The increasing use of the electromagnetic spectrum and the need for more sensitive radio telescopes spurs wide interest in adaptive RFI suppression techniques, such as spatial filtering. We study the effect of spatial filtering techniques on radio astronomical image formation. Current deconvolution procedures such as CLEAN are shown to be unsuitable to spatially filtered data, and the necessary corrections are derived. To that end, we reformulate the imaging (deconvolution/calibration) process as a sequential estimation of the locations of astronomical sources. This leads to an extended CLEAN algorithm and gives estimates of the expected image quality and the amount of interference suppression that can be achieved. Some of the effects are shown in simulated images.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.