Despeckling optical coherence tomograms from the human retina is a fundamental step to a better diagnosis or as a preprocessing stage for retinal layer segmentation. Both of these applications are particularly important in monitoring the progression of retinal disorders. In this study we propose a new formulation for a well-known nonlinear complex diffusion filter. A regularization factor is now made to be dependent on data, and the process itself is now an adaptive one. Experimental results making use of synthetic data show the good performance of the proposed formulation by achieving better quantitative results and increasing computation speed.

In this paper we study the convergence of a centred finite difference scheme on a non-uniform mesh for a 1D elliptic problem subject to general boundary conditions. On a non-uniform mesh, the scheme is, in general, only first-order consistent. Nevertheless, we prove for s ∈ (1/2, 2] order O(h s)-convergence of solution and gradient if the exact solution is in the Sobolev space H 1+s (0, L), i.e. the so-called supraconvergence of the method. It is shown that the scheme is equivalent to a fully discrete linear finite-element method and the obtained convergence order is then a superconvergence result for the gradient. Numerical examples illustrate the performance of the method and support the convergence result.

The use of cross-diffusion problems as mathematical models of different image processes is investigated. Here the image is represented by two real-valued functions which evolve in a coupled way, generalizing the approaches based on real and complex diffusion. The present paper is concerned with linear filtering. First, based on principles of scale invariance, a scalespace axiomatic is built. Then some properties of linear complex diffusion are generalized, with particular emphasis on the use of one of the components of the crossdiffusion problem for edge detection. The performance of the cross-diffusion approach is analyzed by numerical means in some one-and two-dimensional examples.

Abstract. In this paper we present a rigorous proof for the stability of a class of finite difference schemes applied to nonlinear complex diffusion equations. Complex diffusion is a common and broadly used denoising procedure in image processing. To illustrate the theoretical results we present some numerical examples based on an explicit scheme applied to a nonlinear equation in context of image denoising.1. Introduction. The main result of this paper is the proof of a stability condition for a class of finite difference schemes for nonlinear complex diffusion. The stability condition for the linear case is very well known and widely documented in literature [12,13]. In [3] the authors derive, under suitable conditions, a stability result for the linear complex case. Our result, on top of being a non-trivial generalization of the stability condition for the nonlinear case, also requires less regularity in the diffusion coefficient than [3].Diffusion processes are commonly used in image processing, as for example in inpainting

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