ABSTRACT
This chapter shows that the discrete wavelet transforms and focuses on the discrete Fourier transform. It introduces so-called kernelization, in which the dual representations of linear problems. The chapter deals with a brief introduction to Gibbs–Markov random fields. The fast Fourier transform, as its name implies, is very fast and ordinary array multiplication is much faster than convolution. A pitfall when doing convolution in the fashion has to do with so-called wraparound error. Linear filtering of images in the spatial domain generally involves moving a template across the image array, forming some specified linear combination of the pixel intensities within the template and associating the result with the coordinates of the pixel at the template’s center. The motivation for using valid kernels is that it allows to apply known linear methods to nonlinear data simply by replacing the inner products in the dual formulation by an appropriate nonlinear, valid kernel.
