The standard JPEG, is a very popular image compression method results in a good compression with low computational complexity and memory requirements. The PSNR exceeds 33 dB at high bit rate of 0.5 bpp. But at low bit rates compression ratio, JPEG introduces undesirable blocking artifacts. Therefore, other image compression methods namely: Subband-DCT, Wavelet decomposition method, and the Hybrid (combined subband and wavelet) methods are investigated in this work to improve the image quality at low bit rates. The Subband-DCT ( SB-DCT with M=2) gives a good solution to the blocking artifacts at low bit rates, with 73% less complexity and even better PSNR at certain low bit rates. However, at high bit rates, its performance does not reach JPEG standards in terms of PSNR, and it is less by approximately 1.5dB at 0.5 bpp. The performance of the SB-DCT (M=4) at low bit is nearly equal to the standard JPEG in term of PSNR. However, the complexity is reduced by about 91% with no pixelization artifacts. At high bit rates the PSNR is down by about 5 dB, this is due to the fact that the image is approximated to 1/16 of its original size, and totally ignoring the medium and high frequencies. The wavelet image compression method performance varied with the complexity of the wavelet filter in use. Using the Haar (the simplest) filter in a 3 level decomposition, the complexity is the same as standard JPEG at 0.5 bpp, and is 50% less complex at 0.2 bpp. The PNSR is about 3 dB lower than JPEG at 0.5 bpp and 1.5 dB lower at 0.2 bpp. The db10 filter gives higher PSNR than JPEG by 0.7 dB at low bit rates of 0.2 bpp, and is 34% more efficient in term of complexity. However, at high bit rates of 0.5 bpp, the PSNR is about 1.5 dB lower and the complexity is increased by 46% compared to JPEG. A bit allocation algorithm is implemented after decomposition to allocate bits to each subband. To further enhance the perceptual quality of the decoded image, a perceptual weighting factor is introduced to the bit allocation algorithm, re-allocating more bits to the low frequency subbands. Using db10 wavelet filter at 0.5 bpp, PSNR is with 0.8 dB less than JPEG, but at low bit rates of 0.2 bpp the PSNR is better by 1.5 dB. The complexity is increased to 230% at high bit rates and is almost equal at low bit rates. Combining the db10, db10 and haar wavelet filters results in reduction in the complexity by about 20% compared to 3 levels of db10 alone at 0.2 bpp, with almost the same PSNR. Using bior6.8, db10 and bior6.8 wavelet filters results in a reduction of complexity by more than 10% compared with 3 levels of bior6.8 wavelet filters alone, and by about 40 % compared to 3 level of db10 wavelet filters at 0.2 bpp. Using subband decomposition followed by 2 levels of db10 wavelet filters decomposition, the complexity decreases by about 40% at 0.2 bpp, and by an average of 10% at bit rates below 0.35 bpp compared to 3 level of decomposition. The PSNR drops by 1.5 dB at high bit rates and just by 0.63 dB at low bit rates. The approximated wavelet method has advantage in decreasing the complexity by 10 % at high bit rates, and matched at low bit rate compared to 3 level of decomposition. The PSNR is almost the same for all bit rates.