Based on the principle of spatial pyramid for signal, a multi-scale transform of two-dimensional (2D) interpolating pyramid is constructed by the nonlinear median operator. The transform properties of error diffuse halftoning noise on multiple scales are investigated and analyzed through experiments. According to these properties, a robust inverse halftoning method is proposed. The halftoning image is firstly preprocessed by a Gaussian low-pass filter, and decomposed by the one-scale transform. Then a Wiener filter is employed to the detailed coefficients. Finally an inverse image is reconstructed. Experimental results show that the proposed transform has the advantage of separating the halftoning noise and image detail over linear multi-resolution transform. The presented inverse halftoning method performs some excellent abilities on sharp edge, high peak signal-to-noise ratio (PSNR), and small memory requirement.