Image processing by minimising L p norms

Abstract

In this work, we take a novel line of approaches to evolve images. It is motivated by the total variation method, known for its denoising and edge-preserving effect. Our approach generalises the TV method by taking a general L p norm of the gradients instead of the L 1 in the TV method. We generalise this method in a series of first and second order derivatives in terms of gauge coordinates. This method also incorporates the well-known blurring by a Gaussian filter and the balanced forward--backward diffusion. The method and its properties are briefly discussed. The practical results are visualised on a real-life image, showing the expected behaviour. When a constraint is added that penalises the distance of the results to the input image, one can vary the desired amount of blurring and denoising.