In , we have proposed two total variation (TV) minimization wavelet models for the problem of filling in missing or damaged wavelet coefficients due to lossy image transmission or communication. The proposed models can have effective and automatic control over geometric features of the inpainted images including sharp edges, even in the presence of substantial loss of wavelet coefficients, including in the low frequencies. In this paper, we investigate a modification of the model for noisy images to further improve the recovery properties by using multi-level parameters in the fitting term. Some new numerical examples are also shown to illustrate the effectiveness of the recovery.
Halftoning has been a significant topic in image processing due to many emerging
applications, various diversified approaches, and challenging theoretical analysis.
Inspired by the wealthy literature on halftoning, as well as the recent PDE (partial
differential equations) approach in image processing, the current work proposes a novel
progressive halftoning algorithm by empolying the celebrated anisotropic diffusion model
of Perona and Malik (<i>IEEE Trans. Pattern Anal. Machine Intell.,</i> 12:629-639, 1990),
and a properly designed stochastic strategy for binary flipping. The halftone outputs
from the proposed model are typical samples of some random fields, which share many
virtues of existent deterministic halftone algorithms, as well as show many interesting
features like the blue noise behavior. The new model is independent of traditional
windows, tiles, or paths, and allows direct parallel implementation.
Inpainting is an image interpolation problem, with broad applications in image processing and the digital technology. This paper presents our recent efforts in developing inpainting models based on the Bayesian and variational principles. We discuss several geometric image (prior) models, their role in the construction of variational inpainting models, the resulting Euler-Lagrange differential equations, and their numerical implementation.