Parallel Generation Of Fourier And Gabor Transforms And Shape Descriptors By Gaussian Wavelet Groups Using A Set Of Multidimensional Lattices

The paper describes a variety of multi-dimensional signal operators that can be generated in real-time using a set of novel artificial neural architectures that have a multi-layered lattice structure. The lattices are entirely linear and diverge considerably from the common non-linear structures used for neural networks. The lattice’s principle of operation is based on the central limit theorem. Each layer of the lattice performs only simple repetitive convolution, but the multilayered result rapidly evolves into exact Gaussian smoothing. Each layer of the lattice generates Gaussian smoothing of different scale, the deeper the layer in the lattice, the larger the widths (standard deviations) of the Gaussians. The recursive smoothing architecture can be extended to any dimension: 1D data arrays are processed by 2D lattices, 2D arrays by 3D lattices, etc.