Estimador de descomposición de materiales definido implícitamente y proxy neuronal aprendido informado por la física...

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.