Preserving details in restoring images highly corrupted by impulse noise remains a challenging problem. We proposed an algorithm based on radial basis functions (RBF) interpolation which estimates the intensities of corrupted pixels by their neighbors. In this algorithm, first intensity values of noisy pixels in the corrupted image are estimated using RBFs. Next, the image is smoothed. The proposed algorithm can effectively remove the highly dense impulse noise. Experimental results show the superiority of the proposed algorithm in comparison to the recent similar methods both in noise suppression and detail preservation. Extensive simulations show better results in measure of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM), especially when the image is corrupted by very highly dense impulse noise.