We present a novel way of approaching image-based 3D reconstruction based on radiance fields. The problem of volumetric reconstruction is formulated as a non-linear least-squares problem and solved explicitly without the use of neural networks. This enables the use of solvers with a higher rate of convergence than what is typically used for neural networks, and fewer iterations are required until convergence. The volume is represented using a grid of voxels, with the scene surrounded by a hierarchy of environment maps. This makes it possible to get clean reconstructions of 360{\deg} scenes where the foreground and background is separated. A number of synthetic and real scenes from well known benchmark-suites are successfully reconstructed with quality on par with state-of-the-art methods, but at significantly reduced reconstruction times.