On rate-distortion models for natural images and wavelet coding performance

Area of Science:

• Image compression
• Information theory
• Signal processing

Background:

• State-of-the-art wavelet coders compress natural images with power-law rate-distortion (RD) functions (D ∝ R⁻γ).
• This deviates from the exponential RD function (D ∝ 2⁻ˣⁱᴿ) typical for bandlimited stationary processes.
• Natural images often exhibit nonstationary behaviors, necessitating advanced source modeling.

Purpose of the Study:

• To explain the power-law behavior of operational RD functions for natural images during wavelet compression.
• To investigate the theoretical and operational RD characteristics of natural image compression.
• To provide theoretical support for wavelet compression of self-similar processes.

Main Methods:

• Modeling natural images using fractional Brownian motion (fBm) to capture nonstationary characteristics.
• Establishing the theoretical RD function for 1-D and 2-D fBm processes.
• Deriving the operational RD function for fBm processes using wavelet encoding and the water-filling principle.

Main Results:

• The theoretical RD function of the fBm process demonstrates a power-law relationship (D ∝ R⁻γ).
• The operational RD function of the wavelet-encoded fBm process also follows a power law (D ∝ R⁻γ).
• For natural images, the exponent γ is observed to be distributed around 1.

Conclusions:

• The power-law behavior of operational RD functions in wavelet compression of natural images is theoretically supported by the fBm model.
• Wavelet compression is effective for self-similar processes, including natural images modeled by fBm.
• Findings can aid in predicting the performance of rate-distortion optimized image coders.