Purpose: To develop a dose-efficient image-based material decomposition technique for spectral photon-counting computed tomography (PCCT) data and investigate estimating human blood iron concentration from contrast- enhanced scans. Methods: We adapt a maximum a posteriori (MAP) approach to decomposition, formulating spectral material decomposition as maximizing a posterior likelihood that incorporates both the standard linear generative model of decomposition and a smoothness prior. Our approach employs numeric tensor algebra and software, which can naturally handle the high-dimensional nature of decomposition. To ensure accurate priors, we compute smoothness weights using the image created from all detected photons. Our MAP approach only requires a large and sparse linear system to solve, with one tuning parameter. Results: We test the algorithm on 4-energy threshold spectral PCCT scans of a human subject pre- and post- contrast. MAP estimates remain stable while reducing noise standard deviation by 80.1% and 75.4% for iron and iodine, respectively, which again suggests over 4x decrease in radiation. Aortic iron concentration measured from MAP had small bias post-contrast, but with a noise reduction of roughly 80%. This small bias (-5%) in iron content may be attributed to the blood volume increase after contrast injection. Conclusion: The dose-efficient MAP decomposition method shows improved precision over the standard approach in estimating blood-iron concentration. Future work will include additional human studies to determine the optimal trade-off between precision and algorithmic bias.
Lambertian photometric stereo (PS) is a seminal computer vision method. However, using depth maps in the image formation model, instead of surface normals as in PS, reduces model parameters by a third, making it preferred from an information-theoretic perspective. The Akaike information criterion (AIC) quantifies this trade-off between goodness of fit and overfitting. Obtaining superior AIC values requires an effective maximum likelihood (ML) depth-map & albedo estimation method. Recently, the authors published an ML estimation method that uses a two-step approach based on PS. While effective, approximations of noise distributions and decoupling of depth-map & albedo estimation have limited its accuracy. Overcoming these limitations, this paper presents an ML method operating directly on images. The previous two-step ML method provides a robust initial solution, which kick starts a new nonlinear estimation process. An innovative formulation of the estimation task, including a separable nonlinear least-squares approach, reduces the computational burden of the optimization process. Experiments demonstrate visual improvements under noisy conditions by avoiding overfitting. As well, a comprehensive analysis shows that refined depth maps & albedos produce superior AIC metrics and enjoy better predictive accuracy than with literature methods. The results indicate that the new method is a promising means for depth-map & albedo estimation with superior information-theoretic performance.
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