<p>This paper proposes a Weickert-type second-order partial differential equation (PDE) that integrates a diffusion tensor with a bilateral total variation (BTV) term. The model is designed to combine the strengths of several established approaches. In other words, our model adopts the anisotropic diffusion behavior in uniform regions, incorporates the Weickert model’s edge-preserving capabilities near sharp transitions, and leverages the BTV term to suppress blurring artifacts. Given the inherently ill-posed nature of SR problems, the paper also includes a mathematical analysis to establish the existence and uniqueness of solutions within a Sobolev space framework. Experimental results confirm that the method effectively enhances the quality of high-resolution (HR) reconstructions. Notably, the restored images exhibit significantly reduced blur compared to results produced by other techniques. Compared to existing PDE-based methods for super-resolution (SR), the proposed framework demonstrates an improved ability to preserve crucial image features such as corners and smooth areas, while minimizing the emergence of blur in homogeneous regions. To substantiate these implementations, both visual assessments and quantitative metrics are employed, providing clear evidence of the proposed model’s robustness.</p>