A novel inversion technique is proposed to unfold core asymmetries at the source with x-ray emission images, which were obtained from imploded surrogate capsules in symmetry diagnostic experiments. The axisymmetrical core emission can be expanded as a Fourier series, with Legendre polynomials and spherical Bessel functions as bases concerned with polar angle and radius, respectively. A least-squares estimator is employed to obtain the unknown coefficients from its two-dimensional image data. The unfolded Legendre coefficients can be further used to test modeling of drive asymmetries in hohlraums. This technique is also demonstrated with a proof-of-principle experiment performed on the Shenguang II laser facility [L. Zunqi et al., Chin. J. Lasers B10, 6 (2001)].