Quantization noise analysis for discrete wavelet transform image filtering

This paper solves an analysis problem for the quantization noise caused by the rounding of the coefficients of discrete wavelet transform (DWT) filters and its influence on the image processing result in order to determine the minimum bit-width of coefficients at which the quantization noise does not have a significant effect on the image processing result or does not affect it at all. The implementation of the DWT method is proposed, which makes it possible to determine the effective bit-width of the wavelet-filter coefficients and simplify the rounding operations. Formulas are derived for determining the minimum bit-width of the coefficients at which the DWT restored image shows the high quality (40 dB) or matches the original one, depending on the wavelet used. Simulation of image DWT using the bit-width calculated according to the derived formulas confirms the results obtained. All calculations are performed only on fixed-point numbers.