Total variation denoising (TVD) is an effective technique for image denoising, in particular, for recovering blocky, discontinuous images from noisy background. The problem is formulated as an optimization problem in the space of bounded variation functions, and the solution is obtained by solving the associated Euler–Lagrange equation defined on the domain occupied by the entire image. The method offers high quality results, but is computationally expensive for large images, especially for three-dimensional problems. In this paper, we introduce a highly parallel version of the algorithm which formulates the problem as multiple overlapping, but independent, optimization problems, and each is defined on a portion of the image domain. This approach is similar to the overlapping Schwarz type domain decomposition method, but is non-iterative, for solving partial differential equations, and is highly scalable, without using any coarse grids, for parallel computers with a large number of processors. We show by a theory and also by some two- and three-dimensional numerical experiments that the new approach has similar numerical accuracy as the classical TVD approach, but is much more efficient on parallel computers.