A piecewise gradient prior for small structures and contrast preserving image smoothing

Image smoothing is a fundamental task in digital image processing with broad applications. However, traditional texture smoothing techniques often result in the loss or blurring of small structural information and contrast. In this paper, we introduce a piecewise gradient prior aimed at overcoming this drawback. The prior is based on a four-segment piecewise (FSP) penalty function, which can process signals at different scales. We also present an effective iterative algorithm based on the alternate direction method of multipliers framework and provide theoretical proof of global convergence for the proposed algorithm. Our method has shown promising results in various applications, including texture removal, clip art compression artifact removal, and edge detection. Experimental results demonstrate the effectiveness and superior performance of our approach in these applications.