The Telegraph Diffusion Equation (TDE) used in some noise reduction processes in an image includes two main parameters: the damping coefficient and the relaxation time. Classically, the first is determined globally for a given input image, while the second one is set constant. In this paper, we propose to determine the values of these parameters according to the information and the image local structure. We then get an adaptive diffusion equation that permits to better control the degree of smoothness and preserve fine structures and image contours avoiding speckles phenomena and staircase. The acquired results show that the proposed method improves the quality of images that have a weak signal-to-noise ratio, comparatively to the methods based on the TDE whose parameters are not adaptive.

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Abstract:The image fusion technique is widely used in remote sensing. Its purpose is to provide comprehensive information without arte facts by combining the partial information from different source images. In this study, we propose a new model of images fusion with very high spatial resolution. We use the separation capacities of the Morphological Component Analysis (MCA) to extract the smooth and texture components of our images. These morphological components are then fused separately using the decomposition in the Laplacian pyramids for the smooth part and bivariate Hahn polynomials for texture part. Finally the image fusion is obtained through linear combination of merged smooth and texture components. The experiments carried out on IKONOS, LANDSAT and Quick Bird remote sensing images show the good performances of our method which has been compared to conventional methods. The performances obtained in our experiments are characterized by a small global metric such as ERGAS equals to 3.88 for IKONOS image and 3.65 for QuickBird image compared to 8.70 for IKONOS image and 6.97 for QuickBird for conventional HIS algorithms. We also have a mean loss of 15% for spectral information com pare to those of the conventional methods which revolve around 25%. The degradation of spatial information in order of 17% in contrast to conventional HIS algorithms which oscillate around 21%.