Adaptive noise reduction for dual-energy x-ray imaging based on spatial variations in beam attenuation

Purpose. The main goal of this work is to improve the previously proposed patient-specific pixel-based dual-energy (PP-DE) algorithm by developing an adaptive anti-correlated noise reduction (ACNR) method, resulting in reduced image noise. Methods. Theoretical models of contrast-to-noise (CNR) and signal-to-noise (SNR) ratio were developed as functions of weighting factors for DE bone ω Bn or soft tissue ω ST cancellation. These analytical expressions describe CNR and SNR properties of dual-energy (DE) images, obtained with both simple log subtraction (SLS) and ACNR algorithms, and allow for a direct comparison between experimental and theoretical results. The theoretical models demonstrate the importance of ACNR weighting factor (ω A ) optimization leading to the maximization of the SNR of the final image. A step phantom was constructed, which consisted of overlapping slabs of solid water (0-30 cm) and bone-mimicking material (0-6 cm), resulting in a total of 7 × 7 regions. High-energy (HE) and low-energy (LE) images were acquired at 140 kVp and 60 kVp with a clinical ExacTrac imaging system. The CNR and SNR were obtained for the DE images as functions of ω Bn,ST and noise reduction weighting factor ω A for different combinations of thicknesses. Weighting factors for bone cancellation were optimized for each region of interest (ROI) by finding zeros of CNR function for DE images between soft tissue only and soft tissue plus bone regions (and vice versa for soft tissue cancellation). The weighting factor for the ACNR algorithm ω A was then optimized by maximizing the SNR function for each ROI. HE and LE images for an anthropomorphic Rando phantom were obtained with the same acquisition parameters as for the step phantom. DE images for bone only and soft tissue only were obtained with three algorithms: SLS and PP-DE with conventional ACNR (uniform ω A ), and PP-DE with adaptive ACNR (region-varying ω A ). Weighting factor maps for PP-DE and adaptive ACNR methods were obtained for Rando phantom geometry (which was determined from its CT scans) by interpolation (or extrapolation) of weighting factors for the step phantom. CNR values were calculated for different regions. Results. The CNR and SNR characteristics as functions of material cancellation and noise reduction weighting factors were obtained from theoretical models and experimental data from the step phantom. This showed a good qualitative validation of the models. For the ANCR algorithm, both the theory and experiment demonstrated that the material cancellation weighting factors (ω Bn,ST ) can be optimized independently of the noise cancellation weighting factors (ω A ), which can be optimized by maximizing SNR. For each ROI (with different overlapping bone and soft tissue thicknesses) the weighting factors ω Bn,ST were determined as well as corresponding optimal weighting factors ω A for noise reduction. For the Rando phantom, CNR values for regions representing different anatomical structures (ribs, spine, and tumor) were evaluated. It was shown that the proposed adaptive ACNR further improves image quality, compared to the conventional ACNR algorithm. The improvement is maximized for regions with bones (ribs or spine), where the largest attenuation is observed. Conclusion. The ACNR weighting factors are dependent on the material thicknesses due to varying beam attenuation leading to different levels of quantum noise. This was shown with the derived theoretical expressions of the CNR and SNR functions and was validated by experimental data. The adaptive ANCR DE algorithm was developed, which allows for an increase in image quality by spatially varying weighting factors for noise reduction. This algorithm complements the previously developed PP-DE algorithm to obtain better quality DE images.