Piecewise Fourier Transformation for Picture Bandwidth Compression

Recent advances in digital computer and optical technology have made image spectra determination practical. Pratt and Andrews [1] studied bandwidth compression using the Fourier transform of complete pictures. By treating pictures adaptively on a piecewise basis, picture detail is better represented. Also, subjective preferences of human vision can be used, which result in further improvements in picture quality. The original picture is sampled and then divided into small subsections. Each subsection is expanded in a two-dimensional Fourier series. The -Fourier coefficients of largest absolute value are determined for each subsection, where is proportional to the standard deviation of the picture samples in the subsection. The frequencies and complex amplitudes of those -Fourier coefficients are transmitted. The number of quantization levels used for the Fourier coefficients in each subsection is made dependent on the standard deviation of the picture samples in the subsection, and the size of the quantum steps is made dependent on the magnitude of the largest Fourier coefficient of the subsection, aside from the average value. The frequencies of the coefficients correspond to positions in a twodimensional spatial frequency plane. These positions, or twodimensional frequencies, are transmitted by run-length coding. The process is adaptive in the sense that, its parameters vary from subsection to subsection of the picture in an effort to match the properties of the individual subsections. Subsection size and other important system constants are chosen with knowledge of the properties of human vision. We are able to obtain high-quality reconstructed pictures, using on the average 1.25 bits per picture point.