We propose a new color de-quantizing method for paletted images based on maximizing the sparseness of the overcomplete wavelet analysis of the estimation within the consistency set defined by the observation. The sparsity is enforced by minimizing the 0-norm of the coefficients of the wavelet analysis representation. The resulting method iterates between hard-thresholding of the linear response of current estimate and a new proposed consistency projection onto the Voronoi cells defined by color quantization. Results indicate that our method outperforms those based on linear diffusion and minimization of 1-norm.