An extension of the reduced-difference pyramid (RDP) algorithm is deri
ved and proposed for lossy image compression with upper-bounded maximu
m error (semilossy). Quantization has been introduced into the basic R
DP in two different ways: approximations are made either before or aft
er taking the differences among pairs of adjacent nodes. The resulting
peak-error (PE) propagation along the pyramid is theoretically invest
igated, and quantization strategies are suggested. Tests on the standa
rd gray-scale Lena image show significant and steady rate-distortion i
mprovements over the original RDP. As few fixed-point operations are r
equired per pixel, on-line compression/decompression is feasible on ge
neral-purpose computers.