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An illumination adjustable image (IAI) contains a large number of prerecorded images under various light directions. Relighting a scene under complicated lighting conditions can be achieved from the IAI. Using the radial basis function (RBF) approach to represent an IAI is proven to be more efficient than using the spherical harmonic approach. However, to represent high-frequency lighting effects, we need to use many RBFs. Hence, the relighting speed could be very slow. This brief investigates a partial reconstruction scheme for relighting an IAI based on the locality of RBFs. Compared with the conventional RBF and spherical harmonics (SH) approaches, the proposed scheme has a much faster relighting speed under the similar distortion performance.