Description: Synthetic aperture radar (SAR) images display very high dynamic ranges. Man-made structures (like buildings or power towers) produce echoes that are several orders of magnitude stronger than echoes from diffusing areas (vegetated areas) or from smooth surfaces (e.g., roads). The impulse response of the SAR imaging system is, thus, clearly visible around the strongest targets: sidelobes spread over several pixels, masking the much weaker echoes from the background. To reduce the sidelobes of the impulse response, images are generally spectrally apodized, trading resolution for a reduction of the sidelobes. This apodization procedure (global or shift-variant) introduces spatial correlations in the speckle-dominated areas that complicates the design of estimation methods. This paper describes strategies to cancel sidelobes around point-like targets while preserving the spatial resolution and the statistics of speckle-dominated areas. An irregular sampling grid is built to compensate the subpixel shifts and turn cardinal sines into discrete Diracs. A statistically grounded approach for point-like target extraction is also introduced, thereby providing a decomposition of a single look complex image into two components: a speckle-dominated image and the point-like targets. This decomposition can be exploited to produce images with improved quality (full resolution and suppressed sidelobes) suitable both for visual inspection and further processing (multitemporal analysis, despeckling, interferometry).