In [doi{10.1109/ICMEW.2014.6890711}], a~graph-based filtering of noisy images is performed by directly computing a projection of the image to be filtered onto a lower dimensional Krylov subspace of the graph Laplacian, constructed using non-negative graph weights determined by distances between image data corresponding to image pixels. We extend the construction of the graph Laplacian to the case, where some graph weights can be negative. Removing the positivity constraint allows more accurate inference of a graph model behind the data, and thus can improve quality of filters for graph-based signal processing, e.g., denoising, compared to the standard construction, without affecting the computational costs. [http://arxiv.org/abs/1509.02491]