PCM with non-uniform quantization
A simple way to improve performance of basic PCM system is to use non-uniform quantization, when image intensities are not distributed equally in the available dynamic range. One method of performing nonlinear quantization is to apply nonlinearity to  prior to uniform quantisation and then apply inverse nonlinearity after quantisation. The nonlinearity can be chosen such that output is equally probable throughout the available dynamic range .However, amount of improvement using non-uniform quantisation is not very large for typical images.
Example: For Gaussian-shaped image histogram, non-uniform quantisation can reduce the MSE by<3dB for bit rates upto 7 bits/pixel. When image histogram deviates considerably from uniform histogram, non-uniform quantisation can improve the performance of basic PCM system considerably. Roberts Pseudo Noise Technique
Used to remove the signal dependence of the quantization noise and improve the performance of PCM system.
The signal dependent quantisation noise appears as false contours at low bit rates. We can transform the signal dependent noise to signal independent random noise.. This technique is also known as "dithering". In this method a known random noise  is added to original image  before quantisation at the transmitter, and then same noise  is subtracted at the receiver. Since  is known both at transmitter and receiver it does not have to be transmitted.
A white noise sequence with a uniform pdf is given by,
 , otherwise
where Δ is quantiser step size can be used as  .The method is shown in Figure (14 ).
Figure (14):Decorrelation of quantisation noise by Robert's pseudonoise technique
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The effect is that in regions of low luminance gradients (which are regions of contours), the input noise causes pixels to go above or below the prior decisional level, there-by breaking the contours. However the average value of quantized pixels is about the same with and without the additive noise. During display, the noise tends to fill in the regions of contours in such a way that that the spatial average in unchanged. The amount of dither (noise) added should be low enough to maintain spatial resolution, but large enough to allow the luminance values of pixel to vary randomly about the quantizer decision levels. The noise should usually affect the LSB of the quantizer.
The reconstructed image  can be modeled approximately as  degraded by signal independent random noise which is white and has same uniform pdf as given above.
Simply removing the signal dependence of quantisation noise improves performance of PCM system significaulty. In addition it allows us to apply available additive noise reduction systems to reduce signal independent quantisation
Such type of system may be useful in applications such as spacecrafts and remotely piloted vehicles where it is desirable to have simple transmitter and some complexity in receiver can be tolerated. Some method can also be applied to PCM system with non uniform Quantiser . |
