3. Adaptive Rounding Encoding Technique using an Equal Expected-Value Rule

As discussed above, if the input p.d.f. is Laplacian distributed and if we can estimate λ, then the optimal f can be found analytically. But, usually the estimate of input p.d.f. is not available, then, how to select the rounding offset f?

In order to select rounding offset f adaptively, an adaptive quantization encoding technique using an equal expected-value rule is proposed by Gary Sullivan from Microsoft. The adaptive adjustment of the rounding offset f occurs only in the encoding quantization process, which tries to select f without using any priori model knowledge on the input W. The aim is to make that the mean of the absolute value of the input, |W|, is equal to its expected reconstruction value |W’|, i.e.,

                                                                                          (5)

Any values in an interval would be reconstructed to some W’, so the distribution of W’ is a probability mass function (p.m.f.), with the probability mass equal to integral of the input probability distribution function (p.d.f.) over the interval: the change of f leads to the shift of quantization intervals, and thus results in the change of p.m.f. of W’.

Figure 6. Adaptive rounding using an equal expected-value rule

The rounding offset parameter f is updated during encoding as follow:

                                                            (6)

where the positive constant k is determined empirically. This equation means that If |W_i| < |W’_i|, then try to decrease f. By decrease f, we increase the dead-zone and the probability mass of zero, and thus the expected value of |W’| would be shifted towards zero. Otherwise, the expected value of |W’| would be shifted away from zero. Here we summarize the algorithm of adaptive rounding:

• Initially set f₀=Δ/3 (for intra) or f₀= Δ/6 (for inter)
• Quantize incoming transform coefficient W₀, obtain W’₀
• Obtain f₁ ; Use it to quantize W₁
• If |W_i|=|W’_i|, no need to update f
• I(.) is the indicator function, which is equal to 1 when its argument is true, and 0 when its argument is false
• Discard samples that fall into the dead-zone, since dead-zone reconstruction value of 0 is in general optimal (input p.d.f. is symmetric)
• Use different f for each of these frequency components, and update separately, since they have different statistics– 16 frequency components for luma 4×4 block of Inter 4×4 modes

  – 16 frequency components for luma 4×4 block in Intra 4×4 modes

  – …

The adaptive quantization encoding technique using an equal expected-value rule is only performed at the encoding quantization process, and is compatible with the standards, and only need modification only at the encoder. Experiential results show that up to 1dB improvement at high PSNR is observed.

Permanent Link: Quantization Techniques in JM/KTA – Part 3