A class of fast Gaussian binomial filters for speech and image processing

The authors present an efficient, in-place algorithm for the batch processing of linear data arrays. These algorithms are efficient, easily scaled, and have no multiply operations. They are suitable as front-end filters for a bank of quadrature mirror filters and for pyramid coding of images. In the latter application, the binomial filter was used as the low-pass filter in pyramid coding of images and compared with the Gaussian filter devised by P.J. Burt (Comput. Graph. Image Processing, vol.16, p.20-51, 1981). The binomial filter yielded a slightly larger signal-to-noise ratio in every case tested. More significantly, for an ( L+1)×(L+1) image array processed in (N+1)×(N+1) subblocks, the fast Burt algorithm requires a total of 2(L+1)²N adds and 2(L+1)² (N/2+1) multiplies. The binomial algorithm requires 2L²N adds and zero multiplies