A novel full-search vector quantization algorithm based on the law of cosines

Abstract

Vector quantization (VQ) is an essential tool in signal processing. Although many algorithms for vector quantizer design have been developed, the classical generalized Lloyd algorithm (GLA) is still widely used, mainly for its simplicity and relatively good performance. Using law of cosines this letter presents a simple improved method for nearest-neighbor search in GLA. Experiments show that the proposed algorithm outperforms the traditional GLA.Index Terms-Fast nearest-neighbor search, law of cosines, vector quantization.

Comments on: Novel full-search schemes for speeding up image coding using vector quantization

“…In the previous work [2], a FS-equivalent search method is proposed. By using the law-of-cosines, d(u i , v) can also be expressed as…”

“…Let h 1 be the angle between (u i , x) and h 2 be the angle between (v, x), the previous work [2] has shown that h P |h 1 À h 2 | so that cos(h) 6 cos(h 1 À h 2 ) holds because the cosine is an even function and monotonically decreases over [0°, 90°] interval. Based on the discussions above, Mielikainen proposed a very computationally inexpensive estimation for d( Fig.…”

“…A very search-efficient method is based on using the law-of-cosines [2]. Recently, the previous work [3] proposed a new method of Scheme 1 to simplify the computation in [2] and meanwhile introduced a new method of Scheme 2 into [2] that is based on the triangle inequality to reject more candidate codewords. These two schemes in [3] are very search efficient.…”

Fast vector quantization algorithms based on nearest partition set search

“…The TIE based fast search algorithms [6]- [13] require 2N additional memory. The search algorithms in [15] and [19] require and additional memory, respectively, where is the total number of vectors in a training sequence.…”

“…In the search process, codevectors are rejected from being searched through based on an inequality defined by the stored norms and the norm of the training vector. In [15], the distances from training vectors to origin, their squares, sines and cosines are calculated and stored in a pre-defined data structure. An inequality of cosines law was used to reduce the codevector searching area of the full search process.…”