An invertible transform for image representation and its application to image compression

M-dimensional real transform (MRT) is an alternate representation of a signal which is derived from the equation for computation of the discrete Fourier transform (DFT). The raw MRT representation has redundant elements which makes it unsuitable for use in situations where memory usage needs to be minimized. This paper presents a procedure to obtain a lean MRT representation of an image. The lean MRT coefficients are unique, numerically compact and require only the same memory space as required for the original image. Each MRT coefficient is formed by unique, linear, multiplication-less combinations of image data and thus has spatial significance. The inverse transformation to obtain the original signal from the lean MRT is also presented. The inverse transform involves only additions and subtractions. The lean MRT representation is applied to a few images and the resulting coefficients quantized. The performance of this approach to obtain compression is studied, and the results obtained are presented. It is seen that the proposed lean MRT representation can be used effectively to compress images.