An image coding/decoding method based on fuzzy direct and inverse transforms

With some modifications, we adopt the coding/decoding method of image processing based on the direct and inverse fuzzy transforms defined in previous papers. By normalizing the values of its pixels, any image can be considered as a fuzzy matrix (relation) which is subdivided in submatrices (possibly square) called blocks. Each block is compressed with the formula of the discrete fuzzy transform of a function in two variables and successively it is decompressed via the related inverse fuzzy transform. The decompressed blocks are recomposed for the reconstruction of the image, whose quality is evaluated by calculating the PSNR (Peak Signal to Noise Ratio) with respect to the original image. A comparison with the coding/decoding method of image processing based on the fuzzy relation equations with the Lukasiewicz triangular norm and the DCT method are also presented. By using the same compression rate in the three methods, the results show that the PSNR obtained with the usage of direct and inverse fuzzy transforms is higher than the PSNR determined either with fuzzy relation equations method or in the DCT one and it is close to the PSNR determined in JPEG method for small values of the compression rate.