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Bit-depth quantization and reconstruction error in digital images

Abstract

Digital images can be considered as sparse or approximately sparse in the two-dimensional discrete cosine transform domain. According to the compressive sensing theory, these images can be recovered from a reduced set of pixels. Such reconstructions are influenced by the noise and the non-reconstructed coefficients for approximately sparse images. In the literature, this kind of reconstruction error is described by the error bound relations. In some hardware implementations, the pixels may be sensed with a low number of bits, causing quantization error. In this paper, we derive exact formula for the expected error energy in the reconstructed images, caused by the pixels quantization. It is validated trough numerical examples.

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Correspondence to Miloš Brajović.

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Stanković, I., Brajović, M., Daković, M. et al. Bit-depth quantization and reconstruction error in digital images. SIViP 14, 1545–1553 (2020). https://doi.org/10.1007/s11760-020-01694-4

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  • DOI: https://doi.org/10.1007/s11760-020-01694-4

Keywords

  • Compressed sensing
  • Image processing
  • Bit depth
  • Quantization
  • Reconstruction