Multi-scale thermal radiation effects correction via a fast surface fitting with Chebyshev polynomials

In an uncooled infrared imaging system, thermal radiation effects are caused by the heat source from the target or the detection window, which affects the ability of target detection, tracking, and recognition seriously. To address this problem, a multi-scale correction method via a fast surface fitting with Chebyshev polynomials is proposed. A high-precision Chebyshev polynomial surface fitting is introduced into thermal radiation bias field estimation for the first time, to the best of our knowledge. The surface fitting in the gradient domain is added to the thermal radiation effects correction model as a regularization term, which overcomes the ill-posed matrix problem of high-order bivariate polynomials surface fitting, and achieves higher accuracy under the same order. Additionally, a multi-scale iterative strategy and vector representation are adopted to speed up the iterative optimization and surface fitting, respectively. Vector representation greatly reduces the number of basis function calls and achieves fast surface fitting. In addition, split Bregman optimization is used to solve the minimization problem of the correction model, which decomposes the multivariable optimization problem into multiple univariate optimization sub-problems. The experimental results of simulated and real degraded images demonstrate that our proposed method performs favorably against the state of the art in thermal radiation effects correction.