# JSolver: Joint Spectrum Estimation and Multi-Material Decomposition from Single-Energy CT Projections

arXiv: https://arxiv.org/abs/2505.08123 · HTML: https://mlsanity.com/paper/2505.08123/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
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- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [Self-Supervised Coordinate Projection Network for Sparse-View Computed Tomography](https://mlsanity.com/paper/2209.05483/) (2022)
- [DPER: Diffusion Prior Driven Neural Representation for Limited Angle and Sparse View CT Reconstruction](https://mlsanity.com/paper/2404.17890/) (2024)
- [Unsupervised Polychromatic Neural Representation for CT Metal Artifact Reduction](https://mlsanity.com/paper/2306.15203/) (2023)
- [Ray-driven Spectral CT Reconstruction Based on Neural Base-Material Fields](https://mlsanity.com/paper/2404.06991/) (2024)
- [Solving Energy-Independent Density for CT Metal Artifact Reduction via Neural Representation](https://mlsanity.com/paper/2405.07047/) (2024)
- [A deep learning approach for virtual monochromatic spectral CT imaging with a standard single energy CT scanner](https://mlsanity.com/paper/2005.09859/) (2020)

## Built on by (most cited first, 1 of 1)

- [Gaussian Material Fields for Volumetric Multi-Energy CT Decomposition](https://mlsanity.com/paper/2610.09492/) (2026)

## Abstract (arXiv)

Multi-material decomposition (MMD) enables quantitative reconstruction of tissue compositions in the human body, supporting a wide range of clinical applications. However, traditional MMD typically requires spectral CT scanners and pre-measured X-ray energy spectra, significantly limiting clinical applicability. To this end, various methods have been developed to perform MMD using conventional (i.e., single-energy, SE) CT systems, commonly referred to as SEMMD. Despite promising progress, most SEMMD methods follow a two-step image decomposition pipeline, which first reconstructs monochromatic CT images using algorithms such as FBP, and then performs decomposition on these images. The initial reconstruction step, however, neglects the energy-dependent attenuation of human tissues, introducing severe nonlinear beam hardening artifacts and noise into the subsequent decomposition. This paper proposes JSolver, a fundamentally reformulated one-step SEMMD framework that jointly reconstructs multi-material compositions and estimates the energy spectrum directly from SECT projections. By explicitly incorporating physics-informed spectral priors into the SEMMD process, JSolver accurately simulates a virtual spectral CT system from SE acquisitions, thereby improving the reliability and accuracy of decomposition. Furthermore, we introduce implicit neural representation (INR) as an unsupervised deep learning solver for representing the underlying material maps. The inductive bias of INR toward continuous image patterns constrains the solution space and further enhances estimation quality. Extensive experiments on both simulated and real CT datasets show that JSolver outperforms state-of-the-art SEMMD methods in accuracy and computational efficiency.