الملخص

In the field of image processing, there is an urgent need to adopt image transformations. In this paper, work is done on image coefficients after decomposing them through Curvelet transformations obtained through the fan filter. The research deals with two stages: the first is to study the effect of the Fan filter by adopting angles (8, 16, 32) on the image (Lina.jpg) of size (256*256) after being analyzed using Curvelet transformations at scales (2,3,4)  through comparing a set of measurements (Contrast, Energy, Correlation, MSE, and PSNR) for both the original and reconstructed images. It can be found that Contrast and Energy criteria remain the same for the original and reconstructed images according to different levels of analysis or directions, so the value of the Correlation measure is 1. The value of the MSE criterion is very small and is almost not affected by the change of the number of angles in one scale, but it is slightly affected by increasing the scale analysis. What was mentioned above applies to the PSNR criterion as well. As for the second stage of the research, which included decomposing the image to its coefficients, canceling the effect of one of these coefficients, and then reconstructing it. The results proved that the two criteria (Contrast and Energy) were not affected with falling Correlation criteria from 1 to values ​​ranging from (0.9987_0.9997) depending on the number of scales used in the Curvelet analysis and the number of angles used in  Fan filter (8,16,32). The results also showed an increase in the MSE value when dropping some frequencies, and a corresponding decrease in the PSNR value. Whereas, the decrease in the MSE scale was demonstrated at a specific scale with the increase in the number of angles in the Fan filter, in contrast to the PSNR scale.