Piecewise Harmonic Image Restoration with High Order Variational Model

Image denoising is a fundamental problem in image processing and computer vision. A main challenge is to remove noise while preserving features and developing piecewise smoothing image. Piecewise constant and linear image recovery has been focused in the past decades. In this paper, we propose a model recover a class more smoothing image with complex geometrical structure. We first give definition of piecewise harmonic image, which covers a wide range piecewise smoothing image. Then a multiplicative framework for high order variational construction is introduced. Within this framework, we present a geometrical weighted Laplace (GWL) high order model. The proposed model is discussed and compared to some typical related methods. Experimental results on test images show the performance of the proposed method.