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eee508_VQ - Vector qua t at o ecto quantization Scalar...

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Vector quantization Scalar quantizers are special cases of vector quantizers (VQ): they are constrained to look at one sample at a time (memoryless) VQ does not have such constraint better RD perfomance expected ¾ Source coding theorems and other results in rate-distortion theory (due to Shannon) imply that one can always do better (in RD ) if t f l d d it sense) if vector of samples are coded as units Note: We can code samples as units without necessarily exploiting or knowing interdependency between the samples VQ widely used in coding speech image and video VQ widely used in coding speech, image, and video EEE 508
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Vector quantization Brief description ¾ Some main advantages: 9 exploit dependency that may exist within an input vector 9 ability to generate non-cubic multi-dimensional partitions of input hi h id b tt ti f th i t which provides better compaction of the input space 9 ability to track high-order statistical characteristics of the input ¾ Some main disadvantages: 9 encoding complexity and memory requirements increase exponentially encoding complexity and memory requirements increase exponentially with vector size (under a given rate) and with bit-rate 9 Lack of robustness: sensitivity to channel noise Conventional VQ is severely limited to modest vector and codebook size Different more robust methods needed EEE 508
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Vector quantization Brief description ¾ VQ takes blocks of pixels instead pixels 1. Divide image into blocks (common size: 24x24, 16x16, 8x8 ) 1 2 3 4 5 6 7 8 9 x = [ 1 2 3 4 5 6 7 8 9 ] T 2. Turn block into a vector 3. Compare x with best matching in codebook x ˆ 7 8 9 Codebook: Table consisting of representative vectors (reconstruction levels) { r j } j =1,…, M Best matching: with respect to a chosen distance (error) measure. 4 Transmit the inde k ” of that best matching ector Q ) ( ˆ 4. Transmit the index “ ” of that best matching vector: 5. Receiver gets the index “ k ” and retrieves = r k from its own stored codebook which matches transmitter’s codebook k r x x x ˆ EEE 508
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Vector quantization Brief description Image block to vector Search Channel look-up x x ˆ Index Codebook Codebook Encoder Decoder Exp. Find best matching vector in codebook ^ ` N j R I j j I D o r r ; : I R X E N o : 00 01 10 x = 01 EEE 508
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Vector quantization Motivation Theorem (from source coding and rate-distortion theory): As vector size grows, performance improves in the rate- distortion sense Practical constraints: ¾
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