard energy detector operating on the finest available SAR resolution.