Noise modeling and variance stabilization of a computed radiography (CR) mammography system subject to fixed-pattern noise

Abstract

In this work we model the noise properties of a computed radiography (CR) mammography system by adding an extra degree of freedom to a well-established noise model, and derive a variance-stabilizing transform (VST) to convert the signal-dependent noise into approximately signal-independent. The proposed model relies on a quadratic variance function, which considers fixed-pattern (structural), quantum and electronic noise. It also accounts for the spatial-dependency of the noise by assuming a space-variant quantum coefficient. The proposed noise model was compared against two alternative models commonly found in the literature. The first alternative model ignores the spatial-variability of the quantum noise, and the second model assumes negligible structural noise. We also derive a VST to convert noisy observations contaminated by the proposed noise model into observations with approximately Gaussian noise and constant variance equals to one. Finally, we estimated a look-up table that can be used as an inverse transform in denoising applications. A phantom study was conducted to validate the noise model, VST and inverse VST. The results show that the space-variant signal-dependent quadratic noise model is appropriate to describe noise in this CR mammography system (errors< 2.0% in terms of signal-to-noise ratio). The two alternative noise models were outperformed by the proposed model (errors as high as 14.7% and 9.4%). The designed VST was able to stabilize the noise so that it has variance approximately equal to one (errors< 4.1%), while the two alternative models achieved errors as high as 26.9% and 18.0%, respectively. Finally, the proposed inverse transform was capable of returning the signal to the original signal range with virtually no bias.