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Tree coding of image subbands.

S Nanda1, W A Pearlman

  • 1AT&T Bell Lab., Holmdel, NJ.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 1, 1992
PubMed
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This study demonstrates that tree codes for Gaussian image sources achieve optimal rate-distortion performance. A postcoding method significantly enhances image quality and signal-to-noise ratio with minimal rate increase.

Area of Science:

  • Digital image processing
  • Information theory
  • Coding theory

Background:

  • Image compression is crucial for efficient storage and transmission.
  • Subband coding offers advantages over full-band coding for certain source types.
  • Rate-distortion theory provides a theoretical limit for lossy compression.

Purpose of the Study:

  • To analyze the performance of tree codes for encoding image subbands.
  • To prove that optimal subband encoding approaches the rate-distortion bound for Gaussian sources.
  • To investigate the impact of a postcoding procedure on image quality.

Main Methods:

  • Theoretical analysis of tree codes for Gaussian sources.
  • Derivation of bounds for subband coding performance.

Related Experiment Videos

  • Application of tree codes (nonadaptive and adaptive) to image subbands.
  • Implementation of a postcoding procedure to correct errors.

    • Main Results:

    • Optimal encoding of ideally filtered subbands achieves the rate-distortion bound for Mean Squared Error (MSE).
    • Subband coding demonstrates closer proximity to the rate-distortion bound than full-band coding for finite sequences.
    • A postcoding procedure significantly improves signal-to-noise ratio and visual quality.
    • The postcoding procedure results in only a marginal increase in the total data rate.

    Conclusions:

    • Tree codes are asymptotically optimal for encoding Gaussian image subbands under MSE distortion.
    • Subband coding with tree codes offers a near-optimal compression strategy.
    • The proposed postcoding method effectively enhances the fidelity of compressed images.