This paper introduces a new method of compressing digital images by using the Difference Transform applied in medical imaging. The Difference Transform algorithm performs the decorrelation process of image data, and in this way improves the encoding process, achieving a file with a smaller size than the original. The proposed method proves to be competitive and in many cases better than the standards used for medical images such as TIFF or PNG. In addition, the Difference Transform can replace other transforms like Cosine or Wavelet.

Associative memories in min and max algebra are of great interest for pattern recognition. One property of these is that they are one-shot, that is, in an attempt they converge to the solution without having to iterate. These memories have proven to be very efficient, but they manifest some weakness with mixed noise. If an appropriate kernel is not used, that is, a subset of the pattern to be recalled that is not affected by noise, memories fail noticeably. A possible problem for building kernels with sufficient conditions, using binary and gray-scale images, is not knowing how the noise is registered in these images. A solution to this problem is presented by analyzing the behavior of the acquisition noise. What is new about this analysis is that, noise can be mapped to a distance obtained by a distance transform. Furthermore, this analysis provides the basis for a new model of min heteroassociative memory that is robust to the acquisition/mixed noise. The proposed model is novel because min associative memories are typically inoperative to mixed noise. The new model of heteroassocitative memory obtains very interesting results with this type of noise.