OPTIMZED SPIHT CODING

國立台北科技大學資工所

指導教授：楊士萱

研究生：廖武傑

OUTLINE

Wavelet Transform & Quantization Bit rate & Quality Future work

WAVELET TRANSFORM & QUANTIZATION

WAVELET TRANSFORM

Images Wavelet filters Scaling

WAVELET TRANSFORM

Images:

lena baboon

WAVELET TRANSFORM

Wavelet filters:

10/18 5/3

WAVELET TRANSFORM

Scaling:– 5/3 filter

h_subband*0.5

h_subband* 2 h_subband*1.0

QUANTIZATION

Scalar Quantization– Step size q

SPIHT– Decoding bit-rate q– Zero-tree

0 q

BIT RATE & QUALITY (R-D) Coding bit rate(R) vs. Picture quality(D) R-Q and D-Q functions(R(q),D(q)) charact

erize the R-D behavior. R-D functions. (R-D curves) Adjust the quantization setting and control

the R and D. Optimal Scaling for Best D(q) or R(q)

ρ DOMAIN R-D ANALYSIS

ρ: percentage of zeros among the quantized coefficients. (with a quantization parameter q)

ρ monotonically increases with q.– R(q) R(ρ), – D(q) D(ρ), – ρ domain R-D analysis

BIT RATE

R(q) = Qz(q) + Qnz(q)– Qz(q) : total bits required for representation of

all zero coefficients– Qnz(q) : total bits required for representation o

f non-zero coefficients

BIT RATE(SQ,q=32,lena,5/3)

Qnz(k)

Qz(k)

R(k)

BIT RATE(5/3 vs 9/7)

Qz(k) Qnz(k)

R(k)

5/3 5/3

5/3

9/7

9/7

9/7

QUALITY(SQ, q=32,lena)

5/3

9/7

PSNR

SCALING & R-D

Under Certain Quantization Parameter q:– Small scaling High compression ratio– Large scaling High image quality

Given a Quantization Parameter q and a Bit-rate R, We Can Find the Optimal Scaling for Best Image Quality.

OPTIMAL SCALING

SPIHT

SQ

Lena, 5/3, 0.125 bpp

OPTIMAL SCALING

Quality Function : D(k, q) Bit-rate Function : R(k, q)

Where q is the size of Scalar Quantization step(fixed), k is the scaling factor of wavelet high frequency subband (variable).

Cost Function F(k) = F(D(k), R(k))

FUTURE WORK

Find The Cost Function of SQ Accurately. Use SPIHT Model Instead of SQ. Modify SPIHT. (Probably)