We propose an edge-preserving multiscale image decomposition method using filters for non-equispaced signals. It is inspired by the domain transform, which is a high-speed edge-preserving smoothing method, and it can be used in many image processing applications. One of the disadvantages of the domain transform is sensitivity to noise. Even though the proposed method is based on non-equispaced filters similar to the domain transform, it is robust to noise since it employs a multiscale decomposition. It uses the Laplacian pyramid scheme to decompose an input signal into the piecewise-smooth components and detail components. We design the filters by using an optimization based on edge-preserving smoothing with a conversion of signal distances and filters taking into account the distances between signal intervals. In addition, we also propose construction methods of filters for non-equispaced signals by using arbitrary continuous filters or graph spectral filters in order that various filters can be accommodated by the proposed method. As expected, we find that, similar to state-of-the-art edge-preserving smoothing techniques, including the domain transform, our approach can be used in many applications. We evaluated its effectiveness in edge-preserving smoothing of noise-free and noisy images, detail enhancement, pencil drawing, and stylization.