In the conversion of an imager’s pixel data from electrons to digital numbers, a scalar quantization is performed. For CMOS sensors used in consumer applications, this scalar quantization is usually performed by an on-chip analog-to-digital converter (ADC) preceded by an amplifier. It is desired that the scalar quantization operation minimize the error between the analog input signal and the quantized output. One approach is to use a non-uniform quantizer for a signal with a known probability density function to minimize the mean square error. The Lloyd-Max algorithm can be used to determine the optimal quantization intervals and reconstruction levels. However, a probability model for the variations of pixels in a sensor is difficult to determine since the sensor can receive a vast number of greatly differing image data. Additionally, a quantizer with non-uniform intervals is difficult to implement, can be unstable, and has limited flexibility. Thus, it is preferred to use a simple linear, uniform quantization step size ADC to sample the sensor’s data.
The approach taken in this paper is to develop a scalar quantizer that utilizes knowledge of a sensor’s performance characteristics. The decision and reconstruction levels of a non-uniform quantizer are determined from the noise versus signal characteristics of the sensor. A linear, uniform quantization step size ADC can be used to 'over-encode’ (sample using more bits per pixel than required) the sensor’s data. The number of bits per pixel can then be reduced using a sensor characterization optimized mapping to a lower bit depth. This results in a reduction of the sensor’s digitized data.
The conversion function from pixel electrons to the digitized signal value is developed in this paper for a CMOS sensor with small pixel size designed for embedded applications. These sensors will typically exhibit lower signal to noise ratios due to their lower well capacity (lower dynamic range), higher levels of random noise, and higher cross-talk (the loss of photons or electrons from a pixel to neighboring pixels); which makes them ideal for this type of mapping. The performance of the proposed noise-based quantization method is measured through the calculation of mean square errors and relative compressibility of quantized sample images.