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Electronics 2018, 7(8), 135; https://doi.org/10.3390/electronics7080135

Analysis of the Quantization Noise in Discrete Wavelet Transform Filters for Image Processing

1
Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, Stavropol 355009, Russia
2
Department of Automation and Control Processes, St. Petersburg Electrotechnical University “LETI”, St. Petersburg 197376, Russia
3
Youth Research Institute, St. Petersburg Electrotechnical University “LETI”, St. Petersburg 197376, Russia
*
Author to whom correspondence should be addressed.
Received: 30 June 2018 / Revised: 25 July 2018 / Accepted: 31 July 2018 / Published: 2 August 2018
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Abstract

In this paper, we analyze the noise quantization effects in coefficients of discrete wavelet transform (DWT) filter banks for image processing. We propose the implementation of the DWT method, making it possible to determine the effective bit-width of the filter banks coefficients at which the quantization noise does not significantly affect the image processing results according to the peak signal-to-noise ratio (PSNR). The dependence between the PSNR of the DWT image quality on the wavelet and the bit-width of the wavelet filter coefficients is analyzed. The formulas for determining the minimal bit-width of the filter coefficients at which the processed image achieves high quality (PSNR ≥ 40 dB) are given. The obtained theoretical results were confirmed through the simulation of DWT for a test image using the calculated bit-width values. All considered algorithms operate with fixed-point numbers, which simplifies their hardware implementation on modern devices: field-programmable gate array (FPGA), application-specific integrated circuit (ASIC), etc. View Full-Text
Keywords: discrete wavelet transform; digital image processing; quantization noise; bit-width; fixed-point numbers discrete wavelet transform; digital image processing; quantization noise; bit-width; fixed-point numbers
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Chervyakov, N.; Lyakhov, P.; Kaplun, D.; Butusov, D.; Nagornov, N. Analysis of the Quantization Noise in Discrete Wavelet Transform Filters for Image Processing. Electronics 2018, 7, 135.

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