Digital image compression is an important technique in digital image processing. To improve its performance, we would like to speed up the design process and achieve the highest compression ratio possible. For speed improvement, we have used a fast Kohonen self-organizing neural network algorithm to achieve big saving in codebook construction time. For compression purpose, we propose a new approach called FTVQ ( fast transformed vector quantization), combining together the features of speed improvement, transform coding and vector quantization. We use several experiments to demonstrate the feasibility of this FTVQ approach.