Recursive filtering 2D Tikhonov regularization

  • Hermes H. Ferreira UFRGS
  • Eduardo S. L. Gastal UFRGS


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.
Palavras-chave: Graphics, Closed-form solutions, Filtering, Convolution, Frequency-domain analysis, Filtering algorithms, Kernel
FERREIRA, Hermes H.; GASTAL, Eduardo S. L.. Recursive filtering 2D Tikhonov regularization. In: CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI), 35. , 2022, Natal/RN. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2022 .