Morphological regularization neural networks

摘要

In this paper we establish a relationship between regularization theory and morphological shared-weight neural networks (MSNN). We show that a certain class of morphological shared-weight neural networks with no hidden units can be viewed as regularization neural networks. This relationship is established by showing that this class of MSNNs are solutions of regularization problems. This requires deriving the Fourier transforms of the min and max operators. The Fourier transforms of min and max operators are derived using generalized functions because they are only defined in that sense.