A Class of Fast Gaussian Binomial Filters for Speech and Image Processing

The gaussian bionomial filters are a family of one-and two-dimensional FIR filters with binary-valued coefficients (─1, 1). The family can function as a bank of filters, with taps corresponding to low-pass, band-pass with differing center frequencies, and high-pass filters. The low-pass filter (1D and 2D) has a Gaussian shaped amplitude frequency response and a binomial impulse response which approximates a Gaussian point spread function in the (time) spatial domain. We present an efficient, in-place algorithm for the batch processing a 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 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 Burt. The Binomial filter yielded a slightly larger SNR in every case tested. More significantly, for an (L + 1) x (L + 1) image array processed in (N + 1) x (N + 1) subblocks, the fast Burt algorithm requires a total of 2(L + l)²N adds and 2(L + l)² (N/2 + 1) multiplies. The Binomial algorithm requires 2L²N adds and zero multiplies.