Verification results for the choice of projection axes used in fast encoding method of vector quantization

Vector quantization (VQ) is a well-known signal compression method. The encoding process of VQ is extremely time-consuming so that it limits the practical applications of VQ method to a great extent. In order to speed up the process of VQ encoding, the previous works (J.Z.C. Lai, et al, IEEE Trans. Image Processing, Vol. 13, No. 12, pp.1554-1558, 2004; S.J. Back, et al, Signal Processing, Vol.75, pp.89-92,1999) have reported that the projection concept of a vector is very effective for rejecting most of unlikely candidate codewords to speed up VQ encoding process. In both of these two previous works, they used a set of three symmetric projection axes or generalized central axes like p₁ = [111111111111111]^T, P₂ = [11111111-1-1-1-1-1-1-1-1]^T and p₃ = [11-1-111-1-111-1-111-1 -1]^T for rejection tests in the case of 4×4 block size. In addition, they reported that if and only if these three axes of (p₁, p₂, p₃) can experimentally guarantee the best search performance of VQ encoding. However, both of these two previous works did not give out the reasons to show why this set of (p₁, p₂, p₃) axes is the best choice for projection axes. It is a remaining important problem in the two previous works. This paper aims at providing a verification and an explanation to the best choice of (p₁, p₂, p₃) set and meanwhile proposing a criterion on how to choose the projection axes optimally based on the concept of Walsh transform. Experimental results confirmed the effectiveness of the proposed criterion.