TDLT: Difference between revisions

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Optimal real-valued coefficients for V:
Optimal real-valued coefficients for V:


p0 = -0.4045289182698497
p0 = -0.39460731547057293


p1 = -0.33468137871117265
p1 = -0.33002212811740816


p2 = -0.12545831989246597
p2 = -0.12391270981321137


q0 = 0.8222196599456361
q0 = 0.822154737511288


q1 = 0.634500829289973
q1 = 0.632488694485779


q2 = 0.4034606713167927
q2 = 0.40214668677553894


CG = 9.56856
CG = 9.56867


Optimal [maybe] integer-valued coefficients (d=6) for V:
Optimal [maybe] integer-valued coefficients (d=6) for V:

Revision as of 15:00, 12 May 2012

This page holds the results of Time Domain Lapped Transform (TDLT) optimization problems looking for integer transform coefficients that provide optimal coding gain. Wherever possible the assumptions are stated. Later we should include testing against actual image data to verify the results (see test data here).

The coding gain objective used as the objective is taken from slide 13 of Tim's presentation An Introduction to Video Coding

<need figure with block matrix diagrams>

The free parameters are initially just the coefficients p_0,...,p_m,q_0,...,q_m where m=(n/2)-1. We limit these to being dyadic rationals, e.g., x/2^d with d=6, between [-1,1].

Given p's and q's and assuming a linear ramp constrains the s's.

4x8

s0 = 4*(1-q0) s1 = 4*(1-p0*(1-q0))/3

Optimal real-valued coefficients for V:

p0 = -0.18117338915051454

q0 = 0.6331818230771687

CG = 8.60603

Optimal integer-valued coefficients (d=6) for V:

p0 = -12/64 = -0.1875

q0 = 41/64 = 0.640625

CG = 8.60486

Optimal integer-valued coefficients (d=6) were (1-p0*(1-q0)) is divisible by 3:

p0 = -13/64 = -0.203125

q0 = 41/64 = 0.640625

CG = 8.60446

8x16

Optimal real-valued coefficients for V:

p0 = -0.39460731547057293

p1 = -0.33002212811740816

p2 = -0.12391270981321137

q0 = 0.822154737511288

q1 = 0.632488694485779

q2 = 0.40214668677553894

CG = 9.56867

Optimal [maybe] integer-valued coefficients (d=6) for V:

p0 = -26/64 = -0.40625

p1 = -22/64 = -0.34375

p2 = -8/64 = -0.125

q0 = 53/64 = 0.828125

q1 = 41/64 = 0.640625

q2 = 26/64 = 0.40625

9.56627