Abstract: Global illumination is a complex all-frequency phenomenon including subtle effects caused by indirect lighting. Computing global illumination interactively for dynamic lighting conditions has many potential applications, notably in architecture, motion pictures and computer games. It remains a challenging issue, despite the considerable amount of research work devoted to finding efficient methods. This paper presents a novel method for fast computation of indirect lighting; combined with a separate calculation of direct lighting, we provide interactive global illumination for scenes with diffuse and glossy materials, and arbitrarily distributed point light sources. To achieve this goal, we introduce three new tools: a 4D wavelet basis for concise radiance expression, an efficient hierarchical pre-computation of the Global Transport Operator representing the entire propagation of radiance in the scene in a single operation, and a run-time projection of direct lighting on to our wavelet basis. The resulting technique allows unprecedented freedom in the interactive manipulation of lighting for static scenes.