The encoding process of vector quantization (VQ) is very heavy and it constrains VQ's application a great deal. In order to speed up VQ encoding, it is most important to avoid unnecessary Euclidean distance computation (k-D) as much as possible by the difference check that uses simpler features (low dimensional) while winner searching is going on. Sum (1-D) and partial sums (2-D) are used together as the appropriate features in this paper because they are the first 2 simplest features. Then, sum difference and partial sum difference are computed as the estimations of Euclidean distance and they are connected to each other by the Cauchy-Schwarz inequality so as to reject a lot of codewords. For typical standard images with very different details (Lena, F-16, Pepper and Baboon), the final must-do Euclidean distance computation using the proposed method can be reduced to less than 10% as compared to full search (FS) meanwhile keeping the PSNR not degraded.