Layers image compression and reconstruction by fuzzy transforms

Recently we have proved that the fuzzy transforms (F-transforms) are useful in coding/decoding images, showing that the resulting Peak Signal to Noise Ratio (PSNR) is better than that one obtained using fuzzy relation equations and comparable with that one obtained using the JPEG method. Recently some authors have explored a new image compression/reconstruction technique: the range interval [0,1] is partitioned in a finite number of subintervals of equal width in such a way each subinterval corresponds to a image-layer of pixels. Each image-layer is coded using the direct F-transform and afterwards all the inverse F-transforms are put together for reconstructing the whole initial image.We modify slightly this process: indeed the pixels of the original image are normalized with respect to the length of the gray scale, thus is seen as a fuzzy matrix R and we divide it in (possibly square) submatrices RB, called blocks. Hence we divide [0,1] in subintervals by adopting the quantile method, so that each subinterval contains the same number of normalized pixels of every block RB, hence we apply the F-transforms to each block-layer. In terms of quality of the reconstructed image, our method is better than that one based on the standard F-transforms.