This paper aims to propose an effective steerable directional Laplacian regularizer for image denoising. A steerable inhomogeneous directional Laplacian associated with an efficient contextual indicator is presented and taken as the diffusion flux to formulate the desired steerable directional Laplacian regularizer. With the contextual indicator for contextual discontinuities, the steerable directional Laplacian regularizer degenerates to a tangent diffusion equation for sharpening the inter-object boundaries and reduces to a normal diffusion equation for smoothing the homogenous regions. Unlike the traditional Laplacian regularizer, the model in this paper is anticipated to be anisotropic and robust while overcoming the staircase effect caused by most of second-order anisotropic diffusion models. Experimental results support that the proposed model outperforms some benchmark models with regard to both perceptual quality and objective evaluation metrics.

本文旨在提出一种有效的可操纵方向拉普拉斯正则化器用于图像去噪。提出了与有效上下文指标相关联的可操纵非均匀定向拉普拉斯算子，并将其作为扩散通量来制定所需的可操纵定向拉普拉斯正则化器。使用上下文不连续性的上下文指示符，可操纵的定向拉普拉斯正则化器退化为用于锐化对象间边界的切线扩散方程，并简化为用于平滑同质区域的正常扩散方程。与传统的拉普拉斯正则化器不同，本文中的模型预计具有各向异性和鲁棒性，同时克服了大多数二阶各向异性扩散模型引起的阶梯效应。