Lossy dielectric and magnetic obstacles are typically present in many high-frequency scattering applications. We study this problem using the equivalence principle and the method of moments (MoM). When the structure is complex and high accuracy is required; the number of unknowns in the numerical solution naturally grows. Therefore, we propose the use of wavelet-like bases to improve the numerical efficiency and memory requirements. For verification purposes, the results provided by the new technique are successfully compared with those obtained with the conventional MoM approach. The new technique has been applied to characterize the scattering behavior of large square and elliptical obstacles which are composed of lossy dielectric and magnetic media.