Non-local/local image filters using fast eigenvalue filtering

In this paper, we propose a fast and an approximate solution of non-local/local filters using Chebyshev polynomial approximation (CPA). A non-local/local filter is generally expressible in a matrix form. From the matrix notation, image denoising performance is improved by filtering the eigenvalues of the filter matrix. However, it requires much execution time due to computational complexity of eigendecomposition. To reduce the computational cost, we apply the CPA to eigenvalue filtering, leading to an eigendecomposition-free procedure. Moreover, a fast SURE-based parameter optimization is possible by using the CPA. It enables us to determine a suitable filtering parameter efficiently. Numerical examples illustrate that the proposed method is significantly faster than conventional methods while it maintains high approximate precision.