Application of fractal dimension for quantifying noise texture in computed tomography images

Evaluation of noise texture information in CT images is important for assessing image quality. Noise texture is often quantified by the noise power spectrum (NPS), which requires numerous image realizations to estimate. This study evaluated fractal dimension for quantifying noise texture as a scalar metric that can potentially be estimated using one image realization.

The American College of Radiology CT accreditation phantom (ACR) was scanned on a clinical scanner (Discovery CT750, GE Healthcare) at 120 kV and 25 and 90 mAs. Images were reconstructed using filtered back projection (FBP/ASIR 0%) with varying reconstruction kernels: Soft, Standard, Detail, Chest, Lung, Bone, and Edge. For each kernel, images were also reconstructed using ASIR 50% and ASIR 100% iterative reconstruction (IR) methods. Fractal dimension was estimated using the differential box-counting algorithm applied to images of the uniform section of ACR phantom. The two-dimensional Noise Power Spectrum (NPS) and one-dimensional-radially averaged NPS were estimated using established techniques. By changing the radiation dose, the effect of noise magnitude on fractal dimension was evaluated. The Spearman correlation between the fractal dimension and the frequency of the NPS peak was calculated. The number of images required to reliably estimate fractal dimension was determined and compared to the number of images required to estimate the NPS-peak frequency. The effect of Region of Interest (ROI) size on fractal dimension estimation was evaluated. Feasibility of estimating fractal dimension in an anthropomorphic phantom and clinical image was also investigated, with the resulting fractal dimension compared to that estimated within the uniform section of the ACR phantom.

Fractal dimension was strongly correlated with the frequency of the peak of the radially averaged NPS curve, having a Spearman rank-order coefficient of 0.98 (P-value < 0.01) for ASIR 0%. The mean fractal dimension at ASIR 0% was 2.49 (Soft), 2.51 (Standard), 2.52 (Detail), 2.57 (Chest), 2.61 (Lung), 2.66 (Bone), and 2.7 (Edge). A reduction in fractal dimension was observed with increasing ASIR levels for all investigated reconstruction kernels. Fractal dimension was found to be independent of noise magnitude. Fractal dimension was successfully estimated from four ROIs of size 64 × 64 pixels or one ROI of 128 × 128 pixels. Fractal dimension was found to be sensitive to non-noise structures in the image, such as ring artifacts and anatomical structure. Fractal dimension estimated within a uniform region of an anthropomorphic phantom and clinical head image matched that estimated within the ACR phantom for filtered back projection reconstruction.

Fractal dimension correlated with the NPS-peak frequency and was independent of noise magnitude, suggesting that the scalar metric of fractal dimension can be used to quantify the change in noise texture across reconstruction approaches. Results demonstrated that fractal dimension can be estimated from four, 64 × 64-pixel ROIs or one 128 × 128 ROI within a head CT image, which may make it amenable for quantifying noise texture within clinical images.