Analysis of the quantization noise in discrete wavelet transform filters for image processing

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.