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Bit-depth quantization and reconstruction error in digital images

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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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Authors and Affiliations

  1. Faculty of Electrical Engineering, University of Montenegro, 81000, Podgorica, Montenegro

    Isidora Stanković, Miloš Brajović, Miloš Daković & Ljubiša Stanković

  2. GIPSA Lab, INP Grenoble, 38400, Saint-Martin-d’Hères, France

    Isidora Stanković & Cornel Ioana

Authors
  1. Isidora Stanković
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  2. Miloš Brajović
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  3. Miloš Daković
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  4. Cornel Ioana
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  5. Ljubiša Stanković
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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

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