High-fidelity 3D audio experience requires accurate individual head-related transfer function (HRTF) representation. However, the process of measuring individual HRTFs typically involves measurements from hundreds of directions, with specialized and expensive equipment, which makes this process inaccessible for most users. In this paper, a new technique to reconstruct high resolution individual HRTFs from sparse measurements is presented. This is achieved by minimizing the spatial aliasing error in the spherical harmonics (SH) representation of the HRTFs, and by incorporating statistics calculated from a set of reference HRTFs, leading to an optimal minimum mean-square error solution. A quantitative analysis of the proposed method illustrates its benefits even for extreme cases, such as using only 25 individual HRTF measurements and a generic HRTF as a reference.