两变量离散正交多项式及其在图像重建中的应用

主要讨论了构造于三角域上的两变量离散正交多项式的性质，包括正交性和矩阵形式的三阶递推公式。在此基础上，提出了直接计算这类两变量离散正交多项式的矩阵公式，并用这种构造于三角域上的两变量离散正交多项式作为基函数，首次构造出相应的两变量离散正交矩。仿真结果表明：该方法具有较好的可行性和较广的适用范围；在图像重建等方面，两变量离散Charlier正交矩的性能优于Zernike矩。

Orthogonal Polynomials with Two Discrete Variables and Their Applications in Image Reconstruction

The paper firstly discusses the properties of orthogonal polynomials with two discrete variables constructed on the triangle, including orthogonality and three orders recurrence relation of matrix form. And then, this paper proposes two new methods, respectively, for the computation of the orthogonal polynomials with two discrete variables and for the generation of orthogonal moments with two discrete variables by using its orthogonal polynomials as kernel function. The results show that the above methods are of better feasible and the Charlier orthogonal moments of two variables are of better performance than Zernike moments in image reconstruction.