MR noise measurements and signal-quantization effects at very low noise levels

The well-known noise distributions of MRI data (Rayleigh, Rician, or non-central chi-distribution) describe the probability density of real-valued (i.e. floating-point) signal intensities. MR image data, however, is typically quantized to integers before visualization or archiving. Depending on the scaling factors applied before the quantization and the signal-to-noise ratio (SNR), very low noise levels with substantial artifacts due to the quantization process can occur. The purpose of this study was to analyze the consequences of the signal quantization, to determine the theoretical absolute lower limit for noise measurements in discrete data, and to evaluate an improved method for noise and SNR measurements in the presence of very low noise levels. Image data were simulated with original noise levels between 0.02 and 2.00. Noise measurements were performed based on the properties of background and foreground data using the conventional approach, which exploits the standard deviation or mean value of the signal, and a maximum-likelihood approach based on the relative frequencies of the observed discrete signal intensities. Substantial deviations were found for the conventionally determined noise levels, while noise levels comparable to or lower than the quantization error can be accurately estimated with the proposed maximum-likelihood approach.