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Fast VQ Encoding by an Efficient Kick-Out Condition

This paper presents a novel approach to fast Vector Quantization (VQ) encoding through the implementation of an efficient kick-out condition. By leveraging the Cauchy-Schwarz inequality, the proposed algorithm optimizes the nearest codebook search process, significantly reducing preprocessing time and memory usage from O(N²) to O(N log N) and O(N), respectively. The kick-out condition allows for the elimination of multiple vectors, enhancing performance while maintaining accuracy. This method is independent of block size and outperforms existing techniques, making it a valuable asset for video technology applications.

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Fast VQ Encoding by an Efficient Kick-Out Condition

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  1. Fast VQ Encoding by an Efficient Kick-Out Condition Kuang-Shyr Wu and Ja-Chen Lin IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, FEB. 2000

  2. Introduction • Query vector x=(x1,x2,…,xk) and codebook • Used squared Euclidean distance, distortion is • Nearest codebook search • Kick-out condition: • guarantee ,rule out yi

  3. Existing Techniques • Partial Distance Elimination (PDE) • Soleymani and Morgera • Triangular inequality Elimination (TIE) A1

  4. Existing Techniques(cont.) A2 • Torres and Huguet: kick out yi if • Lin and Tai, integral projection method • Massive projection A3

  5. Existing Techniques(cont.) • Vertical projection • Horizontal projection • Kick out if yi satisfies

  6. Proposed Algorithm (15) (16)

  7. Smallest d1 distortion by (15)(16) Due to Cauchy-Schwarz inequality d1(x,yi) >= d1min is guaranteed ,Kick-out yi

  8. Finding the nearest codeword for a query sequence {x} in the k-dimension vector space. • Preprocessing:Evaluate • Steps: • 1. read in an x • 2. Evaluate 2 ||x||

  9. 3. choose an ,let • 4. • (a) R empty goto 5 • (b) choose yi from R • (c) if ||yi||(||yi||-2||x||)>= d1min then do 4ci or 4cii • i) if (||yi|| >=||x||) then delete from R all yj whose j>=i and goto 4a • ii) if (||yi|| <=||x||) then delete from R all yj whose j<=i and goto 4a • (d) Evaluate d1(x, yi); delete yi from R; if (d1(x,yi)>=d1min) goto 4a • (e) d1min = d1(x, yi) ; ymin = yi;(update ymin) • 5. Print out the ymin , it minimizes (16) and (15) for given x.

  10. Kick-out condition : • Kick out not only yi, but also many yj by • Suggest ymin(guess) whose norm is closest to ||x||; f(t)=t ( t – 2 ||x|| ), as function of t absolute minimum at t = ||x||

  11. Experiments

  12. Conclusions • A kick-out condition using the Cauchy-Schwarz inequality is proposed for the fast codeword searching algorithm. • Compared to A2,the O(N2) preprocessing time and O(N2) memory space are reduced to O(NlogN) and O(N) in our method. • Compared to A3, our method uses not only one inequality instead of three but also independent of block size.

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