For image compression, the Discrete Tchebichef Transform (DTT) has recently been proposed as a competitive alternative to the Discrete Cosine Transform (DCT). This chapter presents a compression framework based on an integer approximation of the DTT. For a set of standard test images with varying statistical characteristics, an adopted quantisation matrix is derived from the energy distribution of the integer DTT coefficients. Due to the non-normality of most integer DTT matrices, their diagonal components are integrated into the quantisation process. Experimental results demonstrate that employing the JPEG standard with integer DTT and the proposed quantisation matrix yields improved compression efficiency relative to the conventional JPEG luminance quantisation matrix, while maintaining high visual quality in the reconstructed grayscale images.