  Radiation symmetry evaluation is critical to the laser driven Inertial
Confinement Fusion (ICF), which is usually done by solving a view-factor
equation model. The model is nonlinear, and the number of equations can be very
large when the size of discrete mesh element is very small to achieve a
prescribed accuracy, which may lead to an intensive equation solving process.
In this paper, an efficient radiation symmetry analysis approach based on
sparse representation is presented, in which, 1) the Spherical harmonics,
annular Zernike polynomials and Legendre-Fourier polynomials are employed to
sparsely represent the radiation flux on the capsule and cylindrical cavity,
and the nonlinear energy equilibrium equations are transformed into the
equations with sparse coefficients, which means there are many redundant
equations, 2) only a few equations are selected to recover such sparse
coefficients with Latin hypercube sampling, 3) a Conjugate Gradient Subspace
Thresholding Pursuit (CGSTP) algorithm is then given to rapidly obtain such
sparse coefficients equation with as few iterations as possible. Finally, the
proposed method is validated with two experiment targets for Shenguang II and
Shenguang III laser facility in China. The results show that only one tenth of
computation time is required to solve one tenth of equations to achieve the
radiation flux with comparable accuracy. Further more, the solution is much
more efficient as the size of discrete mesh element decreases, in which, only
1.2\% computation time is required to obtain the accurate result.
