A Zero-Value Prediction Technique for A Zero-Value Prediction Technique for Fast DCT ComputationFast DCT Computation

Y. Nishida, K. Inoue, and V. MoshnyagaY. Nishida, K. Inoue, and V. Moshnyaga

IntroductionIntroduction Discrete Cosine Transform (DCT) is the most commonly Discrete Cosine Transform (DCT) is the most commonly

　　 　　 used transform for video coding (JPEG, MPEG H26x etc).used transform for video coding (JPEG, MPEG H26x etc).

DCT is a very computationally expensive task.DCT is a very computationally expensive task.

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ProblemProblem

DCT requireDCT requiress a measurable amount of energy a measurable amount of energy and many operations.and many operations.

Reducing the number of operationReducing the number of operationss and energy consumption of and energy consumption of DCT becomeDCT becomess important. important.

Our ProposalOur ProposalA Zero-Value Prediction Technique for Fast DCT A Zero-Value Prediction Technique for Fast DCT

ComputationComputation

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AdvantageAdvantage

RReduceeducess the number of DCT and quantization the number of DCT and quantization operations.operations.RReduceeducess energy consumption. energy consumption.Increases Increases DCT DCT operation operation speed.speed.

DisadvantageDisadvantage

The picture quality deteriorateThe picture quality deterioratess..

The feature of DCTThe feature of DCT

7979 7575 7979 8282 8282 8686 9494 9494

7676 7878 7676 8282 8383 8686 8585 9494

7272 7575 6767 7878 8080 7878 7474 8282

7474 7676 7575 7575 8686 8080 8181 7979

7373 7070 7575 6767 7878 7878 7979 8585

6969 6363 6868 6969 7575 7878 8282 8080

7676 7676 7171 7171 6767 7979 8080 8383

7272 7777 7878 6969 7575 7575 7878 7878

616199

-29-29 88 22 11 -3-3 00 11

2222 -6-6 -4-4 00 77 00 -2-2 -3-3

1111 00 55 -4-4 -3-3 44 00 -3-3

22 -10-10 55 00 00 77 33 22

66 22 -1-1 -1-1 -3-3 00 00 88

11 22 11 22 00 22 -2-2 -2-2

-8-8 -2-2 -4-4 11 22 11 -1-1 11

-3-3 11 55 -2-2 11 -1-1 11 -3-3

DCT

The high frequency components at the DCT output are The high frequency components at the DCT output are concentrated nearby zero value.concentrated nearby zero value.

Input data (Pixel Level)Input data (Pixel Level) Output data (DCT coefficient)Output data (DCT coefficient)

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The feature of QuantizationThe feature of Quantization

Quantization Quantization

3939 -2-2 11 00 00 00 00 00

11 00 00 00 00 00 00 00

11 00 00 00 00 00 00 00

00 -1-1 00 00 00 00 00 00

00 00 00 00 00 00 00 11

00 00 00 00 00 00 00 00

-1-1 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

616199

--2929

88 22 11 -3-3 00 11

2222 -6-6 -4-4 00 77 00 -2-2 -3-3

1111 00 55 -4-4 -3-3 44 00 -3-3

22--1010

55 00 00 77 33 22

66 22 -1-1 -1-1 -3-3 00 00 88

11 22 11 22 00 22 -2-2 -2-2

-8-8 -2-2 -4-4 11 22 11 -1-1 11

-3-3 11 55 -2-2 11 -1-1 11 -3-3Input data (DCT coefficient)Input data (DCT coefficient) Quantization output data Quantization output data

In the case Quantization step = 16In the case Quantization step = 16

The probability of elements in the encoding block toThe probability of elements in the encoding block tobecome zero after quantization is very high.become zero after quantization is very high.

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Zero-Value Prediction TechniqueZero-Value Prediction Technique

616199

--2929

88 22 11 -3-3 00 11

2222 -6-6 -4-4 00 77 00 -2-2 -3-3

1111 00 55 -4-4 -3-3 44 00 -3-3

22--1010

55 00 00 00 00 00

00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

In the case with N=2In the case with N=2

The detected string The detected string of zerosof zeros

Starting point ofStarting point ofzero-value predictionzero-value prediction

Reducing Reducing operations for operations for 35 DCT coefficient35 DCT coefficients s is possible.is possible.

The predicted The predicted valuevalue

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When the DCT output N zeros, we predict the remaining When the DCT output N zeros, we predict the remaining result result is is also zero also zero without actual DCT computing.without actual DCT computing.

A Zero-Value Prediction TechniqueA Zero-Value Prediction Technique Example (1/2) Example (1/2)

616199

-29-29 88 22 11 -3-3 00 11

2222 -6-6 -4-4 00 77 00 -2-2 -3-3

1111 00 55 -4-4 -3-3 44 00 -3-3

22 -10-10 55 00 00 77 33 22

66 22 -1-1 -1-1 -3-3 00 00 88

11 22 11 22 00 22 -2-2 -2-2

-8-8 -2-2 -4-4 11 22 11 -1-1 11

-3-3 11 55 -2-2 11 -1-1 11 -3-3

Conventional TechniqueConventional Technique

616199

-29-29 88 22 11 -3-3 00 11

2222 -6-6 -4-4 00 77 00 -2-2 -3-3

1111 00 55 -4-4 -3-3 44 00 -3-3

22 -10-10 55 00 00 00 00 00

00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

A Zero-Value Prediction techniqueA Zero-Value Prediction technique

DCT coefficientDCT coefficient

The prediction The prediction errorerror increases increases but but most of most of the DCT coefficientthe DCT coefficientss will be will be zerozeross after quantization. after quantization. 77

