This paper presents a lossy image compression scheme which employs a pyramidal coding technique with segmentation based on the local activity levels. A novel prediction method is introduced, rendering significantly reduced variance of the quantizer input. Consequently, the coding efficiency is much enhanced due to the greatly reduced quantization distortion. Both theoretical analysis and simulation results show that the proposed scheme yields high quality performance. In particular, a reconstruction PSNR of 30.5 dB is achieved at a bit rate of 0.181 bpp for a 512X512 image 'Zenna" before entropy coding.