Sparse Rational Polynomial Coefficient Estimation Method via Low-Rank Matrix Constraint

The rational function model (RFM) is an important general imaging model in remote sensing image geometric processing, which is composed of many rational polynomial coefficients (RPCs). However, due to the correlation among the high-order polynomials, the RPCs can be overfitting and the design matrix is ill-posed. Existing methods either alleviate the overfitting problem through parameter regularization or alleviate the ill-posedness of the design matrix through variable selection. However, these two problems exist simultaneously, and there is a lack of a unified optimization framework to alleviate overfitting and ill-posedness simultaneously. To address this issue, this paper proposes a sparse RPC estimation method via low-rank matrix constraint, called LRMC-RFM. The proposed method assumes that the observed design matrix constructed from GCPs is a noisy perturbation of an latent low-rank geometric design matrix. In a unified optimization framework, the latent low-rank geometric design matrix and the sparse RPCs are jointly estimated by introducing the nuclear norm and the ℓ1 norm. To ensure computational efficiency, an alternating direction method of multipliers (ADMM)-based optimization algorithm is derived. Extensive experiments demonstrate that the proposed method achieves better performance than existing competing methods.