Image compression is one of the most interested fields of image processing which is used to reduce image size. The 2D curve fitting is a method to convert the image data (pixel values) to a set of mathematical equations that are used to represent the image. These equations have a fixed form with a few coefficients estimated from the image which has been divided into a number of blocks. Since the number of coefficients is lower than the original block pixel size; it can be used as a tool for image compression.

In this paper, a new curve fitting model has been proposed to be derived from the symmetric function (hyperbolic tangent) with only three coefficients. The main disadvantages of previous approaches were the additional errors and degradation of edges of the reconstructed image as well as the blocking effect. To overcome this deficiency, it is proposed that this hyperbolic tangent (tanh) function be used instead of the classical 1st and 2nd order curve fitting functions for reformulating the blocks of the image. This will reduce the reconstruction error and improve fine details and texture of the reconstructed image.The results of this work have been tested and compared with 1st order curve fitting, and standard image compression (JPEG) methods. The main advantages of the proposed approach are: strengthening the edges of the image, removing the blocking effect, improving the SSIM index, and increasing the PSNR up to 20 dB. Simulation results. show that the proposed method has a significant improvement on the objective and subjective quality of the reconstructed image.