A novel hybrid multi-regularization total variation model for edge-aware image smoothing

Image smoothing is a fundamental technique in numerous image processing applications, and continuous advancements enhance its performance. However, existing methods still face a challenge in maintaining an optimal balance between smoothing intensity and edge preservation. They often suffer from halos and gradient reversal artifacts. To address these issues, this paper introduces a novel Hybrid Multi-Regularization Total Variation model for smoothing tasks, termed HMRTV. It aims to decompose an image into primary structural and textural components via embedding three hybrid regularizations. Specifically, the HMRTV model introduces exponential functions acting as regularizations to achieve edge-aware capability, which can provide a more precise separation of edge structures and textures. Additionally, a dedicated texture regularization term is incorporated into the HMRTV model to enhance texture sparsity, leading to mitigating the occurrence of halos and gradient reversal artifacts. We provide a complete mathematical derivation for a numerical solution to the HMRTV model. Extensive experiments demonstrate that HMRTV significantly outperforms state-of-the-art smoothing approaches.