In this paper we have proposed a novel method for image denoising using local polynomial approximation (LPA) combined with the relative intersection of confidence intervals (RICI) rule. The algorithm performs separable column-wise and row-wise image denoising (i.e., independently by rows and by columns), combining the obtained results into the final image estimate. The newly developed method performs competitively among recently published state-of-the-art denoising methods in terms of the peak signal-to-noise ratio (PSNR), even outperforming them for small to medium noise variances for images that are piecewise constant along their rows and columns.