Equalized Net Diffusion (END) for the Preservation of Fine Structures in PDE-based Image Restoration

Abstract

The article is concerned with a mathematical modeling which can improve performances of PDE-based restoration models. Most PDE-based restoration models tend to lose fine structures due to certain degrees of nonphysical dissipation. Sources of such an undesirable dissipation are analyzed for total variation-based restoration models. Based on the analysis, the so-called equalized net diffusion (END) modeling is suggested in order for PDE-based restoration models to significantly reduce nonphysical dissipation. It has been numerically verified that the END-incorporated models can preserve and recover fine structures satisfactorily, outperforming the basic models for both quality and efficiency. Various numerical examples are shown to demonstrate effectiveness of the END modeling.Key Words : Fine structures, nonphysical dissipation, total variation (TV) model, non-convex (NC) model, equalized net diffusion (END). [2,13,19,20,21,24,27] .There have been various partial differential equation (PDE)-based restoration models such as the Perona-Malik model [25] , the total variation (TV) model [18,26] , and color restoration models [3,10,15,17,28] . These PDE-based models have been extensively studied to answer fundamental questions in image restoration and have allowed researchers and practitioners not only to introduce new mathematical models but also to improve traditional algorithms [1,4,9,22,30] .However, most PDE-based restoration models and their numerical realizations show a common drawback: loss of fine structures. Such an undesirable loss is due to an excessive numerical dissipation introduced particularly on regions where the image content changes rapidly such as on edges and textures. Thus the reduction of nonphysical dissipation becomes an interesting problem in image restoration, requiring challenges and innovative ideas. Although advanced models have been recently suggested for the preservation of fine structures [19,23] , more effective strategies have yet to be developed. In this article, we will first analyze sources of nonphysical dissipation for popular PDE-based restoration models. Based on the analysis, we will study the so-called equalized net diffusion (END) modeling for PDE-based restoration models, first introduced in [14] . Here we will study mathematical 논문 / Equalized Net Diffusion (END) for the Preservation of Fine Structures in PDE-based Image Restoration 999properties of the END in detail and suggest a heuristic method for parameter choices. It has been numerically verified that with the new parameters, the END modeling can reduce nonphysical dissipation significantly and more effectively for most of natural images we have tested.The article is organized as follows. In the next section, we review TV-based models along with recent studies for the reduction of nonphysical dissipation. Section III analyzes sources of nonphysical dissipation for PDE-based models: nonphysical dissipation occurs more excessively at pixels where the diffusion term evaluates larger in modulus. In Section IV...