Abstract: Critically sampled graph filter banks with spectral domain sampling requires to perform eigendecomposition of the Laplacian matrix, which leads to high computational complexity. To solve this problem, an improved Jacobi algorithm is proposed to approximate the eigenmatrix of the framework to reduce the computational complexity. In this algorithm, the approximate solution of eigenmatrix is formulated into a constrained optimization problem, whose objective function is the approximation error of Laplacian matrix, and the constraint function is the sparse orthogonality of the approximate eigenmatrix. Theoretical and simulation experiments show that using the approximate feature matrix in the filter banks will not destroy its perfect reconstruction conditions. Compared with the existing critically sampled graph filter banks with spectral domain sampling, the improved algorithm reduces the computational complexity while maintaining good denoise performance.