Recursive filtering 2D Tikhonov regularization - Ferreira, Hermes H.; Gastal, Eduardo S. L. (Anais da Conference on Graphics, Patterns and Images (SIBGRAPI), 2022)
In this work we describe an implementation of the 2D Tikhonov regularization filter which scales linearly with the input signal’s size. We propose a novel algorithm to decompose the filter’s 2D kernel as a sum of axis-aligned Gaussians. Our algorithm uses symmetries of the kernel to provide a fast computation of the Gaussian decomposition in the frequency domain, where the 2D Tikhonov kernel has a closed-form expression. The convolution with each Gaussian is then computed using linear-time separable recursive filtering. This way, a fast solution to the 2D Tikhonov regularization problem is obtained.