Multi-scale representation, Fuzzy partition, Fuzzy transform

We analyze various multi-scale representations of a one-dimensional signal in spaces with a closeness relation determined by a symmetric and positive semi-definite kernel. We discuss other kernels than the predominant Gaussian kernel in a scale space representation of a one-dimensional signal. We show that kernels arising from generating functions of fuzzy partitions can be treated with the same success. We also show that the reconstruction from the proposed multi-scale representations of better quality than the reconstruction from MLP with almost double the number of neurons in 4 hidden layers.