Photon counting detector-based CT (PCCT) systems provide spectral count measurements, enabling material decomposition (MD) for quantitative imaging. Maximum-likelihood estimation (MLE) for MD offers asymptotically unbiased and efficient (minimum variance) results but is usually solved iteratively, making the entire process computationally expensive and time-consuming. Conversely, representative empirical methods relying on calibration aim to construct a direct measurement-decomposition conversion, which can be fast but may suffer from bias or noise amplification. In this work, we show that the iterative MLE method implicitly defines the functional mapping from measurements to estimates, i.e., MD results, and the corresponding mean and noise yield analytical approximation forms from the Implicit Function Theorem. From this perspective, we demonstrate that it is possible to distill knowledge from the implicit function defined by the iterative MLE, i.e., finding the explicit proxy, by leveraging universal approximators such as neural networks and the derivative-aware Sobolev Training paradigm. We show that the proposed method, namely Proxy MD, is both computationally efficient (providing >200 times speedup) and approaches the performance of iterative MLE. Thus it outperforms conventional empirical methods, enabling high-quality real-time quantitative spectral imaging. Furthermore, we also demonstrate that the theoretical Jacobian analysis provides new perspectives in making iterative MD differentiable, enabling differentiable PCCT quantitative imaging and corresponding cross-domain end-to-end training and optimization. The code has been made available at: https://github.com/senwang320/ProxyMD_Demo.

In computed tomography (CT) imaging, optimizing the balance between radiation dose and image quality is crucial due to the potentially harmful effects of radiation on patients. Although subjective assessments by radiologists are considered the gold standard in medical imaging, these evaluations can be time-consuming and costly. Thus, objective methods, such as the peak signal-to-noise ratio and structural similarity index measure, are often employed as alternatives. However, these metrics, initially developed for natural images, may not fully encapsulate the radiologists' assessment process. Consequently, interest in developing deep learning-based image quality assessment (IQA) methods that more closely align with radiologists' perceptions is growing. A significant barrier to this development has been the absence of open-source datasets and benchmark models specific to CT IQA. Addressing these challenges, we organized the Low-dose Computed Tomography Perceptual Image Quality Assessment Challenge in conjunction with the Medical Image Computing and Computer Assisted Intervention 2023. This event introduced the first open-source CT IQA dataset, consisting of 1,000 CT images of various quality, annotated with radiologists' assessment scores. As a benchmark, this challenge offers a comprehensive analysis of six submitted methods, providing valuable insight into their performance. This paper presents a summary of these methods and insights. This challenge underscores the potential for developing no-reference IQA methods that could exceed the capabilities of full-reference IQA methods, making a significant contribution to the research community with this novel dataset. The dataset is accessible at https://zenodo.org/records/7833096.

X-ray computed tomography (CT) is widely used for medical diagnosis and treatment planning; however, concerns about ionizing radiation exposure drive efforts to optimize image quality at lower doses. This study introduces Poisson Flow Consistency Models (PFCM), a novel family of deep generative models that combines the robustness of PFGM++ with the efficient single-step sampling of consistency models. PFCM are derived by generalizing consistency distillation to PFGM++ through a change-of-variables and an updated noise distribution. As a distilled version of PFGM++, PFCM inherit the ability to trade off robustness for rigidity via the hyperparameter $\text {D} \in \text {(}{0},\infty \text {)}$ . A fact that we exploit to adapt this novel generative model for the task of low-dose CT image denoising, via a "task-specific" sampler that "hijacks" the generative process by replacing an intermediate state with the low-dose CT image. While this "hijacking" introduces a severe mismatch-the noise characteristics of low-dose CT images are different from that of intermediate states in the Poisson flow process-we show that the inherent robustness of PFCM at small D effectively mitigates this issue. The resulting sampler achieves excellent performance in terms of LPIPS, SSIM, and PSNR on the Mayo low-dose CT dataset. By contrast, an analogous sampler based on standard consistency models is found to be significantly less robust under the same conditions, highlighting the importance of a tunable D afforded by our novel framework. To highlight generalizability, we show effective denoising of clinical images from a prototype photon-counting system reconstructed using a sharper kernel and at a range of energy levels.

Photon counting CT (PCCT) acquires spectral measurements and enables generation of material decomposition (MD) images that provide distinct advantages in various clinical situations. However, noise amplification is observed in MD images, and denoising is typically applied. Clean or high-quality references are rare in clinical scans, often making supervised learning (Noise2Clean) impractical. Noise2Noise is a self-supervised counterpart, using noisy images and corresponding noisy references with zero-mean, independent noise. PCCT counts transmitted photons separately, and raw measurements are assumed to follow a Poisson distribution in each energy bin, providing the possibility to create noise-independent pairs. The approach is to use binomial selection to split the counts into two low-dose scans with independent noise. We prove that the reconstructed spectral images inherit the noise independence from counts domain through noise propagation analysis and also validated it in numerical simulation and experimental phantom scans. The method offers the flexibility to split measurements into desired dose levels while ensuring the reconstructed images share identical underlying features, thereby strengthening the model's robustness for input dose levels and capability of preserving fine details. In both numerical simulation and experimental phantom scans, we demonstrated that Noise2Noise with binomial selection outperforms other common self-supervised learning methods based on different presumptive conditions.

It is well known that the energy dependence of X-ray attenuation can be used to characterize materials. Yet, even with energy discriminating photon counting X-ray detectors, it is still unclear how to best form energy dependent measurements for spectral imaging. Common ideas include binning photon counts based on their energies and detectors with both photon counting and energy integrating electronics. These approaches can be generalized to energy weighted measurements, which we prove can form a sufficient statistic for spectral X-ray imaging if the weights used, which we term μ-weights, are basis attenuation functions that can also be used for material decomposition. To study the performance of these different methods, we evaluate the Cramér-Rao lower bound (CRLB) of material estimates in the presence of quantum noise. We found that the choice of binning and weighting schemes can greatly affect the performance of material decomposition. Even with optimized thresholds, binning condenses information but incurs penalties to decomposition precision and is not robust to changes in the source spectrum or object size, although this can be mitigated by adding more bins or removing photons of certain energies from the spectrum. On the other hand, because μ-weighted measurements form a sufficient statistic for spectral imaging, the CRLB of the material decomposition estimates is identical to the quantum noise limited performance of a system with complete energy information of all photons. Finally, we show that μ-weights lead to increased conspicuity over other methods in a simulated calcium contrast experiment.