3939 -2-2 11 00 00 00 00 00

11 00 00 00 00 00 00 00

11 00 00 00 00 00 00 00

00 -1-1 00 00 00 00 00 00

00 00 00 00 00 00 00 11

00 00 00 00 00 00 00 00

-1-1 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

3939 -2-2 11 00 00 00 00 00

11 00 00 00 00 00 00 00

11 00 00 00 00 00 00 00

00 -1-1 00 00 00 00 00 00

00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00

Quantization output dataQuantization output data

Prediction mistakePrediction mistake

When a picture is decoded, When a picture is decoded, tthe prediction he prediction errorerror degraddegradeses image quality image quality

A Zero-Value Prediction Technique A Zero-Value Prediction Technique Example (2/2)Example (2/2)

Prediction mistakePrediction mistake

Conventional TechniqueConventional Technique A Zero-Value Prediction techniqueA Zero-Value Prediction technique

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EvaluationEvaluationUsing the MPEG software from MPEG Software Simulation GroupUsing the MPEG software from MPEG Software Simulation Group

Video benchmarksVideo benchmarks

missamissa carpohnecarpohne foremanforeman salesmansalesman

QCIFQCIF QCIFQCIF QCIFQCIF CIFCIF

150frame150frame 382frame382frame 298rame298rame 300rame300rame

2D-DCT algorithm use addition 1024 and multiplication 1024 times 2D-DCT algorithm use addition 1024 and multiplication 1024 times per 1 block. per 1 block. 2D-DCT use partitionable method (1D-DCT×1D-DCT).2D-DCT use partitionable method (1D-DCT×1D-DCT). RRaster scanaster scan order of DCT computation order of DCT computation..

99

PSNR as a function of NPSNR as a function of N

The PSNR is low when N is small.The PSNR is low when N is small. The PSNR does not change a lot after N=9.The PSNR does not change a lot after N=9.

0011 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020

NN

PS

NR

(d

B)

PS

NR

(d

B)

1010

2020

3030

4040

5050

6060

7070 ▲ ×carphone foreman missa salesman

1010

Operation reduction rate as a function Operation reduction rate as a function of Nof N （（ DCTDCT ））

The reduction rate is high when N is small.The reduction rate is high when N is small.

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020NN

Op

era

tio

n r

ed

uc

tio

n r

ate

O

pe

rati

on

re

du

cti

on

ra

te

0.30.3

0.40.4

0.20.2

0.50.5

0.10.1

00

▲ ×carphone foreman missa salesman

1111

Operation reduction rate as a function Operation reduction rate as a function of Nof N （（ quantizationquantization ））

The reduction rate is high when N is small The reduction rate is high when N is small (similarly to t(similarly to the DCT operationhe DCT operation)). .

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020

Op

era

tio

n r

ed

uc

tio

n r

ate

O

pe

rati

on

re

du

cti

on

ra

te

00

0.60.6

0.80.8

0.40.4

1.01.0

0.20.2

NN

▲ ×carphone foreman missa salesman

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48.75dB48.75dB 47.67dB47.67dB

Original methodOriginal method Zero-value predictionZero-value prediction （（ N=9N=9））

The PThe PNSRNSR decreases decreasesby 1.07dB.by 1.07dB.

The example of a pictureThe example of a picture

Assumption toAssumption to accept accept N=9 as a tradeoff for both picture quality aN=9 as a tradeoff for both picture quality and the reduction rate.nd the reduction rate.

Example of reconstructed picture for N=9Example of reconstructed picture for N=9

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ConclusionConclusion

When N=9, the number of computations When N=9, the number of computations is reduced bis reduced by 29% fy 29% for DCT and by 59% for quantization.or DCT and by 59% for quantization.

The The aaverage PSNR verage PSNR value value degreases by -1.6dB.degreases by -1.6dB.

A Zero-Value Prediction Technique for Fast DCT A Zero-Value Prediction Technique for Fast DCT ComputationComputation

Future workFuture work

Estimating the effect of the proposed technique on energy Estimating the effect of the proposed technique on energy consumption.consumption.

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ComparisonComparison of of the algorithmthe algorithm

Number of operationNumber of operationAverage PSNR Average PSNR

degradation (dB)degradation (dB)MaxMax MinMin AverageAverage

NormalNormal 22.9%22.9% 11.8%11.8% 14.4%14.4% -1.55-1.55

ChenChen 17.4%17.4% 7.9%7.9% 10.0%10.0% -0.94-0.94

FFTFFT 23.3%23.3% 13.6%13.6% 16.0%16.0% -2.14-2.14

The number of operations per 1block.The number of operations per 1block.

Normal : addition 1024 and multiplication 1024 times.Normal : addition 1024 and multiplication 1024 times.Chen : addition 416Chen : addition 416 　　 and multiplication 224 times.and multiplication 224 times.FFT : addition 464FFT : addition 464 　　 and multiplication 176 times.and multiplication 176 times.

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