Vector quantization of image

Original image, 768x512 pixels, 8 bits/pixel

One-dimensional VQ (scalar quantization), 1 bit/pixel

R=1, L=1
Vectors in the codebook: M=2^RL=2¹=2
Bits required to store codebook: M*L*8=16 (0.000041 extra bits/pixel)

Two-dimensional VQ, 1 bit/pixel

R=1, L=2
Vectors in the codebook: M=2^RL=2²=4
Bits required to store codebook: M*L*8=64 (0.00016 extra bits/pixel)

Four-dimensional VQ, 1 bit/pixel

R=1, L=4
Vectors in the codebook: M=2^RL=2⁴=16
Bits required to store codebook: M*L*8=512 (0.0013 extra bits/pixel)

Six-dimensional VQ, 1 bit/pixel

R=1, L=6
Vectors in the codebook: M=2^RL=2⁶=64
Bits required to store codebook: M*L*8=3072 (0.0078 extra bits/pixel)

Eight-dimensional VQ, 1 bit/pixel

R=1, L=8
Vectors in the codebook: M=2^RL=2⁸=256
Bits required to store codebook: M*L*8=16384 (0.042 extra bits/pixel)

What if we had tried 12 dimensions?
R=1, L=12
Vectors in the codebook: M=2^RL=2¹²=4096
Bits required to store codebook: M*L*8=393216 (1 extra bit/pixel!)

What if we had tried 16 dimensions?
R=1, L=16
Vectors in the codebook: M=2^RL=2¹⁶=65536
Bits required to store codebook: M*L*8=8388608 (21.33 extra bits/pixel!)

As you can see, having a too large dimension is not feasible.

Vector quantization of audio

Original audio: Mono, 16 bits/sample, 44100 sample/s, 705.6 kbps

• One-dimensional VQ (scalar quantization), 1 bit/sample, 44.1 kbps, 4.61 dB
• Two-dimensional VQ, 1 bit/sample, 44.1 kbps, 9.48 dB
• Four-dimensional VQ, 1 bit/sample, 44.1 kbps, 14.86 dB
• Six-dimensional VQ, 1 bit/sample, 44.1 kbps, 16.81 dB
• Eight-dimensional VQ, 1 bit/sample, 44.1 kbps, 18.22 dB
• Ten-dimensional VQ, 1 bit/sample, 44.1 kbps, 19.90 dB

• One-dimensional VQ, 2 bits/sample, 88.2 kbps, 9.78 dB
• Two-dimensional VQ, 2 bits/sample, 88.2 kbps, 17.94 dB
• Four-dimensional VQ, 2 bits/sample, 88.2 kbps, 21.98 dB
• Six-dimensional VQ, 2 bits/sample, 88.2 kbps, 25.14 dB