QUANTIZATION NOISE OF MULTILEVEL DISCRETE WAVELET TRANSFORM FILTERS IN IMAGE PROCESSING
N. I. Chervyakov, P. A. Lyakhov, N. N. Nagornov
North-Caucasus Federal University, ul. Pushkina 1, Stavropol, 355009 Russia
Keywords: дискретное вейвлет-преобразование, цифровая обработка изображений, шум квантования, разрядность, формат с фиксированной точкой, discrete wavelet transform, digital image processing, quantization noise, bit-width, fixed-point format
Abstract
The effect of the quantization noise of the coefficients of discrete wavelet transform (DWT) filters on the image processing result is analyzed. A multilevel DWT method is proposed for determining the effective bit-width of DWT filter coefficients at which quantization noise has little effect on the image processing result. The dependence of the peak signal-to-noise ratio (PSNR) in DWT of images on the wavelet used, the effective bit-width of the coefficients, and the number of processing levels is revealed. Formulas are derived for determining the minimum bit-width of the coefficients that provide high quality of the processed image ($\textrm{PSNR} \geq 40$ dB) depending on the wavelet used and the number of processing levels. Experimental modeling of a multilevel DWT image confirmed the results obtained. In the proposed method, all data are represented in fixed-point format, making possible its hardware-efficient implementation on modern devices (FPGA, ASIC, etc.)
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