Compression and decompression of images with discrete fuzzy transforms

In foregoing papers we have used the compression/decompression method of images based on the concept of discrete fuzzy transform (and its inverse) of a function f defined on a real interval with respect to the fuzzy sets A₁,…,A_n forming a fuzzy partition of such interval. Here we make a detailed experimental comparison with the similar method based on the fuzzy transforms F^↑ and F^↓ of f defined via a continuous triangular norm and its corresponding residuum, respectively. We consider some images of sizes 256 × 256 (pixels) extracted from the well-known database Corel Galery (Arizona Directory). By using the same compression rate in both methods, we have that the PSNR (Peak Signal to Noise Ratio) obtained with the discrete fuzzy transform (and its inverse) of f is more higher than the PSNR determined with the operators F^↑ and F^↓ defined via the usual Lukasiewicz, product and minimum triangular norms. Moreover, we compare our results with the classical JPEG method for values of compression rate approximately equal to those used in the previous methods.