Quantization Noise of Multilevel Discrete Wavelet Transform Filters in Image Processing

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 (PSNR ≥ 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 hardwareefficient implementation on modern devices (FPGA, ASIC, etc.).