We propose a new image inpainting technique which uses approximation properties of the fuzzy (F-)transform. The proposed technique is based on the inverse F-transform and combines it with an original image on an undamaged or missing area. We present two algorithms of the F-transform based reconstruction: one-step and multi-step. We demonstrate how these algorithms cope with various damage and compare it with interpolation and advanced inpainting techniques. We show various application in addition to inpainting, such as resampling, filtering, or denoising. Experimental results are based on testing on various sets of grayscale and color images.