The massive digitization of heritage documents has raised new prospects for research like degraded document image restoration. Degradations harm the legibility of the digitized documents and limit their processing. As a solution, we propose to tackle the problem of degraded text characters with PDE (partial differential equation)-based approaches. Existing PDE approaches do not preserve singularities and edge continuities while smoothing. Hence, we propose a new anisotropic diffusion by adding new constraints to the Weickert coherence-enhancing diffusion filter in order to control the diffusion process and to eliminate the inherent corner rounding. A qualitative improvement in the singularity preservation is thus achieved. Experiments conducted on degraded document images illustrate the effectiveness of the proposed method compared with other anisotropic diffusion approaches. We illustrate the performance with the study of the optical recognition accuracy rates.