Data-driven estimation of noise variance stabilization parameters for low-dose x-ray images

Denoising x-ray images corrupted by signal-dependent mixed noise is usually approached either by considering noise statistics directly or by using noise variance stabilization (NVS) techniques. An advantage of the latter is that the noise variance can be stabilized to a known constant throughout the image, facilitating the application of denoising algorithms designed for the removal of additive Gaussian noise. A well-performing NVS is the generalized Anscombe transform (GAT). To calculate the GAT, the system gain as well as the variance of electronic noise are required. Unfortunately, these parameters are difficult to predict from the x-ray tube settings in clinical practice, because the system gain observed at the detector depends on the beam hardening caused by the patient.

We propose a data-driven method for estimating the parameters required to carry out an NVS using the GAT. It utilizes the energy compaction property of the discrete cosine transform to obtain the NVS parameters using a robust regression approach relying on a linear Poisson-Gaussian model. The method has been experimentally validated with respect to beam hardening as well as denoising performance for different dose and scatter levels.

Across a range of low-dose x-ray settings, the proposed robust regression approach has estimated both system gain and electronic noise level with an average error of only 4.2%. When used to perform a GAT followed by the denoising of low-dose x-ray images, performance gains of 5% for peak-signal-to-noise ratio and 4% for structural similarity index can be obtained.

The parameters needed to calculate the GAT can be estimated efficiently and robustly using a data-driven approach. The improved parameter estimation method facilitates a more accurate GAT-based NVS and, hence, better denoising of low-dose x-ray images when algorithms designed for additive Gaussian noise are applied.