A relaxation algorithm for minimizing the L2 reconstruction error in 2-D nonorthogonal subband coding

Research output: Contribution to journalConference article

Abstract

We present a technique for improving the applicability of complete, nonorthogonal, multiresolution transforms to image coding. As is well known, the L2 norm of the quantization error is not preserved by nonorthogonal transforms, so the L2 reconstruction error may be unacceptably large. However, given the quantizers and synthesis filters, we show that this artifact can be eliminated by formulating the coding problem as that of minimizing the L2 reconstruction error over the set of possible encoded images. This high-dimensional, discrete optimization problem is solved using a multiscale relaxation algorithm. Bounds on the coding gain over the standard coding technique are derived. Experiments using biorthogonal spline filters demonstrate appreciable SNR gains over the standard coding technique, and comparable visual improvements.

Original languageEnglish (US)
Article number413486
Pages (from-to)908-912
Number of pages5
JournalProceedings - International Conference on Image Processing, ICIP
Volume2
DOIs
StatePublished - Jan 1 1994
EventProceedings of the 1994 1st IEEE International Conference on Image Processing. Part 3 (of 3) - Austin, TX, USA
Duration: Nov 13 1994Nov 16 1994

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Image coding
Splines
Experiments

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Signal Processing

Cite this

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abstract = "We present a technique for improving the applicability of complete, nonorthogonal, multiresolution transforms to image coding. As is well known, the L2 norm of the quantization error is not preserved by nonorthogonal transforms, so the L2 reconstruction error may be unacceptably large. However, given the quantizers and synthesis filters, we show that this artifact can be eliminated by formulating the coding problem as that of minimizing the L2 reconstruction error over the set of possible encoded images. This high-dimensional, discrete optimization problem is solved using a multiscale relaxation algorithm. Bounds on the coding gain over the standard coding technique are derived. Experiments using biorthogonal spline filters demonstrate appreciable SNR gains over the standard coding technique, and comparable visual improvements.",
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AB - We present a technique for improving the applicability of complete, nonorthogonal, multiresolution transforms to image coding. As is well known, the L2 norm of the quantization error is not preserved by nonorthogonal transforms, so the L2 reconstruction error may be unacceptably large. However, given the quantizers and synthesis filters, we show that this artifact can be eliminated by formulating the coding problem as that of minimizing the L2 reconstruction error over the set of possible encoded images. This high-dimensional, discrete optimization problem is solved using a multiscale relaxation algorithm. Bounds on the coding gain over the standard coding technique are derived. Experiments using biorthogonal spline filters demonstrate appreciable SNR gains over the standard coding technique, and comparable visual improvements.

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