Thermal Noise

Thermal noise, in this context, refers to any random, gaussian distributed noise sources present in the image, such as the thermal noise generated by resistors. All the components in the circuit produce such noise intrinsically, due to their own temperature. Furthermore, the intrinsically quantum random nature of photon and electron interactions leads to a certain amount of shot noise. This produces a gaussian distributed error voltage at each pixel in the image, with a zero mean and a variance dependent on the temperature of the circuit.

These noise sources affect each pixel individually, independent of any other pixel in the image. Hence the noise is ``white''. A typical image, which consists of many smooth areas separated by sudden steps, will thus develop a jagged appearance, as shown in Figure 2.1. Over a region of the image with a constant intensity value $s$, the fact that the gaussian function has zero mean implies that the average observed intensity value $\overline{s}$ will be close to the original signal value $s$. Thus, the original image can be recovered. In practice, this is achieved by spatially smoothing the image. Smoothing the image involves replacing each pixel's voltage with a weighted average of the intensities of itself and it's neighbours, with weight given according to the proximity of the neighbours. This weighting allows gradual changes in image intensity to be passed unchanged; however, sudden changes in intensity in the original image will be smoothed out. This process is effectively a low pass filter. Because most scenes tend to have a much smaller high frequency component than white noise [13], this tends to eliminate the noise and leave the signal.

Figure 2.1: Gaussian noise