SCALAR QUANTIZATION-ERROR ANALYSIS FOR IMAGE SUBBAND CODING USING QMFS

Filter design for signal splitting and reconstruction in subband coding is based in practice on the assumption that coding errors are negligible. In the absence of coding the aliasing errors are explicitly canceled when quadrature mirror filters (QMF's) are used. The fact that aliasing errors occur in the presence of coding errors is acknowledged in the literature. However, no quantitative evaluation has been made so far. This paper explicitly incorporates quantization errors into a QMF system by means of a quantizer model. This enables us to discriminate between different types of coding errors, such as the aliasing error. Other distinguished errors are a QMF design error, a signal error, and a random error, which is uncorrelated with the original image. Both a mean-squared error calculation and a subjective judgement of the coding errors show that the aliasing errors can be neglected for filter lengths of 12 taps or more. The signal error determines the sharpness of the reconstructed image, while the random error is most visible in the flat areas.